<?xml version="1.0" encoding="UTF-8"?>
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<Text-field style="Normal268" layout="Normal268">THE REAL PHOTOVOLTAIC SOLAR CELL</Text-field>
<Text-field style="Normal" layout="Normal"></Text-field>
<Text-field style="Normal268" layout="Normal268">LA CELLULE SOLAIRE PHOTOVOLTAIQUE REELLE </Text-field>
<Text-field style="Normal" layout="Normal"></Text-field>
<Text-field style="Normal261" layout="Normal261">Safae AAZOU<Font style="Text" size="14">*</Font></Text-field>
<Text-field style="Normal261" layout="Normal261">&amp;</Text-field>
<Text-field style="Normal261" layout="Normal261">Prof El Mahdi ASSAID<Font style="Text" size="14">**</Font> </Text-field>
<Text-field style="Normal" layout="Normal"></Text-field>
<Text-field style="Normal269" layout="Normal269">Equipe d'Optique et Electronique du Solide</Text-field>
<Text-field style="Normal269" layout="Normal269"><Font encoding="UTF-8">D\303\251partement de Physique, Facult\303\251 des Sciences</Font></Text-field>
<Text-field style="Normal269" layout="Normal269"><Font encoding="UTF-8">Universit\303\251 Choua\303\257b Doukkali</Font></Text-field>
<Text-field style="Text" italic="true" size="14" bold="true" layout="Normal264"><Font bold="true" italic="true" size="14">El Jadida</Font></Text-field>
<Text-field style="Normal264" layout="Normal264">* e-mail: <Font style="Text" underline="true">aazou.safae@yahoo.fr</Font></Text-field>
<Text-field style="Normal264" layout="Normal264">**e-mail: <Font style="Text" underline="true">eassaid@yahoo.fr</Font></Text-field>
<Text-field style="Normal264" layout="Normal264"></Text-field>
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<Text-field style="Normal270" layout="Normal270">ABSTRACT :<Font style="Text"> In this contribution, we use Maple software to study a solar cell modeled by an electronic circuit containing five physical parameters. The physical parameters are:  the series resistance </Font><Equation executable="false" style="2D Comment" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRInNGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation><Font style="Text">, the reverse saturation current </Font><Equation executable="false" style="2D Comment" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRInNGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation><Font style="Text">, the ideality factor </Font><Equation executable="false" style="2D Comment" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEmJmV0YTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn</Equation><Font style="Text">, the shunt resistance </Font><Equation executable="false" style="2D Comment" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRI3NoRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=</Equation><Font style="Text"> and the photocurrent </Font><Equation executable="false" style="2D Comment" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRI3BoRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=</Equation><Font style="Text"> (see figure 1). First, we solve the characteristic equation giving the output current </Font><Equation executable="false" style="2D Comment" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRJG91dEYnRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation><Font style="Text"> as a function of the output voltage </Font><Equation executable="false" style="2D Comment" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRJG91dEYnRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation><Font style="Text"> of the solar cell. Then, we determine the analytical expressions of the short circuit current </Font><Equation executable="false" style="2D Comment" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRI3NjRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=</Equation><Font style="Text">, the open circuit voltage </Font><Equation executable="false" style="2D Comment" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRI29jRidGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=</Equation><Font style="Text">,  the dynamical resistance </Font><Equation executable="false" style="2D Comment" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRJGR5bkYnRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation><Font style="Text"> of the solar cell and the different kinds of powers involved : the output power </Font><Equation executable="false" style="Text" input-equation="">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</Equation><Font style="Text">,  the power dissipated by Joule Effect </Font><Equation executable="false" style="Text" input-equation="">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</Equation><Font style="Text"> in the internal components of the solar cell and the solar cell total power</Font> <Equation executable="false" style="Text" input-equation="">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</Equation><Font style="Text">. Next, we determine a new expression of the optimal load resistance </Font><Equation executable="false" style="2D Comment" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRJGxtcEYnRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation><Font style="Text"> corresponding to the maximal power point. Finally, we investigate the effects of the different physical parameters on the current-voltage characteristic </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2Ji1JJW1zdWJHRiQ2JS1GLDYmUSJJRicvJSdpdGFsaWNHUSV0cnVlRicvJTBmb250X3N0eWxlX25hbWVHUTJDaGFyYWN0ZXJTdHlsZTMwM0YnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYsNiZRJG91dEYnRjdGOkY9LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYuUSI9RidGOi9GPlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRlAvJSlzdHJldGNoeUdGUC8lKnN5bW1ldHJpY0dGUC8lKGxhcmdlb3BHRlAvJS5tb3ZhYmxlbGltaXRzR0ZQLyUnYWNjZW50R0ZQLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGaW4tRiM2JS1GLDYmUSJmRidGN0Y6Rj0tRkk2LVEwJkFwcGx5RnVuY3Rpb247RidGTEZORlFGU0ZVRldGWUZlbi9GaG5RJjAuMGVtRicvRltvRmVvLUkobWZlbmNlZEdGJDYlLUYjNiMtRjI2JS1GLDYmUSJWRidGN0Y6Rj1GQEZFRjpGTEYrRis=</Equation><Font style="Text"> and on the output power </Font><Equation executable="false" style="Text" input-equation="">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</Equation><Font style="Text"> of the solar cell.</Font></Text-field>
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<Text-field style="Normal" layout="Normal"><Font bold="true" style="Text" size="14">SUBJECTS : </Font>Optoelectronics, Semiconductor Physics, Renewable Energy.</Text-field>
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<Text-field style="Normal" layout="Normal"><Font bold="true" style="Text" size="14">KEYWORDS :</Font><Font style="Text"> Solar Cell, Current-Voltage characteristic, Maximum Power Point, LambertW function</Font>.</Text-field>
<Text-field style="Normal" layout="Normal"></Text-field>
<Text-field style="Normal" layout="Normal"><Font bold="true" style="Text" size="14">RESUME :</Font><Font bold="true" style="Text"> </Font><Font encoding="UTF-8">Dans cette contribution, nous utilisons le logiciel de calcul formel Maple dans l'\303\251tude d'une cellule solaire mod\303\251lis\303\251e par un circuit \303\251lectronique comprenant cinq param\303\250tres physiques. Les cinq param\303\250tres physiques sont : la r\303\251sistance s\303\251rie </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyODZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSJzRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation><Font style="Text">, le courant de saturation inverse </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyODdGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSJzRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation><Font style="Text" encoding="UTF-8">, le facteur d'id\303\251alit\303\251 </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JlEmJmV0YTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJTBmb250X3N0eWxlX25hbWVHUTJDaGFyYWN0ZXJTdHlsZTI4OEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==</Equation><Font style="Text" encoding="UTF-8">, la r\303\251sistance shunt </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyODlGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSNzaEYnRjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=</Equation><Font style="Text"> et le photocourant </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyOTBGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSNwaEYnRjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=</Equation><Font style="Text" encoding="UTF-8"> (voir figure 1). Dans un premier temps, nous r\303\251solvons l'\303\251quation caract\303\251ristique donnant le courant de sortie </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyOTRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation><Font style="Text"> en fonction de la tension de sortie de la cellule solaire </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyOTNGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation><Font style="Text" encoding="UTF-8">. Ensuite, nous d\303\251terminons les expressions analytiques du courant en court-circuit </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNThGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSNzY0YnRjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=</Equation><Font style="Text">, de la tension en circuit ouvert </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMDBGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSNvY0YnRjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=</Equation><Font style="Text" encoding="UTF-8">, de la r\303\251sistance dynamique </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMDFGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRkeW5GJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation><Font style="Text" encoding="UTF-8"> de la cellule solaire ainsi que des differentes puissances mises en jeu : la puissance d\303\251livr\303\251e par la cellule solaire </Font><Equation