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Homework Help: Current dependent on Voltage

  1. Jun 9, 2008 #1
    1. The problem statement, all variables and given/known data

    A solar cell has a current–voltage characteristic given by [tex]I=I_0\cos\(\frac{\pi V}{2V_0}\)[/tex] where [tex]I_0[/tex] and [tex]V_0[/tex] 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?

    2. Relevant equations


    3. The attempt at a solution

    Somehow I get the feeling this is incredibly simple and i'm just missing something. But anyhow, using [tex]P=IV[/tex] I get [tex]P=I_0\cos\(\frac{\pi V}{2V_0}\)V[/tex]. Then taking [tex]\frac{dP}{dV}[/tex] to find a maximum, I get [tex]\tan z = z^{-1}[/tex] where [tex]z=\frac{\pi V}{2V_0}[/tex]. Am I on the right track? Or am I missing something. Thanks!
  2. jcsd
  3. Jun 9, 2008 #2


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    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...
  4. Jun 9, 2008 #3


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    Staff: Mentor

    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).
  5. Jun 9, 2008 #4


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    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.
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