# IV relation changing load resistor of a solar cell

Consider the configuration in picture, where a solar cell is kept at fixed distance from a light source and the load resistance is changed among different values. simulate this circuit – Schematic created using CircuitLab

What mathematical relation is there between current and voltage while Rv is changed?

Since the solar cell is at constant distance from source I expect constant open circuit voltage of the cell $V_{op}$, therefore it should be

$$IV=P_{load}=\frac{V_{op}^2}{(R_v+R_i)^2} R_v\tag{1}$$

But also, at the same time, $$I=\frac{V}{R_v}\tag{2}$$

So will the current-voltage curve be the intersection of these two curves?

I found on many sites that the current voltage characteristic of a cell is a curve like the one in picture.

Is the blue curve what I would find also in the situation I described? That is, are the blue curve points given by the intersections of $(1)$ and $(2)$ (for different values of $R_v$)?

Or is the blue curve in picture given by different mathematical relations? If so, what is this relation?

• I do not totally get what you mean, however you should take the non linear behavior of solar cells in consideration. The current-to-voltage relation is similar to a diode. – auoa Feb 27 '17 at 19:12

Do you think there is any relationship between Voc/Isc=Ra ( some value Ra) and ESR at MPT? 