executable="false" style="Text" input-equation="">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</Equation><Font style="Text" encoding="UTF-8">, la puissance dissip\303\251e par effet joule dans les composants internes de la cellule </Font><Equation executable="false" style="Text" input-equation="">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</Equation><Font style="Text"> et la puissance totale de la cellule solaire </Font><Equation executable="false" style="Text" input-equation="">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</Equation><Font style="Text" encoding="UTF-8">. Puis, nous d\303\251terminons une nouvelle expression de la r\303\251sistance charge optimale </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGU0MjZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRsbXBGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation><Font style="Text" encoding="UTF-8"> correspondant au point de puissance maximale. Finalement, nous \303\251tudions les effets des diff\303\251rents param\303\250tres physiques sur la caract\303\251ristique </Font><Equation executable="false" style="Text" input-equation="">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</Equation><Font style="Text" encoding="UTF-8"> et sur la puissance d\303\251livr\303\251e par la cellule solaire </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JS1JJW1zdWJHRiQ2JS1GLDYmUSJQRicvJSdpdGFsaWNHUSV0cnVlRicvJTBmb250X3N0eWxlX25hbWVHUTJDaGFyYWN0ZXJTdHlsZTI5OUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYsNiZRJG91dEYnRjdGOkY9LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUTAmQXBwbHlGdW5jdGlvbjtGJy9GPlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRlAvJSlzdHJldGNoeUdGUC8lKnN5bW1ldHJpY0dGUC8lKGxhcmdlb3BHRlAvJS5tb3ZhYmxlbGltaXRzR0ZQLyUnYWNjZW50R0ZQLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGaW4tSShtZmVuY2VkR0YkNiUtRiM2Iy1GMjYlLUYsNiZRIklGJ0Y3RjpGPUZARkVGOkZMRis=</Equation><Font style="Text">.</Font></Text-field>
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<Text-field style="Normal" layout="Normal"><Font bold="true" style="Text" size="14">SUJETS : </Font><Font encoding="UTF-8">Opto\303\251lectronique, Physique des Semi-conducteurs, Energies Renouvelables.</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true" size="14">KEYWORDS :</Font><Font encoding="UTF-8"> Cellule Solaire, Caract\303\251ristique Courant-Tension, Point de Puissance Maximale, Fonction de LambertW.</Font></Text-field>
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<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">INTRODUCTION</Text-field></Title>
<Text-field style="Normal" layout="Normal"><Font encoding="UTF-8">For more than five decades, it was not possible to derive an analytical solution to the problem of current flow in a diode driven by a voltage source through a series resistance. This problem was even qualified as elusive because it led to a transcendental equation giving the current through the diode as a function of the input voltage and the current itself. In the same way, it was not possible to solve the characteristic equation giving the output current as a function of the output voltage and the output current of a solar cell containing parasitic series and shunt resistances (see figure 1). In the year 2000, T.C. Banwell and A. Jayakumar have proposed an exact analytical solution for the first problem using the LambertW function [1]. In 2004, A. Jain and A. Kapoor have presented an exact closed form solution for the second problem based on the LambertW function also [2]. In july 2005, M. Vargas-Drechsler has used Maple software [3, 4] and found the same exact analytical solution as T.C. Banwell and A. Jayakumar. Later, E. Assaid et al. have determined exact analytical expressions for the currents and the voltages of the circuit known as Gra\303\253tz bridge using LambertW function [5, 6]. This circuit is used in electronics as full wave rectifier, it is formed by four non-ideal identical diodes and one diagonal resistance. In the present paper, we use Maple software to study the electronic circuit modelling a solar cell and containing the five following physical parameters: a series resistance </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSJzRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation>, a shunt resistance <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSNzaEYnRjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=</Equation>, a diode reverse saturation current <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSJzRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation>, a diode ideality factor <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JlEmJmV0YTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJTBmb250X3N0eWxlX25hbWVHUTJDaGFyYWN0ZXJTdHlsZTQzMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==</Equation> and a photocurrent <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSNwaEYnRjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=</Equation> [7]. At the beginning, the exact analytical solution for the transcendental equation giving the output current <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> as a function of the output voltage <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> is determined. Then, exact expressions of the short cicuit current <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSNzY0YnRjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=</Equation>, the open cicuit voltage <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and the dynamical resistance of the solar cell <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRkeW5GJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> are derived. Next, expressions of the output power <Equation executable="false" style="Text" input-equation="">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</Equation>, the power dissipated by Joule Effect in the internal components <Equation executable="false" style="Text" input-equation="">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</Equation> and the solar cell total power <Equation executable="false" style="Text" input-equation="">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</Equation> are determined analytically. Last, the effects of each physical parameter on the current-voltage characteristic and on the output power curve are investigated.</Text-field>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">SOLAR CELL TRANSCENDENTAL EQUATION</Text-field></Title>
<Text-field style="Normal" layout="Normal">First, we consider an illuminated solar cell modeled by an electronic circuit containing five physical parameters (see figure1) [7].</Text-field>
<Text-field style="Normal" layout="Normal">The application of the Kirchhoff voltage and current laws leads to the following equations :</Text-field>
<Text-field style="Normal" layout="Normal"><Equation executable="false" style="Text" input-equation="">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</Equation> (1)</Text-field>
<Text-field style="Normal263" layout="Normal263"><Equation executable="false" style="2D Comment" input-equation="">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</Equation><Font style="Text"> (2)</Font></Text-field>
<Text-field style="Normal263" layout="Normal263"><Equation executable="false" style="2D Comment" input-equation="">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</Equation> = <Equation executable="false" style="2D Comment" input-equation="">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</Equation> <Font style="Text">(3)</Font></Text-field>
<Text-field style="Normal" layout="Normal">The diode equation writes :</Text-field>
<Text-field style="Normal" layout="Normal"><Equation executable="false" style="Text" input-equation="">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</Equation>  (4)</Text-field>
<Text-field style="Normal" layout="Normal">where <Equation executable="false" style="Text" input-equation="">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</Equation><Font style="Text" italic="true"> </Font> is the thermal voltage. </Text-field>
<Text-field style="Normal264" layout="Normal264"></Text-field>
<Text-field style="Text" size="14" layout="Normal264"><Font size="14">                     Figure 1: Single diode model for solar cell</Font></Text-field>
<Text-field style="Normal" layout="Normal">By substituting equation (1) into (4),we obtain :</Text-field>
<Text-field style="Normal263" layout="Normal263"><Equation executable="false" style="2D Comment" input-equation="">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</Equation><Font style="Text"> (5) </Font></Text-field>
<Text-field style="Normal" layout="Normal">Now, we introduce the expressions of <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMDlGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSJkRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation> and <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMTBGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSNzaEYnRjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=</Equation> in equation (2) which leads to the characteristic equation of the solar cell :</Text-field>
<Text-field style="Normal" layout="Normal"><Equation executable="false" style="Text" input-equation="">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</Equation><Font bold="true" style="Text" italic="true"> </Font> (6)</Text-field>
<Text-field style="Normal" layout="Normal">Equation (6) is a transcendental equation giving the solar cell output current <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMjBGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> as a function of the output voltage <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMjFGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and the output current <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation>.</Text-field>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">ANALYTICAL RESOLUTION OF THE TRANSCENDENTAL EQUATION</Text-field></Title>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:with(Optimization):Digits:=12:</Text-field>
