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Capacitance and RC circuit

  1. Feb 19, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider a series RC circuit with R = 151 Ω and an unknown capacitor C as shown below.


    http://www.flickr.com/photos/67342906@N0… [Broken]


    The circuit is driven by an alternating electromotive force with εRMS = 174 V at a frequency of f = 7.70 Hz. The current in the circuit is IRMS = 0.310 A. Calculate the capacitance C.

    2. Relevant equations

    (1) I(rms)=V(source) / ( R+ (1/C))
    (2) I(rms)=C x V(source) / ( 1+ RC)

    3. The attempt at a solution

    tried to plug them into equation (1) to get C but it didn't work

    0.31 =174 / (151+ 1/C )

    C=0.00244 F
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Feb 19, 2013 #2
  4. Feb 19, 2013 #3

    gneill

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    Staff: Mentor

    Your Relevant Equations are not correct in that they are not handling the summation of resistance (of the resistor) and reactance (of the capacitor) properly; they should add in quadrature (square root of sum of squares, just like vector components). Also, the reactance should depend upon the frequency of the driving signal, which in this case is given as 7.70 Hz.
     
    Last edited by a moderator: May 6, 2017
  5. Feb 19, 2013 #4
    So

    Irms = sqrt( R^2 + (1/2(pi)fC)^2)
     
  6. Feb 19, 2013 #5

    gneill

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    Staff: Mentor

    Now you're missing the electric potential :smile: Remember you're writing Ohm's law, so I = E/Z, where here Z is the sum of resistance and reactance as you've calculated above.
     
  7. Feb 19, 2013 #6
    So

    Erms/Irms = sqrt( R^2 + (1/2(pi)fC)^2)
     
  8. Feb 20, 2013 #7

    gneill

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    Staff: Mentor

    Yes. Solve for C.
     
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