$4.$ The GEPV$-030-$M photovoltaic module consists of $36$ cells wired in series, and has performance characteristics as listed below under standard test conditions at $\backslash (1000\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash )$ irradiance. The equivalent circuit for each photovoltaic cell has a parallel resistance $\backslash (\backslash$mathrm$\{$R$\}\_\{\backslash$mathrm$\{$p$\}\}=10\backslash$Omega $\backslash ),$ and a reverse saturation current $\backslash (\backslash$mathrm$\{$I$\}\_\{0\}=10^\{-9\}\backslash$mathrm$\{$~A$\}\backslash ).$

a$.$ Find the current $($A$)$ delivered when the junction voltage of each cell is $0\mathrm{.}5$ V $.$

b$.$ How many modules are required to provide $100$ volts and $900$ W at the rated conditions?

c$.$ What arrangement of the modules in series and in parallel is needed to achieve the desired voltage and power?

d$.$ What is the fill factor for the module?