</Input>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">At the beginning, we write the solar cell characteristic equation :</Text-field>
</Input>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tr_equa := Iout = Iph-Is*(exp((Vout+Iout*Rs)/(eta*Vth))-1)-Gp*(Vout+Rs*Iout);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSh0cl9lcXVhRy8lJUlvdXRHLCglJElwaEciIiIqJiUjSXNHIiIiLCYtJSRleHBHNiMqKCwmJSVWb3V0RyIiIiomJSVJb3V0RyIiIiUjUnNHIiIiIiIiIiIiJSRldGFHISIiJSRWdGhHISIiIiIiIiIiISIiIiIiISIiKiYlI0dwRyIiIiwmJSVWb3V0RyIiIiomJSVJb3V0RyIiIiUjUnNHIiIiIiIiIiIiISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">where <Equation executable="false" style="Text" input-equation="">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</Equation> is the shunt conductance.</Text-field>
<Text-field style="Normal" layout="Normal">Then, we solve this equation and give the expression of the output current <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMjNGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> in term of the output voltage <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMjJGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> :</Text-field>
</Input>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cur_sol:=solve(tr_equa,Iout);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JShjdXJfc29sRyomLCYlJVZvdXRHISIiKigsJi0lKUxhbWJlcnRXRzYjLCQqKiUjUnNHIiIiJSNJc0ciIiIsJioqJSNHcEciIiIlI1JzRyIiIiUkZXRhRyIiIiUkVnRoRyIiIiEiIiomJSRldGFHIiIiJSRWdGhHIiIiISIiISIiLSUkZXhwRzYjKiosKComJSNSc0ciIiIlJElwaEciIiIiIiIqJiUjUnNHIiIiJSNJc0ciIiIiIiIlJVZvdXRHIiIiIiIiJSRldGFHISIiJSRWdGhHISIiLCYiIiIiIiIqJiUjR3BHIiIiJSNSc0ciIiIiIiIhIiIiIiIhIiIhIiIqKiwoKiYlI1JzRyIiIiUkSXBoRyIiIiIiIiomJSNSc0ciIiIlI0lzRyIiIiIiIiUlVm91dEciIiIiIiIlJGV0YUchIiIlJFZ0aEchIiIsJiIiIiIiIiomJSNHcEciIiIlI1JzRyIiIiIiIiEiIiIiIiIiIiUkZXRhRyIiIiUkVnRoRyIiIiIiIiIiIiUjUnNHISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The expression of <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> contains the LambertW function [8]. </Text-field>
</Input>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Iout := unapply(cur_sol,Vout);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">We can also solve equation (6) and give the expression of the output voltage <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> in term of the output current <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> :</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vol_sol:=solve(tr_equa,Vout);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSh2b2xfc29sRywmKiYlJUlvdXRHIiIiJSNSc0ciIiIhIiIqKCwmLSUpTGFtYmVydFdHNiMqLCUjSXNHIiIiJSNHcEchIiIlJGV0YUchIiIlJFZ0aEchIiItJSRleHBHNiMqKiwoJSVJb3V0RyEiIiUkSXBoRyIiIiUjSXNHIiIiIiIiJSNHcEchIiIlJGV0YUchIiIlJFZ0aEchIiIiIiIhIiIqKiwoJSVJb3V0RyEiIiUkSXBoRyIiIiUjSXNHIiIiIiIiJSNHcEchIiIlJGV0YUchIiIlJFZ0aEchIiIiIiIiIiIlJGV0YUciIiIlJFZ0aEciIiIiIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Vout := unapply(vol_sol,Iout);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSVWb3V0R2YqNiMlJUlvdXRHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwmKiYlJUlvdXRHIiIiJSNSc0ciIiIhIiIqKCwmLSUpTGFtYmVydFdHNiMqLCUjSXNHIiIiJSNHcEchIiIlJGV0YUchIiIlJFZ0aEchIiItJSRleHBHNiMqKiwoJSVJb3V0RyEiIiUkSXBoRyIiIiUjSXNHIiIiIiIiJSNHcEchIiIlJGV0YUchIiIlJFZ0aEchIiIiIiIhIiIqKiwoJSVJb3V0RyEiIiUkSXBoRyIiIiUjSXNHIiIiIiIiJSNHcEchIiIlJGV0YUchIiIlJFZ0aEchIiIiIiIiIiIlJGV0YUciIiIlJFZ0aEciIiIiIiI2IjYiNiI=</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 3265" layout="Heading 3265"><Font bold="true" style="Text" size="18">ANALYTICAL EXPRESSIONS OF THE SOLAR CELL ELECTRICAL CHARACTERISTIC</Font>S</Text-field></Title>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The dynamical resistance  <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRkeW5GJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation>  is obtained by applying the derivative of the output voltage with regard to the output current :</Text-field>
</Input>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Rdyn:=Iout-&gt;-diff(Vout(Iout),Iout);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSVSZHluR2YqNiMlJUlvdXRHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwkLSUlZGlmZkc2JC0lJVZvdXRHNiMlJUlvdXRHJSVJb3V0RyEiIjYiNiI2Ig==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The load resistance <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMjVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSVsb2FkRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation> is the ratio of the output voltage and the output current :</Text-field>
</Input>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Rload:=Iout-&gt;Vout(Iout)/Iout;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSZSbG9hZEdmKjYjJSVJb3V0RzYiNiQlKW9wZXJhdG9yRyUmYXJyb3dHNiIqJi0lJVZvdXRHNiMlJUlvdXRHIiIiJSVJb3V0RyEiIjYiNiI2Ig==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The analytical expression of the short-circuit current <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSNzY0YnRjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=</Equation> is obtained by setting <Equation executable="false" style="Text" input-equation="">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</Equation> which corresponds to <Equation executable="false" style="Text" input-equation="">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</Equation> :</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Isc:=Iout(0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSRJc2NHKiosJi0lKUxhbWJlcnRXRzYjLCQqKiUjUnNHIiIiJSNJc0ciIiIsJioqJSNHcEciIiIlI1JzRyIiIiUkZXRhRyIiIiUkVnRoRyIiIiEiIiomJSRldGFHIiIiJSRWdGhHIiIiISIiISIiLSUkZXhwRzYjKiosJiomJSNSc0ciIiIlJElwaEciIiIiIiIqJiUjUnNHIiIiJSNJc0ciIiIiIiIiIiIlJGV0YUchIiIlJFZ0aEchIiIsJiIiIiIiIiomJSNHcEciIiIlI1JzRyIiIiIiIiEiIiIiIiEiIiEiIioqLCYqJiUjUnNHIiIiJSRJcGhHIiIiIiIiKiYlI1JzRyIiIiUjSXNHIiIiIiIiIiIiJSRldGFHISIiJSRWdGhHISIiLCYiIiIiIiIqJiUjR3BHIiIiJSNSc0ciIiIiIiIhIiIiIiIiIiIlJGV0YUciIiIlJFZ0aEciIiIlI1JzRyEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The analytical expression of the open-circuit voltage <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSNvY0YnRjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=</Equation>  is obtained by setting  <Equation executable="false" style="Text" input-equation="">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</Equation> which corresponds to <Equation executable="false" style="Text" input-equation="">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</Equation> :</Text-field>
</Input>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Voc := Vout(0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSRWb2NHKigsJi0lKUxhbWJlcnRXRzYjKiwlI0lzRyIiIiUjR3BHISIiJSRldGFHISIiJSRWdGhHISIiLSUkZXhwRzYjKiosJiUkSXBoRyIiIiUjSXNHIiIiIiIiJSNHcEchIiIlJGV0YUchIiIlJFZ0aEchIiIiIiIhIiIqKiwmJSRJcGhHIiIiJSNJc0ciIiIiIiIlI0dwRyEiIiUkZXRhRyEiIiUkVnRoRyEiIiIiIiIiIiUkZXRhRyIiIiUkVnRoRyIiIg==</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">ANALYTICAL EXPRESSIONS OF DIFFERENT KINDS OF POWERS INVOLVED</Text-field></Title>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The expression of the output (useful, exploitable, delivered) power <Equation executable="false" style="Text" input-equation="">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</Equation> as a function of the output voltage writes : </Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Pow_vol:=Vout-&gt;Vout*Iout(Vout);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JShQb3dfdm9sR2YqNiMlJVZvdXRHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiomJSVWb3V0RyIiIi0lJUlvdXRHNiMlJVZvdXRHIiIiNiI2IjYi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The expression of the output (useful, exploitable, delivered) power<Font bold="true" style="Text"> </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JS1JJW1zdWJHRiQ2JS1GLDYmUSJQRicvJSdpdGFsaWNHUSV0cnVlRicvJTBmb250X3N0eWxlX25hbWVHUTJDaGFyYWN0ZXJTdHlsZTI1NkYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYsNiZRJG91dEYnRjdGOkY9LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUTAmQXBwbHlGdW5jdGlvbjtGJy9GPlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRlAvJSlzdHJldGNoeUdGUC8lKnN5bW1ldHJpY0dGUC8lKGxhcmdlb3BHRlAvJS5tb3ZhYmxlbGltaXRzR0ZQLyUnYWNjZW50R0ZQLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGaW4tSShtZmVuY2VkR0YkNiUtRiM2Iy1GMjYlLUYsNiZRIklGJ0Y3RjpGPUZARkVGOkZMRis=</Equation> in term of the output current is :</Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Pow_cur:=Iout-&gt;Iout*Vout(Iout);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JShQb3dfY3VyR2YqNiMlJUlvdXRHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiomJSVJb3V0RyIiIi0lJVZvdXRHNiMlJUlvdXRHIiIiNiI2IjYi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The power dissipated by Joule Effect <Equation executable="false" style="Text" input-equation="">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</Equation> in the internal components of the solar cell writes :</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Pow_Joule_Effect:=Iout-&gt;Rs*Iout^2+Gp*(Vout(Iout)+Rs*Iout)^2+(Vout(Iout)+Rs*Iout)*(Iph-Iout-Gp*(Vout(Iout)+Rs*Iout));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JTFQb3dfSm91bGVfRWZmZWN0R2YqNiMlJUlvdXRHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwoKiYlI1JzRyIiIiklJUlvdXRHIiIjIiIiIiIiKiYlI0dwRyIiIiksJi0lJVZvdXRHNiMlJUlvdXRHIiIiKiYlJUlvdXRHIiIiJSNSc0ciIiIiIiIiIiMiIiIiIiIqJiwmLSUlVm91dEc2IyUlSW91dEciIiIqJiUlSW91dEciIiIlI1JzRyIiIiIiIiIiIiwoJSRJcGhHIiIiJSVJb3V0RyEiIiomJSNHcEciIiIsJi0lJVZvdXRHNiMlJUlvdXRHIiIiKiYlJUlvdXRHIiIiJSNSc0ciIiIiIiIiIiIhIiIiIiIiIiI2IjYiNiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The solar cell total power <Equation executable="false" style="Text" input-equation="">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</Equation> which is the sum of the output power <Equation executable="false" style="Text" input-equation="">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</Equation> and the power dissipated by Joule Effect <Equation executable="false" style="Text" input-equation="">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</Equation> in the internal components is : </Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Pow_sol_cell:=Iout-&gt;Pow_Joule_Effect(Iout)+Iout*Vout(Iout);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JS1Qb3dfc29sX2NlbGxHZio2IyUlSW91dEc2IjYkJSlvcGVyYXRvckclJmFycm93RzYiLCYtJTFQb3dfSm91bGVfRWZmZWN0RzYjJSVJb3V0RyIiIiomJSVJb3V0RyIiIi0lJVZvdXRHNiMlJUlvdXRHIiIiIiIiNiI2IjYi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The solar cell total power may be written as the power delivered by the photovoltaic generator :</Text-field>
