A series RLC circuit consists of an 12.00-? resistor, a 5.00-?F capacitor, and a

Question

A series RLC circuit consists of an 12.00-? resistor, a 5.00-?F capacitor, and a 41.0-mH inductor. A variable-frequency source applies an emf of 428 V (rms) across the combination. Assuming the frequency is equal to one-half the resonance frequency, determine the power delivered to the circuit.

Problem 33.75 Serway and Jewett A series RLC circuit consists of an 12.00-32 resistor, a 5.00-uF capacitor, and a 41.0-mH inductor. A variable-frequency source applies an emf of 428 V (rms) across the combination. Assuming the frequency is equal to one-half the resonance frequency, determine the power delivered to the circuit. Answer 1343.385 W Check

Explanation / Answer

R = 12 Ohm

C = 5.0 uF = 5 * 10^-6 F

L = 41 mH = 41 * 10^-3 H

resonant frequency
w = 1/2 * 1/sqrt(LC) = 1 / (2 * sqrt(LC))

w= 1/(2 * sqrt( 5*41*10^-9) ) = 1104 rad / s

P = I^2 * R = IV

P= V^2 / R

Because the voltage used in P is the voltage across the resistor, we'll use P = I^2 * R so that we wont need to find the V across resistor.

Irms = Erms / Z

Z = sqrt(R^2 + (wL - 1/(wC))^2

= sqrt(12^2 + (1104*0.041 - 1/(1104*5*10^-6))^2) = 136.424 Ohm

Irms = 428 / 136.424 =3.138
P = 3.138^2 * 12 = 118.16 W

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