# Current dependent on Voltage

## 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!

## Answers and Replies

nicksauce
Science Advisor
Homework Helper
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
Mentor
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
Staff Emeritus
Science Advisor
Homework Helper
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.