# Decrease of internal resistance of a solar cell while increasing the load resistor?

Imagine to model a solar cell as a power supply $V_p$ in series with an internal resistance $R_p$. This solar cell is connected to a variable load resistance $R_{load}$.

Suppose that I keep the solar cell at fixed distance from a fixed light source (say, a light bulb). The power incident on the solar cell should be a constant, as the distance or the source do not change.

Now I change the value of $R_{load}$ many times and everytime I measure the current $I$ flowing in $R_{load}$ and the voltage across load, $V_{load}$.

Before taking all the measurements I measure, one time only (as it should be a constant), the voltage across the cell once i disconnected the load $V_{open \, circuit}$: that should be $V_p$ and it should not change, as said.

I tried all this procedure experimentally but I noticed one strange thing: Everytime I calculated $R_p$ as $$R_p=\frac{V_{open \, circuit}-V_{load}}{I}$$ and I noticed that $R_p$ changed while $R_{load}$ was being varied! $R_p$ decreased as $R_{load}$ increased!

Is there an explanation for that?

The most strange thing is that, since we are at constant distance and source $P_{incident}$ is constant and we have $P_{produced}=\frac{V^2_p}{R_p}=\eta P_{incident}$, where $\eta$ is the efficiency: if both $\eta$ and $V_p$ are constant, $R_p$ should be a constant too!!

Therefore, is it wrong to assume that $V_p$ is a constant? Or maybe is just $\eta$ changing?

• What range of load resistance did you measure? Mar 5, 2017 at 4:08

• Thanks a lot for the answer! If I may ask: since $R_{p}$ varies with $R_{load}$, I cannot use maximum power transfer theorem to say that $P_{load}$ is max for $R_{load}=R_{p}$ (the equality does not make sense). I tried to plot measured $P_{load}$ vs $R_{load}$ and indeed the maximum is near the resistance $R_{p}$ calculated when $R_{load}$ was $0 \, \Omega$ but it's not exactly there. So is there a relation that describes for what $R_{load}$ I have the maximum $P_{load}$? Is it necessary to know the function $R_{p}=f(R_{load})$ (assuming that such function exists)? Mar 6, 2017 at 0:04