# 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 $$\R_{load}\$$ many times and every time I measure the current $$\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: Every time 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