$1.$ Considere a solar module with $36$ cells. Each cell has an area of $100$ cm$2$ with a reverese saturation current of $1$ x $109$ mA$/$cm$2.$ Under full sunlight illmuniation, each cell has a short$-$circuit current of $45$ mA$/$cm$2$ at $25$C$.$ The cells are connected in series with one another within the module. Recall that in an ideal solution, the cells of this solar module can be thought of as a current source driven by sunlight in conjunction with a diode. In this case, these cells have an I$-$V curve that can be represented by the equation below:

$($a$)$ What is the total VOC of a given cell within this module, under ideal conditions?

$($b$)$ In non$-$ideal situations, a parallel leakage resistance $($Rp$)$ is usually added, so that the current of the cell can be given by the modified equation below. What parallel resistance would be necessary to experience losses of less than $1\%?$