Question

A solar cell generates a potential difference of 0.320 V when a 445.0 ? resistor is connected across it and a potential difference of 0.504 V when a 945.0 ? resistor is substituted.

A) What is the internal resistance of the cell in Ohms?

B) What is the emf of the cell?

C) The area of the cell is 27.0 cm² and the rate per unit area at which it receives light energy is 58.0 mW/ cm². What is the efficiency of the cell for converting light energy to thermal energy in the 945.0 ? external resistor?

Answer 1

Here's one way to set it up.

Assume the cell has a constant voltage supply of V in it, with a resistor in series of R. This R represents the internal resistance.

If you sketch out the first situation, you'll see that the current through the 500 ohm resistor, by Ohm's law, is 0.320/500 . This is the same current as V/(R+500), so

V/(R+500) = 0.320/500

or

V = (0.320/500)(R+500)

You can derive a similar equation for the 1000-ohm resistor, and since in both cases, V is supposed to be the same, you can set the two equations equal to each other and solve for R, the internal resistance.

Once you have that, you can plug back into either equation to get V, the open-circuit emf.

(By the way, this is not a very good model of how actual crystalline silicon solar cells work. But I digress.)

For the third problem, remember that the power dissipated by a resistor is current * voltage (VI), or I^2*R, or V^2/R. All give the same answer.