</Input>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Pow_sol_cell_new:=Iout-&gt;Iph*(Vout(Iout)+Rs*Iout);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JTFQb3dfc29sX2NlbGxfbmV3R2YqNiMlJUlvdXRHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiomJSRJcGhHIiIiLCYtJSVWb3V0RzYjJSVJb3V0RyIiIiomJSVJb3V0RyIiIiUjUnNHIiIiIiIiIiIiNiI2IjYi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The solar cell total power <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1JI21uR0YkNiVRIjBGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R0ZA</Equation> corresponding to <Equation executable="false" style="Text" input-equation="">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</Equation> and <Equation executable="false" style="Text" input-equation="">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</Equation> writes :</Text-field>
</Input>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P0:=Pow_sol_cell(0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output12"><Equation executable="false" style="2D Output">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</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">THE MAXIMUM POWER POINT EQUATIONS</Text-field></Title>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">First of all, we define <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMzFGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRtYXhGJy9GM1EmZmFsc2VGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMzJGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRtYXhGJy9GM1EmZmFsc2VGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> as the current and the voltage corresponding to the maximum power point. We also define <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMzNGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRsbXBGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> as the optimal load resistance corresponding to this point. The expression of <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMzRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRsbXBGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> is : <Equation executable="false" style="Text" input-equation="">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</Equation> . </Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">In order to derive another expression giving <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMzVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRtYXhGJy9GM1EmZmFsc2VGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> as a function of <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMzZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRsbXBGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and the five physical parameters, we substitute <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzMzdGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRtYXhGJy9GM1EmZmFsc2VGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and <Equation executable="false" style="Text" input-equation="">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</Equation><Font bold="true" style="Text"> </Font>respectively for <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNDBGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNDFGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> in equation (6) :</Text-field>
</Input>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">equa1:=subs([Iout=Imax,Vout=Rlmp*Imax],tr_equa);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSZlcXVhMUcvJSVJbWF4RywoJSRJcGhHIiIiKiYlI0lzRyIiIiwmLSUkZXhwRzYjKigsJiomJSVSbG1wRyIiIiUlSW1heEciIiIiIiIqJiUlSW1heEciIiIlI1JzRyIiIiIiIiIiIiUkZXRhRyEiIiUkVnRoRyEiIiIiIiIiIiEiIiIiIiEiIiomJSNHcEciIiIsJiomJSVSbG1wRyIiIiUlSW1heEciIiIiIiIqJiUlSW1heEciIiIlI1JzRyIiIiIiIiIiIiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I_max:=solve(equa1,Imax);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">We can also derive an expression giving <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNThGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRsbXBGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> as a function of <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNTlGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRtYXhGJy9GM1EmZmFsc2VGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and the five physical parameters : </Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">R_lmp_1:=solve(equa1,Rlmp);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JShSX2xtcF8xRywkKiYlJUltYXhHISIiLCYqJiUlSW1heEciIiIlI1JzRyIiIiIiIiooLCYtJSlMYW1iZXJ0V0c2IyosJSNJc0ciIiIlJGV0YUchIiIlJFZ0aEchIiIlI0dwRyEiIi0lJGV4cEc2IyoqLCglJUltYXhHISIiJSRJcGhHIiIiJSNJc0ciIiIiIiIlJGV0YUchIiIlJFZ0aEchIiIlI0dwRyEiIiIiIiEiIioqLCglJUltYXhHISIiJSRJcGhHIiIiJSNJc0ciIiIiIiIlJGV0YUchIiIlJFZ0aEchIiIlI0dwRyEiIiIiIiIiIiUkZXRhRyIiIiUkVnRoRyIiIiEiIiIiIiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The expression giving <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNDJGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRtYXhGJy9GM1EmZmFsc2VGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> in term of <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNDNGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRtYXhGJy9GM1EmZmFsc2VGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and the five physical parameters is obtained by substituting <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNDRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRtYXhGJy9GM1EmZmFsc2VGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkmbWZyYWNHRiQ2KC1GIzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GNDYmUSRtYXhGJy9GOFEmZmFsc2VGJ0Y6L0Y+USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUYjNiMtRjE2JS1GNDYmUSJJRidGN0Y6Rj1GQEZJLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZYLyUpYmV2ZWxsZWRHRkY=</Equation> respectively for <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNDVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNDZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> in equation (6) :</Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">equa2:=subs([Iout=Imax,Vout=Pmax/Imax],tr_equa);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSZlcXVhMkcvJSVJbWF4RywoJSRJcGhHIiIiKiYlI0lzRyIiIiwmLSUkZXhwRzYjKigsJiomJSVQbWF4RyIiIiUlSW1heEchIiIiIiIqJiUlSW1heEciIiIlI1JzRyIiIiIiIiIiIiUkZXRhRyEiIiUkVnRoRyEiIiIiIiIiIiEiIiIiIiEiIiomJSNHcEciIiIsJiomJSVQbWF4RyIiIiUlSW1heEchIiIiIiIqJiUlSW1heEciIiIlI1JzRyIiIiIiIiIiIiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P_max_1:=solve(equa2,Pmax);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JShQX21heF8xRywmKiYpJSVJbWF4RyIiIyIiIiUjUnNHIiIiISIiKiosJi0lKUxhbWJlcnRXRzYjKiwlI0lzRyIiIiUkZXRhRyEiIiUkVnRoRyEiIiUjR3BHISIiLSUkZXhwRzYjKiosKCUlSW1heEchIiIlJElwaEciIiIlI0lzRyIiIiIiIiUkZXRhRyEiIiUkVnRoRyEiIiUjR3BHISIiIiIiISIiKiosKCUlSW1heEchIiIlJElwaEciIiIlI0lzRyIiIiIiIiUkZXRhRyEiIiUkVnRoRyEiIiUjR3BHISIiIiIiIiIiJSVJbWF4RyIiIiUkZXRhRyIiIiUkVnRoRyIiIiIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The expression giving <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRtYXhGJy9GM1EmZmFsc2VGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation>  as a function of <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNDdGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRsbXBGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and the five physical parameters is obtained by substituting <Equation executable="false" style="Text" input-equation="">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</Equation> and <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkmbXNxcnRHRiQ2Iy1GIzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNDlGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GNDYmUSRtYXhGJy9GOFEmZmFsc2VGJ0Y6L0Y+USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LlExJkludmlzaWJsZVRpbWVzO0YnL0Y7UTJDaGFyYWN0ZXJTdHlsZTI1NkYnRkcvJSZmZW5jZUdGRi8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0Zcby1GMTYlLUY0NiZRIlJGJ0Y3RjpGPS1GIzYjLUY0NiZRJGxtcEYnRjdGOkY9Rkk=</Equation> respectively for <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNTBGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNTFGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> in equation (6) :</Text-field>
</Input>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">equa3:=subs([Iout=sqrt(Pmax/Rlmp),Vout=sqrt(Rlmp*Pmax)],tr_equa);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSZlcXVhM0cvKiQpKiYlJVBtYXhHIiIiJSVSbG1wRyEiIiMiIiIiIiMiIiIsKCUkSXBoRyIiIiomJSNJc0ciIiIsJi0lJGV4cEc2IyooLCYqJCkqJiUlUmxtcEciIiIlJVBtYXhHIiIiIyIiIiIiIyIiIiIiIiomKSomJSVQbWF4RyIiIiUlUmxtcEchIiIjIiIiIiIjIiIiJSNSc0ciIiIiIiIiIiIlJGV0YUchIiIlJFZ0aEchIiIiIiIiIiIhIiIiIiIhIiIqJiUjR3BHIiIiLCYqJCkqJiUlUmxtcEciIiIlJVBtYXhHIiIiIyIiIiIiIyIiIiIiIiomKSomJSVQbWF4RyIiIiUlUmxtcEchIiIjIiIiIiIjIiIiJSNSc0ciIiIiIiIiIiIhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P_max_2:=solve(equa3,Pmax);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output12"><Equation executable="false" style="2D Output">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</Equation></Text-field>
</Output>
