Question

Consider a RLC circuit with R = 105 ohms, L = 518 mH, and C = 0.200 microF. This circuit is driven by an AC source with f = 120 Hz, and Vmax = 60.0 V. (a) What is Imax? (b) What is its average power? (c) At what frequency is this circuit in resonance? (d) Calculate (a) and (b) again if the circuit is driven with the resonant frequency and Vmax is unchanged.

Answer 1

impedance of circuit

Z^2 = R^2 + ( XL - Xc) ^2

Z^2 = R^2 + ( 2 pi f L - 1/(2pi f C))^2

Z^2 = 150^2 + ( 2* 3.14* 120* 0.518 - 1/ ( 2* 3.14* 120* 0.2* 10^-6))^2

Z = 6246.256 ohm

max current through circuit

i = V/Z

i = 0.0096 A

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b)

av power

P = V i ( R/Z) = 60* 0.0096* 150 / 6246.256

P = 0.01384 W

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c)

at resonance, circuit acts purely as resistive circuit

i = 60 / 150 = 0.4 A

d)

P = Vi = 60* 0.4 = 24 W

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