physics

An AC voltage of the form Δv = (100 V) sin(1000t) is applied to a series RLC circuit. Assume the resistance is 400 , the capacitance is 4.60 µF, and the inductance is 0.500 H. Find the average power delivered to the circuit.
W

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  1. v = Vmax*sinWt
    v = 100*sin(1000t)
    Vrms = 0.707 * 100 = 70.7 Volts.

    W = 2pi*F = 1000
    6.28*F = 1000
    F = 159 Hz.

    Xl = W*L = 1000 * 0.5 = 500 Ohms.
    Xc=1/W*C=1/(1000*4.6*10^-6)=-217.4 Ohms

    tan A = (Xl+Xc)/R
    tanA = (500+(-217.4))/400 = 0.7065
    A = 35.2o

    Z = R/cos A = 400/cos35.2 = 489.5 Ohms
    [35.2o].

    Irms = Vrms/Z =
    70.7/489.5[35.2]= 0.1444A[-35.2o]

    P=Irms^2 * R = (0.1444)2 * 400= 8.34 W.

    NOTE: All of the power is consumed in the resistor.

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