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<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The expression giving <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNTJGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRtYXhGJy9GM1EmZmFsc2VGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> in term of <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNTNGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRsbXBGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and the five physical parameters is obtained by substituting <Equation executable="false" style="Text" input-equation="">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</Equation> and <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNTVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRtYXhGJy9GM1EmZmFsc2VGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> respectively for <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNTdGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> in equation (6) :</Text-field>
</Input>
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<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">equa4:=subs([Iout=Vmax/Rlmp,Vout=Vmax],tr_equa);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSZlcXVhNEcvKiYlJVZtYXhHIiIiJSVSbG1wRyEiIiwoJSRJcGhHIiIiKiYlI0lzRyIiIiwmLSUkZXhwRzYjKigsJiUlVm1heEciIiIqKCUlVm1heEciIiIlJVJsbXBHISIiJSNSc0ciIiIiIiIiIiIlJGV0YUchIiIlJFZ0aEchIiIiIiIiIiIhIiIiIiIhIiIqJiUjR3BHIiIiLCYlJVZtYXhHIiIiKiglJVZtYXhHIiIiJSVSbG1wRyEiIiUjUnNHIiIiIiIiIiIiISIi</Equation></Text-field>
</Output>
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<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">V_max:=solve(equa4,Vmax);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output12"><Equation executable="false" style="2D Output">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</Equation></Text-field>
</Output>
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<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The expression giving <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNjBGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRsbXBGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> as a function of <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzNjFGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRtYXhGJy9GM1EmZmFsc2VGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and the five physical parameters is : </Text-field>
</Input>
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<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">R_lmp_2:=solve(equa4,Rlmp);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output12"><Equation executable="false" style="2D Output">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</Equation></Text-field>
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<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The expression giving <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzOTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRtYXhGJy9GM1EmZmFsc2VGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> in term of <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzOTdGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRtYXhGJy9GM1EmZmFsc2VGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and the five physical parameters is obtained by substituting <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkmbWZyYWNHRiQ2KC1GIzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzOThGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GNDYmUSRtYXhGJy9GOFEmZmFsc2VGJ0Y6L0Y+USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUYjNiMtRjE2JS1GNDYmUSJWRidGN0Y6Rj1GQEZJLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZYLyUpYmV2ZWxsZWRHRkY=</Equation> and <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzOTlGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRtYXhGJy9GM1EmZmFsc2VGJ0Y1L0Y5USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> respectively for <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGU0MDBGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> and <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiVkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGU0MDFGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSRvdXRGJ0YyRjVGOC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn</Equation> in equation (6) :</Text-field>
</Input>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">equa5:=subs([Iout=Pmax/Vmax,Vout=Vmax],tr_equa);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSZlcXVhNUcvKiYlJVBtYXhHIiIiJSVWbWF4RyEiIiwoJSRJcGhHIiIiKiYlI0lzRyIiIiwmLSUkZXhwRzYjKigsJiUlVm1heEciIiIqKCUlUG1heEciIiIlJVZtYXhHISIiJSNSc0ciIiIiIiIiIiIlJGV0YUchIiIlJFZ0aEchIiIiIiIiIiIhIiIiIiIhIiIqJiUjR3BHIiIiLCYlJVZtYXhHIiIiKiglJVBtYXhHIiIiJSVWbWF4RyEiIiUjUnNHIiIiIiIiIiIiISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P_max_3:=solve(equa5,Pmax);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">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</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">THE CURRENT-VOLTAGE CHARACTERISRTIC AND THE POWERS CURVES </Text-field></Title>
<Group labelreference="L54" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The physical constants are : The Boltzmann Constant <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSJCRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation>, The Electron Charge <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JlEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNThGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation>  and the Thermal Voltage <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JS1JJW1zdWJHRiQ2JS1GLDYmUSJWRicvJSdpdGFsaWNHUSV0cnVlRicvJTBmb250X3N0eWxlX25hbWVHUTJDaGFyYWN0ZXJTdHlsZTI1NkYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYsNiZRI3RoRidGN0Y6Rj0vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y6L0Y+USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGUC8lKXN0cmV0Y2h5R0ZQLyUqc3ltbWV0cmljR0ZQLyUobGFyZ2VvcEdGUC8lLm1vdmFibGVsaW1pdHNHRlAvJSdhY2NlbnRHRlAvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Zpbi1JJm1mcmFjR0YkNigtRiM2JS1GMjYlLUYsNiZRImtGJ0Y3RjpGPS1GIzYjLUYsNiZRIkJGJ0Y3RjpGPUZFLUZJNi5RMSZJbnZpc2libGVUaW1lcztGJ0Y6RkxGTkZRRlNGVUZXRllGZW4vRmhuUSYwLjBlbUYnL0Zbb0ZfcC1GLDYmUSJURidGN0Y6Rj0tRiM2Iy1GLDYmUSJxRidGN0Y6Rj0vJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl5xLyUpYmV2ZWxsZWRHRlBGKw==</Equation>. <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JlEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation>  is the temperature.</Text-field>
</Input>
</Group>
<Group labelreference="L55" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">kB:=1.38062*10^(-23):T:=300:q:=1.60219*10^(-19):Vth:=(kB*T)/q:</Text-field>
</Input>
</Group>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">In order to make some illustrations, we borrow the numerical values of the five physical parameters from reference [9] :</Text-field>
</Input>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Gp:=5.07*10^(-3):Rs:=8.59:Iph:=7.94*10^(-3):eta:=2.31:Is:=13.6*10^(-9):</Text-field>
</Input>
</Group>
<Group labelreference="L58" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The values of  physical constants and five physical parameters are introduced in the expressions of output current, output power in term of output voltage, output voltage, output power in term of output current, dynamical resistance, load resistance and in the expressions of solar cell electrical characteristics :</Text-field>
</Input>
</Group>
<Group labelreference="L59" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Iout(Vout):Pow_vol(Vout):Vout(Iout):Pow_cur(Iout):Rdyn(Iout):Rload(Iout):</Text-field>
</Input>
</Group>
<Group labelreference="L60" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Isc;Voc;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiMkIi1qIT4zJzN3ISM5</Equation></Text-field>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiMkIi1DOjoib2AoISM3</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L61" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiMkIi01ViRHVSlmISM5</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L62" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal270">In the following figure, we present the current-voltage characteristic : </Text-field>
</Input>
</Group>
<Group labelreference="L63" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(Iout(Vout),Vout=0..Voc,Iout=0..Isc,colour=blue,axes=boxed,title=&quot;Current-Voltage Characteristic&quot;);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="485" type="two-dimensional" width="485" gridlinevisibility="1" legendvisibility="false">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L64" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">In the next figure, we draw the output voltage against the output current :</Text-field>
</Input>
</Group>
<Group labelreference="L65" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(Vout(Iout),Iout=0..Isc,Vout=0..Voc,axes=boxed,title=&quot;Voltage-Current Curve&quot;);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="485" type="two-dimensional" width="485" gridlinevisibility="1" legendvisibility="false">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L66" drawlabel="true">
<Input>
<Text-field style="Normal267" layout="Normal267">Then, we plot the output power of the solar cell versus the output voltage :</Text-field>
</Input>
</Group>
<Group labelreference="L67" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font encoding="UTF-8">plot(Pow_vol(Vout),Vout=0..Voc,Power=0..0.0026,axes=boxed,title=&quot;Output Power\134n versus\134nOutput Voltage&quot;);</Font></Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="485" type="two-dimensional" width="485" gridlinevisibility="1" legendvisibility="false">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L68" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">In the following line, we determine the maximum power and the corresponding voltage :</Text-field>
</Input>
</Group>
<Group labelreference="L69" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">MPP_vol:=Maximize(Pow_vol(Vout),{0&lt;=Vout,Vout&lt;=Voc});</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JShNUFBfdm9sRzckJCIzIykqel5wO1JbZCMhIz83Iy8lJVZvdXRHJCIzMV8xW14mPWhZJiEjPQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L70" drawlabel="true">
