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Homework Help: Complex voltage across a capacitor

  1. Jul 11, 2009 #1
    1. The problem statement, all variables and given/known data
    I'm given the power for a capacitor. I know the voltage across the capacitor has a complex component. How do I find the value of the capacitor?

    Power (purely reactive) = -50000j VA
    Voltage = 200 + 100j V @ 60 Hz

    2. Relevant equations
    Power = (V*V) / Z
    Impedance of a capacitor = -j / (2*pi*f*C)

    3. The attempt at a solution
    (200 + 100j)^2 / Z = -50000j
    (30000+40000j) / -50000j = Z
    -j / (2*pi*f*C) = (0.8 - 0.6j)
    -j / (0.8 - 0.6j) = 2*pi*f*C

    C -> complex?

    I get a complex component in the value of C
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jul 11, 2009 #2
    The voltage and capacitor current are not orthogonal. I think its strange though that the voltage was defined with a non-zero phase... compared to what?? Either that cap has some internal resistance, or there's a mistake in the givens, or you are suppose to assume the stated phase of the applied voltage is a phase from some other unrelated signal (but the cap phase given is NOT relative to that phase!), and therefore normalize the applied voltage to zero phase (which would mean its a bad question, IMO). I wouldn't feel comfortable assuming any of those unless your teacher wants you to notice the cap has internal resistance and has intentionally defined zero-phase as 90 degrees from the current's phase--which is a rather weird thing to do. But then if the teacher specified the cap is "purely reactive" with no real component, yet defined the applied voltage as having a non-zero phase, then its time to ask your teacher what the heck he meant.
    Last edited: Jul 11, 2009
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