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Series RC circuit

  1. May 6, 2017 #1
    1. The problem statement, all variables and given/known data

    Three lamps are rated 110 V, 60 W. They are connected in parallel and a capacitor is connected in series with the group. The circuit is then connected to a 230 V 50 Hz power supply. Detremine:

    a) The capacitance which is required to provide the correct voltage across the lamps.
    b) The active and reactive currents.

    2. Relevant equations

    ##P = 60 W, U_S = 230 V, U_R = 110 V, f = 50 Hz##

    ##C = \frac {1} {2 \pi f X_C}##

    3. The attempt at a solution

    Part a)

    ##U_C = \sqrt {230^2 - 110^2} = 202 V##

    ##I = \frac {3P} {U_R} = \frac {3*60} {110} = 1.63 A##

    ##X_C = \frac {U_C} {I} = \frac {202} {1.63} = 124 \Omega##

    ##C = \frac {1} {2 \pi f X_C} = \frac {1} {2*110*50 \pi} = 25.7 \mu F##

    Part b)

    ##\phi = \cos^{-1} (\frac {U_R} {U_S}) = \cos^{-1} (\frac {110} {230}) = 61.4^{\circ}##

    ##I_C = I \sin (\phi) = 1.63 \sin (61.4) = 1.42 A##

    ##I_R = I \cos (\phi) = 1.63 \cos (61.4) = 0.79 A##

    I'm pretty confident this is correct but really my question is: is there a way of answering part b without working out the phase difference?
     
  2. jcsd
  3. May 6, 2017 #2

    gneill

    User Avatar

    Staff: Mentor

    You could do the computation using impedance (complex arithmetic). Then it's just Ohm's law to find the circuit's current.
     
  4. May 6, 2017 #3
    Thanks for the help.
     
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