<Input>
<Text-field style="Normal267" layout="Normal267">Next, we present the output power of the solar cell against the output current :</Text-field>
</Input>
</Group>
<Group labelreference="L71" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font encoding="UTF-8">plot(Pow_cur(Iout),Iout=0..Isc,Power=0..0.0026,axes=boxed,title=&quot;Output Power\134n versus\134nOutput Current&quot;);</Font></Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="485" type="two-dimensional" width="485" gridlinevisibility="1" legendvisibility="false">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L72" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">In the following line, we determine the maximum power and the corresponding current :</Text-field>
</Input>
</Group>
<Group labelreference="L73" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">MPP_cur:=Maximize(Pow_cur(Iout),{0&lt;=Iout,Iout&lt;=Isc});</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JShNUFBfY3VyRzckJCIzLytFIXA7UltkIyEjPzcjLyUlSW91dEckIjNTMlBzY1JhNVohIz8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L74" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">In the next figure, the dynamical resistance and the load resistance are drawn against the output current. In the maximal power point, one can remark that <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JS1JJW1zdWJHRiQ2JS1GLDYmUSJSRicvJSdpdGFsaWNHUSV0cnVlRicvJTBmb250X3N0eWxlX25hbWVHUTJDaGFyYWN0ZXJTdHlsZTM2NEYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYsNiZRJGR5bkYnRjdGOkY9LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYuUSI9RidGOi9GPlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRlAvJSlzdHJldGNoeUdGUC8lKnN5bW1ldHJpY0dGUC8lKGxhcmdlb3BHRlAvJS5tb3ZhYmxlbGltaXRzR0ZQLyUnYWNjZW50R0ZQLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGaW4tRjI2JUY0LUYjNiMtRiw2JlElbG9hZEYnRjdGOkY9RkVGKw==</Equation> [10] : </Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([Rdyn(Iout),Rload(Iout)],Iout=0..Isc,R=0..250,title=&quot;Dynamical Resistance &amp; Load Resistance&quot; ,axes=boxed,linestyle=[SOLID,DASHDOT],colour=[blue,red],legend=[&quot;Rdyn&quot;, &quot;Rload&quot;]);</Text-field>
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<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="485" type="two-dimensional" width="485" gridlinevisibility="1" legendvisibility="true">LSUlUExPVEc2KS0lJ0NVUlZFU0c2JjdTNyQkIiIhISIiJCIsc1VjJjRBISIqNyQkIi1EZCtZZTshIzokIiwkKVInUWVBISIqNyQkIi1LJkd4OTUkISM6JCIsKnomPVBJIyEiKjckJCItdnk1SUNaISM6JCIrPmw9ZUIhIik3JCQiLDwrIyl5TichIzkkIixkRU9yVCMhIio3JCQiLW4qeilwJCl6ISM6JCIsVW11LlsjISIqNyQkIi1WITRSNVwqISM6JCIsOzpTTmEjISIqNyQkIixgRSE9MDYhIzgkIixvNHdTaCMhIio3JCQiLGlsJWZtNyEjOCQiLHJvdUpwIyEiKjckJCItNipRIlxGOSEjOSQiLGNwTCF6RiEiKjckJCItamJNKkhmIiEjOSQiLDpRU2MoRyEiKjckJCIsZnduKFE8ISM4JCIsZWlNJ29IISIqNyQkIi1yN14oRyE+ISM5JCIsI29RViQzJCEiKjckJCItMStqbG4/ISM5JCIsSnprNUAkISIqNyQkIi1IMk5YRUEhIzkkIix5OUZ3TSQhIio3JCQiLVwlZWMxUCMhIzkkIiojXClcWyQhIig3JCQiLDQqejdVRCEjOCQiLEpYMndtJCEiKjckJCItMmtuUShvIyEjOSQiLGYscTklUSEiKjckJCItXlxzTmNHISM5JCIsKVFSJCpwUyEiKjckJCItMWdaI2YrJCEjOSQiLFxlUCtJJSEiKjckJCItS0NTLXFKISM5JCIsLU9rJyllJSEiKjckJCItKipIYEdFTCEjOSQiLERvS2UhXCEiKjckJCItYzR3SypbJCEjOSQiLHQxWS5IJiEiKjckJCIsJj04MFJPISM4JCIsaSRwMS1kISIqNyQkIi1kbCZbMCFRISM5JCIsdmQxSkEnISIqNyQkIi1IPCkpSG9SISM5JCIsa09leidvISIqNyQkIi1iL2ZLOVQhIzkkIiw2ZFJRYCghIio3JCQiLUxmIlI/RiUhIzkkIiwoXCVvT1EpISIqNyQkIi14JFFzXFYlISM5JCIsWUsra1UqISIqNyQkIi1rYzJQJWYlISM5JCItL3BnTGk1ISIqNyQkIiwmeW9mW1ohIzgkIi1PQyUqSCU+IiEiKjckJCItKj5wUSk+XCEjOSQiLTRsT3RhOCEiKjckJCIseDIyUDImISM4JCItR1E9YS06ISIqNyQkIi0qPlUlKnpCJiEjOSQiLTY7IUc1bCIhIio3JCQiLSNRPGpvUSYhIzkkIi1HKD0ybXciISIqNyQkIi0oNC87J1xiISM5JCItVS5Gbmw9ISIqNyQkIi1LMFF2LWQhIzkkIi1oaDchRyQ+ISIqNyQkIi1yJCpvI0cnZSEjOSQiLWlNUU8hKT4hIio3JCQiLGpmRiQ+ZyEjOCQiLT1HNEo1PyEiKjckJCItPkckcEo9JyEjOSQiLVUiUih5SD8hIio3JCQiLTAqUW80TSchIzkkIi1DJXBqNi8jISIqNyQkIi1APzJNLWwhIzkkIi0lUiJlO1s/ISIqNyQkIi0qcCFvUGltISM5JCItaFBlSF8/ISIqNyQkIi0uXUxWNG8hIzkkIi0+PUBmYT8hIio3JCQiLW9Wbih6KHAhIzkkIi1NemU7Yz8hIio3JCQiLT1rUnNHciEjOSQiLTxJbCpwMCMhIio3JCQiLSJIJT5YKkcoISM5JCIsbl1GdjAjISIpNyQkIi0qcDcqR1Z1ISM5JCIteGgoSHkwIyEiKjckJCItaiE+MyczdyEjOSQiLXhCPi1lPyEiKi0lJ0xFR0VOREc2Iy0lKV9UWVBFU0VURzYjLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IjY2LUkjbXNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2I1ElUmR5bjYiLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuNiIvJSVzaXplR1EjMTI2Ii8lJWJvbGRHUSZmYWxzZTYiLyUnaXRhbGljR1EmZmFsc2U2Ii8lKnVuZGVybGluZUdRJmZhbHNlNiIvJSpzdWJzY3JpcHRHUSZmYWxzZTYiLyUsc3VwZXJzY3JpcHRHUSZmYWxzZTYiLyUrZm9yZWdyb3VuZEdRKFswLDAsMF02Ii8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdNiIvJSdvcGFxdWVHUSZmYWxzZTYiLyUrZXhlY3V0YWJsZUdRJmZhbHNlNiIvJSlyZWFkb25seUdRJmZhbHNlNiIvJSljb21wb3NlZEdRJmZhbHNlNiIvJSpjb252ZXJ0ZWRHUSZmYWxzZTYiLyUraW1zZWxlY3RlZEdRJmZhbHNlNiIvJSxwbGFjZWhvbGRlckdRJmZhbHNlNiIvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHUSZmYWxzZTYiLyUwZm9udF9zdHlsZV9uYW1lR1ErTWFwbGV+UGxvdDYiLyUsbWF0aHZhcmlhbnRHUSdub3JtYWw2Ii0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiM1ISIiLSUqTElORVNUWUxFRzYjIiIiLSUnQ1VSVkVTRzYmN2JwNyQkIiwqeXdvIz0mISM7JCItNF90K2E5ISInNyQkIi15TnZgTzUhIzskIixYKDMkKm9zISInNyQkIi1uLmohW2IiISM7JCItTWxoQFhbISIoNyQkIi1jcl0ydD8hIzskIi0kKVIlZUxqJCEiKDckJCItWFJRTSJmIyEjOyQiLTEyTkMxSCEiKDckJCItTTJFaDRKISM7JCItPXEqKlxAQyEiKDckJCItQnY4KXlpJCEjOyQiLU90VkR2PyEiKDckJCItN1YsOllUISM7JCItbikpKnBiIj0hIig3JCQiLSw2Kj1XbSUhIzskIi1SeUlmODshIig3JCQiLCp5d28jPSYhIzokIi0nKSpSNj9YIiEiKDckJCIsb1djNHEmISM6JCItVHIhMyk+OCEiKDckJCIsWkBEIz5pISM6JCItRjAmUSc0NyEiKDckJCIsRSlSXFBuISM6JCIteicpelQ7NiEiKDckJCIsMHZpZEQoISM6JCItKXBkOWwuIiEiKDckJCIsJT06LnV4ISM6JCIta1EmW0VuKiEiKTckJCItRCdHK0JIKSEjOyQiLS01RHJtISohIik3JCQiLFQwcDAiKSkhIzokIi12dkAxSyYpISIpNyQkIitBeSQpRyQqISM5JCItdSVlO28wKSEiKTckJCIsKiplMXIlKSohIzokIi02UmdmSnchIik3JCQiLXlOdmBPNSEjOiQiLU8heScqKVtzISIpNyQkIi1kN1dPKTMiISM6JCItUFBWay1wISIpNyQkIi1PKkciPlM2ISM6JCItUClvb3llJyEiKTckJCItOm0iPT8+IiEjOiQiLTRqVFkraiEiKTckJCItJUgvWFFDIiEjOiQiLW1wJDRxLichIik3JCQiLXQ+Pm4mSCIhIzokIi0nKlEuaiV6JiEiKTckJCItXyd6KVxaOCEjOiQiLSQzRCYqM2QmISIpNyQkIi1KdGNLKlIiISM6JCItLGJEdGpgISIpNyQkIiwsYl82WCIhIzkkIi10T21Pcl4hIik3JCQiLW8uaiFbYiIhIzokIi1QPGs1RFshIik3JCQiLURkK1llOyEjOiQiLUJnbjdBWCEiKTckJCItdzVzJClRPSEjOiQiLTFDJj5qMiUhIik3JCQiLUVrVkA+PyEjOiQiLWInZWIsciQhIik3JCQiLXg8OmYqPiMhIzokIi0kW11UU1MkISIpNyQkIi1HcidvKnpCISM6JCIteWhQS1dKISIpNyQkIiwkeUhzU0YhIzkkIi1AJSpcVkZGISIpNyQkIi1LJkd4OTUkISM6JCItXyRHOnZTIyEiKTckJCItb0xLPTJOISM6JCItLyp6V2o3IyEiKTckJCItLyM9KilHIlIhIzokIi0ieVttTSE+ISIpNyQkIiwvOCZmPVYhIzkkIi0zSzpYQTwhIik3JCQiLXZ5NUlDWiEjOiQiLUcqXDlEZCIhIik3JCQiLC1hIjRUYiEjOSQiLVxMIT5zTCIhIik3JCQiLDwrIyl5TichIzkkIi1WTD9NaTYhIik3JCQiLW4qeilwJCl6ISM6JCItKlFRV2w/KiEiKjckJCItViE0UjVcKiEjOiQiLUFSJylcL3ghIio3JCQiLGBFIT0wNiEjOCQiLWNJeC4hZSchIio3JCQiLGlsJWZtNyEjOCQiLWEhSHB3cSYhIio3JCQiLTYqUSJcRjkhIzkkIi0mb3QzTi4mISIqNyQkIi1qYk0qSGYiISM5JCItL0BAPiJbJSEiKjckJCIsZnduKFE8ISM4JCItVDdpKyIzJSEiKjckJCItcjdeKEchPiEjOSQiLFs0a0hxJCEiKTckJCItMStqbG4/ISM5JCIsKEdYeSNRJCEiKTckJCItSDJOWEVBISM5JCItMWNPOD1KISIqNyQkIi1cJWVjMVAjISM5JCItTS4qKW8ySCEiKjckJCIsNCp6N1VEISM4JCItZjMnXHVvIyEiKjckJCItMmtuUShvIyEjOSQiLUwkKT4hPl8jISIqNyQkIi1eXHNOY0chIzkkIi05ajdMXEIhIio3JCQiLTFnWiNmKyQhIzkkIi04V0VpNkEhIio3JCQiLUtDUy1xSiEjOSQiLShSOlpUMiMhIio3JCQiLSoqSGBHRUwhIzkkIi1MTFpVYT4hIio3JCQiLWM0d0sqWyQhIzkkIiwlUldJUj0hIik3JCQiLCY9ODBSTyEjOCQiLWtrbS5UPCEiKjckJCItZGwmWzAhUSEjOSQiLSopbyhbPGsiISIqNyQkIi1IPCkpSG9SISM5JCItKnpGPlphIiEiKjckJCIt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<Text-field style="Normal" layout="Normal">Finally, we draw the output power <Equation executable="false" style="Text" input-equation="">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</Equation>, the power dissipated by Joule Effect in the internal components <Equation executable="false" style="Text" input-equation="">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</Equation> and the total power of the solar cell <Equation executable="false" style="Text" input-equation="">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</Equation> as functions of the output current : </Text-field>
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<Group labelreference="L77" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([Pow_cur(Iout),Pow_Joule_Effect(Iout),Pow_sol_cell(Iout)],Iout=0..Isc,Power=0..P0,linestyle=[SOLID,DASHDOT,DOT],legend=[&quot;Output Power&quot;, &quot;Joule-Effect Power&quot;,&quot;Total Power&quot;],linestyle=[SOLID,DASHDOT],colour=[blue,red,black],axes=boxed,title=&quot;Different Kinds of Powers&quot;);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="485" type="two-dimensional" width="485" gridlinevisibility="1" 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</Output>
</Group>
<Group labelreference="L78" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">In the following lines, we calculate the values of the maximum power point coordinates given by the different expressions shown in the previous section.</Text-field>
</Input>
</Group>
