What is the Maximum Energy a Solar Cell Can Deliver Per Year?

[jae05]

Homework Statement

A solar cell has a current–voltage characteristic given by $$I=I_0\cos\(\frac{\pi V}{2V_0}\)$$ where $$I_0$$ and $$V_0$$ are given constants. If the sun shines 12 out of 24 hours what is the maximum energy that can the cell can deliver to a load per year?

Homework Equations

$$P=IV$$

The Attempt at a Solution

Somehow I get the feeling this is incredibly simple and I'm just missing something. But anyhow, using $$P=IV$$ I get $$P=I_0\cos\(\frac{\pi V}{2V_0}\)V$$. Then taking $$\frac{dP}{dV}$$ to find a maximum, I get $$\tan z = z^{-1}$$ where $$z=\frac{\pi V}{2V_0}$$. Am I on the right track? Or am I missing something. Thanks!

 

[nicksauce]

Your approach looks correct... however the question seems strange. The power can be made arbitrarily high by making the voltage arbitrarily high and keeping the cosine term in phase... so I am confused...

 

[berkeman]

Your approach looks correct... however the question seems strange. The power can be made arbitrarily high by making the voltage arbitrarily high and keeping the cosine term in phase... so I am confused...

I agree the problem is confusing, but as V increases, I decreases, according to the given equation.

cos(0) = 1, cos(PI/4) = 1/SQRT(2), cos(PI/2) = 0

So you would want to find the angle where you get the greates product P = VI, and use that to calculate what the total cumulative energy is over a year (looks like they are assuming sun-tracking mounts for the solar cells).

 

[Redbelly98]

We are to assume that the angle of the cell w.r.t. the sun is maintained so that the given i-v characteristic is always true during daylight. The load on the cell can be adjusted in order to get the current and voltage that results in maximum power.