Current dependent on Voltage

  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

    [tex]P=IV[/tex]

    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. nicksauce

    nicksauce 1,275
    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...
     
  4. berkeman

    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. Redbelly98

    Redbelly98 12,017
    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.
     
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