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Homework Help: Current in AC Generator

  1. Feb 21, 2007 #1
    1. The problem statement, all variables and given/known data

    An ac generator with a frequency of F=25 Hz and an rms voltage of 15 V is connected to a C=32 µF capacitor. Assume that the generator produces a sinusoidal waveform.

    (a) What is the maximum current in the circuit? mA

    (b) What is the current in the circuit when the voltage across the capacitor is 7.5 V and increasing?
    (c) What is the current in the circuit when the voltage across the capacitor is 7.5 V and decreasing?

    2. Relevant equations

    Irms= Vrms*Xc

    Irms= [1/(2)^(1/2)]* Imax







    3. The attempt at a solution

    part (a): already figured it out using Irms= Vrms*Xc and got the answer of 106.629 mA, which is correct.

    part (b) and (c): I tried using the Irms= Vrms*Xc equation and plugging in 7.5 Volts as V and solving for I, since I already have Xc which is just 1/(angular freq. * Capacitance)
     
  2. jcsd
  3. Feb 21, 2007 #2
    What again is ohms law?
     
  4. Feb 21, 2007 #3
    Ohm's Law is V=IR

    The equation I was using above (Irms= Vrms*Xc ), is analagous to Ohm's law (well, according to my textbook), just rearranged.

    *Edit*

    I meant to type Irms= Vrms/Xc, not multiplied in my previous 2 posts.
     
  5. Feb 21, 2007 #4
    Ah, okay its [tex]V = I X[/tex]. units look okay now
    But what again is X and how might I calculate it?

    *edit*
    sorry, i see you got it, those formulae disturb me though:biggrin:
     
    Last edited: Feb 21, 2007
  6. Feb 21, 2007 #5
    I solved the equation!

    X is just 1/(2*pi*frequency*capacitance).

    To figure the problem out, I used the equation to find the instanteous voltage on a capacitator:

    V=Vmax*sin(theta-90degrees).

    To find theta, I just found the Vmax by using the Vrms (15V) and multiplying it by 2^(0.5). Then, I plugged in for the equation:

    7.5=Vmax*sin(theta) and solved for theta.

    Then, I took theta and plugged it in to

    Current=Current (max) *sin (theta)
     
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