<Group labelreference="L79" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Imax:=fsolve(Rdyn=Rload);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSVJbWF4RyQiLVZcUmE1WiEjOQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L80" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">R_lmp_1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiMkIi1xNjJTZzYhIio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L81" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Vmax:=Vout(Imax);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSVWbWF4RyQiLVVeJj1oWSYhIzc=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L82" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">R_lmp_2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiMkIi1xNjJTZzYhIio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L83" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Rlmp:=Vmax/Imax;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSVSbG1wRyQiLXE2MlNnNiEiKg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L84" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I_max;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiMkIi1UXFJhNVohIzk=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L85" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">V_max;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiMkIi1UXiY9aFkmISM3</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L86" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P_max_1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiMkIi0kcDtSW2QjISM5</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L87" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P_max_2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiQkIi0mUiZHOUlOISM4JCItJnA7UltkIyEjOQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L88" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P_max_3;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiMkIi0mcDtSW2QjISM5</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L89" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Rload(Imax);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiMkIi1xNjJTZzYhIio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L90" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The fill factor is given by:</Text-field>
</Input>
</Group>
<Group labelreference="L91" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">FF:=Imax*Vmax/(Isc*Voc);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSNGRkckIi10KWY3LFwlISM3</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L92" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">FF:=I_max*V_max/(Isc*Voc);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSNGRkckIi1wKWY3LFwlISM3</Equation></Text-field>
</Output>
</Group>
</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Text" size="18" bold="true" layout="Heading 1"><Font bold="true" size="18">PHYSICAL PARAMETERS EFFECT</Font></Text-field></Title>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 3" layout="Heading 3"> <Font bold="true" style="Text" size="18">Effect of the series resistance<Font italic="true"> </Font></Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2J1EjUnNGJy8lJXNpemVHUSMxOEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNjFGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation><Font bold="true" style="Text" size="18"> :</Font></Text-field></Title>
<Group labelreference="L93" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:with(plots):Digits:=12:</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, the name changecoords has been redefined
</Text-field>
</Output>
</Group>
<Group labelreference="L94" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">We begin by introducing the current-voltage characteristic (equation (6)) :</Text-field>
</Input>
</Group>
<Group labelreference="L95" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tr_equa := Iout = Iph-Is*(exp((Vout+Iout*Rs)/(eta*Vth))-1)-Gp*(Vout+Rs*Iout):
cur_sol:=solve(tr_equa,Iout):
Iout := unapply(cur_sol,Vout):
vol_sol:=solve(tr_equa,Vout):
Vout := unapply(vol_sol,Iout):
Isc:=Iout(0):
Voc:=Vout(0):
Pow_cur:=Iout-&gt;Vout(Iout)*Iout:</Text-field>
</Input>
</Group>
<Group labelreference="L96" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">For <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzODRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSJwRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIixGJ0Y1L0Y5USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0ZLLyUqc3ltbWV0cmljR0ZLLyUobGFyZ2VvcEdGSy8lLm1vdmFibGVsaW1pdHNHRksvJSdhY2NlbnRHRksvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlLUYvNiZRIklGJ0YyRjVGOC1GIzYjLUYvNiZRI3BoRidGMkY1RjhGQEZDLUYvNiZRJiZldGE7RicvRjNGS0Y1RkdGQy1GLDYlRmpuLUYjNiMtRi82JlEic0YnRjJGNUY4RkA=</Equation>, we use the numerical values given in the previous section. <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzODVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSJzRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation> lies in the range 10^(-6) ohms to 100 ohms.</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">kB:=1.38062*10^(-23):T:=300:q:=1.60219*10^(-19):Vth:=(kB*T)/q:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Gp:=5.07*10^(-3):Iph:=7.94*10^(-3):eta:=2.31:Is:=13.6*10^(-9):</Text-field>
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<Text-field style="Normal" layout="Normal">In the next figures, we give animations to evidence the effect of the series resistance on the current-voltage characteristic and on the output power of the solar cell <Equation executable="false" style="Text" input-equation="">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</Equation> :</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font encoding="UTF-8">animate(plot,[Iout(Vout),Vout=0..Voc,Iout=0..Isc,axes=boxed,numpoints=100,thickness=2,linestyle=SOLID,color=blue,title=&quot;Effect of the Series Resistance\134n on the Current-Voltage Characteristic&quot;], Rs=10^(-6)..100);</Font></Text-field>
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<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Text" italic="true" size="18" bold="true" layout="Heading 3"><Font bold="true" italic="false" size="18">Effect of the shunt conductance </Font><Font bold="true" italic="true" size="18">Gp</Font><Font bold="true" italic="false" size="18"> :</Font></Text-field></Title>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:with(plots):Digits:=12:</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, the name changecoords has been redefined
</Text-field>
</Output>
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<Group labelreference="L103" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tr_equa := Iout = Iph-Is*(exp((Vout+Iout*Rs)/(eta*Vth))-1)-Gp*(Vout+Rs*Iout):
cur_sol:=solve(tr_equa,Iout):
Iout := unapply(cur_sol,Vout):
vol_sol:=solve(tr_equa,Vout):
Vout := unapply(vol_sol,Iout):
Isc:=Iout(0):
Voc:=Vout(0):
Pow_cur:=Iout-&gt;Vout(Iout)*Iout:</Text-field>
</Input>
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<Input>
<Text-field style="Normal" layout="Normal">The numerical values of <Equation executable="false" style="Text" input-equation="">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</Equation> and <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzODhGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSJzRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation> are given in the previous section. <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzOTBGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSJwRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation><Font style="Text"> increases from 10^(-6) Siemens to 0.01 Siemens.</Font></Text-field>
</Input>
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<Group labelreference="L105" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">kB:=1.38062*10^(-23):T:=300:q:=1.60219*10^(-19):Vth:=(kB*T)/q:</Text-field>
</Input>
</Group>
<Group labelreference="L106" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Rs:=8.59:Iph:=7.94*10^(-3):eta:=2.31:Is:=13.6*10^(-9):</Text-field>
</Input>
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<Group labelreference="L107" drawlabel="true">
<Input>
<Text-field style="Normal270" layout="Normal270"><Font style="Text">Now, we present the animation of the current-voltage characteristic when the shunt conductance </Font><Equation executable="false" style="2D Comment" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUYvNiVRInBGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation><Font style="Text"> increases :</Font></Text-field>
</Input>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font encoding="UTF-8">animate(plot,[Iout(Vout),Vout=0..Voc,Iout=0..Isc,axes=boxed,numpoints=100,thickness=2,linestyle=SOLID,color=blue,title=&quot;Effect of the Shunt Conductance\134n on the Solar Cell Characteristic&quot;], Gp=10^(-6)..0.01);</Font></Text-field>
</Input>
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<Text-field style="Normal" layout="Normal">Next, we give the animation of the output power curve when the <Font style="Text">shunt conductance </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUzOTFGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSJwRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation> increases :</Text-field>
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</Output>
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</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Text" italic="true" size="18" bold="true" layout="Heading 3"><Font bold="true" italic="false" size="18">Effect of the saturation current </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2J1EjSXNGJy8lJXNpemVHUSMxOEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNjNGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation><Font bold="true" italic="false" size="18"> :</Font></Text-field></Title>
<Group labelreference="L111" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:with(plots):Digits:=12:</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, the name changecoords has been redefined
</Text-field>
</Output>
</Group>
<Group labelreference="L112" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tr_equa := Iout = Iph-Is*(exp((Vout+Iout*Rs)/(eta*Vth))-1)-Gp*(Vout+Rs*Iout):
cur_sol:=solve(tr_equa,Iout):
Iout := unapply(cur_sol,Vout):
vol_sol:=solve(tr_equa,Vout):
Vout := unapply(vol_sol,Iout):
Isc:=Iout(0):
Voc:=Vout(0):
Pow_cur:=Iout-&gt;Vout(Iout)*Iout:</Text-field>
</Input>
</Group>
<Group labelreference="L113" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">kB:=1.38062*10^(-23):T:=300:q:=1.60219*10^(-19):Vth:=(kB*T)/q:</Text-field>
</Input>
</Group>
