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Rms current in circuit with capacitor resistor and rms output

  1. Nov 15, 2010 #1
    1. The problem statement, all variables and given/known data

    A 39.5 uF capacitor is connected to a 47.0 ohm resistor and a generator whose rms output is 25.2 V at 60.0 Hz. Calculate the rms current in the circuit.
    (also asks for voltage drop across resistor, capacitor and the phase angle for the circuit, but I mostly want to get the first one first)

    2. Relevant equations

    I=current, V=voltage, R=resistance, f=frequency

    Irms=1/sqrt(2)*Imax
    Irms=delta Vc, rms/Xc
    Xc=1/(2pi*f*c)
    delta Vc,rms=Irms*Xc

    and then I start going in circles

    Other formulas that might be appropriate:
    Vmax=Imax*Z
    Z=sqrt(R^2+(Xl-Xc)^2)
    Xl=2pi*f*L
    L=?? not given in this problem
    Power average=Irms^2*R

    3. The attempt at a solution
    combining lots of these formulas trying to come up with the correct Vrms has proven unsuccessful. I came up with 17.819 A, .37515 A, .21739 A, none of which were right. None of them were successful and I don't remember or care to explain how I got them precisely because I wasn't confident in those anyway.
    Overall I still haven't been able to link my given information directly to the answer I need
     
  2. jcsd
  3. Nov 15, 2010 #2

    rock.freak667

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    Homework Helper

    Formulate the expression for Z, then you know that I = V/Z.
     
  4. Nov 15, 2010 #3
    but what do I use for L while setting it up for Z? I don't have it directly in the given information and I don't think I can derive it. Should I just use a default value like 1 or 0?

    ps thanks for a response :D
     
  5. Nov 15, 2010 #4

    collinsmark

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    Gold Member

    Calculate the impedance Z of the RC network.

    [tex] Z = R + \frac{1}{j \omega C} [/tex]

    (true for this particular problem)

    [tex] Z = R +j \left( \frac{-1}{\omega C} \right)[/tex]

    For this problem, the resistance is R, and the reactance is -1/(ωC).

    In general,

    [tex] Z = \Re \{ Z \} + j \Im \{ Z \} [/tex]

    Use the Pythagorean Theorem to find the magnitude of Z.

    [tex] |Z| = \sqrt{\left( \Re \{ Z \} \right)^2 + \left( \Im \{ Z \} \right)^2} [/tex]

    And finally [the complex version of] Ohms law to find the current.

    [tex] i_{RMS} = \frac{v_{RMS}}{|Z|} [/tex]
     
  6. Nov 15, 2010 #5
    What is j for those equations?
     
  7. Nov 16, 2010 #6

    collinsmark

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    Here I used the symbol j to represent [itex] \sqrt{-1}[/itex]. This is common in electrical engineering courses, since the symbol i is already taken, representing current.
     
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