<Group labelreference="L114" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The numerical values of <Equation executable="false" style="Text" input-equation="">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</Equation> and <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTdGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSJwRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation> are given in the previous section. <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTlGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSJzRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation><Font style="Text"> increases from 10^(-9) A to </Font>10^(-7) A<Font style="Text">.</Font></Text-field>
</Input>
</Group>
<Group labelreference="L115" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Gp:=5.07*10^(-3):Rs:=8.59:Iph:=7.94*10^(-3):eta:=2.31:</Text-field>
</Input>
</Group>
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<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Text" size="18" bold="true" layout="Heading 3"><Font bold="true" size="18">Effect of the ideality factor </Font><Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2J1EmJmV0YTtGJy8lJXNpemVHUSMxOEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lMGZvbnRfc3R5bGVfbmFtZUdRMkNoYXJhY3RlclN0eWxlMjYyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn</Equation><Font bold="true" size="18"> :</Font></Text-field></Title>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:with(plots):Digits:=12:</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, the name changecoords has been redefined
</Text-field>
</Output>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tr_equa := Iout = Iph-Is*(exp((Vout+Iout*Rs)/(eta*Vth))-1)-Gp*(Vout+Rs*Iout):
cur_sol:=solve(tr_equa,Iout):
Iout := unapply(cur_sol,Vout):
vol_sol:=solve(tr_equa,Vout):
Vout := unapply(vol_sol,Iout):
Isc:=Iout(0):
Voc:=Vout(0):
Pow_cur:=Iout-&gt;Vout(Iout)*Iout:</Text-field>
</Input>
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<Group labelreference="L121" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">kB:=1.38062*10^(-23):T:=300:q:=1.60219*10^(-19):Vth:=(kB*T)/q:</Text-field>
</Input>
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<Group labelreference="L122" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal">The numerical values of <Equation executable="false" style="Text" input-equation="">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</Equation> and <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTdGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSJwRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation> are given in the previous section. <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JlEmJmV0YTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJTBmb250X3N0eWxlX25hbWVHUTJDaGFyYWN0ZXJTdHlsZTI1OEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==</Equation><Font style="Text"> increases from 1 to 3.</Font></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Gp:=5.07*10^(-3):Rs:=8.59:Iph:=7.94*10^(-3):Is:=13.6*10^(-9):</Text-field>
</Input>
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<Group labelreference="L124" drawlabel="true">
<Input>
<Text-field style="Normal267" layout="Normal267">In the next figures, we give the effect of the ideality factor <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JlEmJmV0YTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJTBmb250X3N0eWxlX25hbWVHUTJDaGFyYWN0ZXJTdHlsZTQxM0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==</Equation> on the current-voltage characteristic and on the output power of the solar cell :</Text-field>
</Input>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font encoding="UTF-8">animate( plot,[Iout(Vout),Vout=0..Voc,Iout=0..Isc,axes=boxed,numpoints=100,thickness=2,linestyle=SOLID,color=blue,title=&quot;Effect of the Ideality Factor\134n on the Current-Voltage Characteristic&quot;], eta=1..3);</Font></Text-field>
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<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Text" size="18" bold="true" layout="Heading 3265"><Font bold="true" size="18">Effect of the photocurrent Iph :</Font></Text-field></Title>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:with(plots):Digits:=12:</Text-field>
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<Output>
<Text-field style="Warning" layout="Warning">Warning, the name changecoords has been redefined
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tr_equa := Iout = Iph-Is*(exp((Vout+Iout*Rs)/(eta*Vth))-1)-Gp*(Vout+Rs*Iout):
cur_sol:=solve(tr_equa,Iout):
Iout := unapply(cur_sol,Vout):
vol_sol:=solve(tr_equa,Vout):
Vout := unapply(vol_sol,Iout):
Isc:=Iout(0):
Voc:=Vout(0):
Pow_cur:=Iout-&gt;Vout(Iout)*Iout:</Text-field>
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<Group labelreference="L129" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">kB:=1.38062*10^(-23):T:=300:q:=1.60219*10^(-19):Vth:=(kB*T)/q:</Text-field>
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<Input>
<Text-field style="Normal" layout="Normal">The numerical values of <Equation executable="false" style="Text" input-equation="">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</Equation> and <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiR0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNTdGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSJwRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==</Equation> are given in the previous section. <Equation executable="false" style="Text" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EyQ2hhcmFjdGVyU3R5bGUyNThGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Iy1GLzYmUSNwaEYnRjJGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRic=</Equation><Font style="Text"> increases from 10^(-3) to 10^(-2) A.</Font></Text-field>
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<Group labelreference="L131" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Gp:=5.07*10^(-3):Rs:=8.59:eta:=2.31:Is:=13.6*10^(-9):</Text-field>
</Input>
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<Input>
<Text-field style="Normal267" layout="Normal267">In the following figure, we present the effect of the photocurrent on the current-voltage characteristic :</Text-field>
</Input>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Font encoding="UTF-8">animate(plot,[Iout(Vout),Vout=0..Voc,Iout=0..0.01,axes=boxed,numpoints=100,thickness=2,linestyle=SOLID,color=blue,title=&quot;Effect of the Photocurrent\134n on the Current-Voltage Characteristic&quot;],Iph=10^(-3)..10^(-2));</Font></Text-field>
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<Text-field style="Text" size="18" bold="true" layout="Heading 1"><Font bold="true" size="18">CONCLUSION:</Font></Text-field></Title>
<Text-field style="Normal" layout="Normal">In this paper, exact analytical solutions for output current, output voltage, short circuit current and open circuit voltage <Font style="Text">were determined. New expressions of different kinds of powers involved were derived. Seven original relationships between maximum power point coordinates were presented for the first time. Finally, animations illustrating the effect of each physical parameter on solar cell characteristic and on output power were given. The reader </Font>of the present worksheet can do the following modifications : </Text-field>
<Text-field style="Normal" layout="Normal">i) He can change the physical parameters values and looks for the effect produced in the graphs and in the animations.</Text-field>
<Text-field style="Normal" layout="Normal">ii) He can change the temperature <Equation executable="false" style="2D Comment" input-equation="">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==</Equation> and looks for the influence on the graphs and on the animations.</Text-field>
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<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Normal272" layout="Normal272">REFERENCES</Text-field></Title>
<Text-field style="Normal" layout="Normal">[1] T. C Banwell &amp; A. Jayakumar, Exact Analytical Solution for Current flow through Diode with Series Resistance, Electronics letters, 36, 291-292,2000.
[2] A. Jain and A. Kapoor, Exact Analitycal Solutions of the Parameters of Real Solar Cells Using Lambert W-Function, Solar Energy Materials &amp; Solar Cells, 81, 269-277, 2004.
[3] Manuel A. Vargas-Drechsler, Analytical Solution of Diode Circuits, Maple application center, July 2005. Available online at the electronic address :</Text-field>
<Text-field style="Normal" layout="Normal">http://www.maplesoft.com/Applications/appviewer.aspx?F=DiodeNew1.html&amp;ID=969</Text-field>
<Text-field style="Normal" layout="Normal">[4] Maple V Release 4, Copyright 1981-1995, Waterloo Maple Inc.
[5] E. Assaid and M. El Aydi, Exact Analytical Solutions of Diodes Bridge, Maple application center, January 2007. Available online at the electronic address:
http://www.maplesoft.com/applications/app_center_view.aspx?AID=2039
<Font encoding="UTF-8">[6] E. Assaid, E. Feddi and M. El Aydi, Exact Analytical Expressions of Gra\302\250etz Bridge Currents and Voltages Using LambertW Function, The 14th IEEE International Conference on Electronics, Circuits and Systems, Marrakech, Morocco, december 11-14, 2007.
</Font>[7] S. Yadir, S. Aazou, N. Maouhoub, K. Rais, M. Benhmida and E. Assaid, Illuminated Solar Cell Physical Parameters Extraction Using Mathematica, The 7th ACS/IEEE International Conference on Computer Systems and Applications, Rabat, Morocco, May 10-13, 2009.
[8] R. M. Corless, G. H. Gonnet, D. E. G. Hare, D.J. Jeffrey and D. E. Knuth, On Lambert0s W function, Adv. Comput. Math, 5, 329-359, 1996.
[9] A. Ortiz-conde, F. J. Garcia Sanchez, J. Muci, New Method to Extract the Model Parameters of Solar Cells from the Explicit Analytic Solution of their Illuminated I-V Characteristics, Solar Energy Materials &amp; Solar Cells, 90, 352-361, 2006.
[10] J. Ding, R. Radhakrishnan, A New Method to Determine the Optimum Load of a Real Solar Cell Using the Lambert W-Function, Solar Energy Materials &amp; Solar Cells, 92, 1566-1569, 2008.</Text-field>
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