An RLC Circuit with R = 29.1 ohm , L = 343mH , and C = 42.4 mu F is connected to

Question

An RLC Circuit with R = 29.1 ohm , L = 343mH , and C = 42.4 mu F is connected to an ac generator with an rms voltage of 26 V. Determine the average power delivered to this circuit when the frequency of the generator is equal to the resonance frequency. Express your answer using two significant figures. Determine the average power delivered to this circuit when the frequency of the generator is twice the resonance frequency. Express your answer using two significant figures. Determine the average power delivered to this circuit when the frequency of the generator is half the resonance frequency. Express your answer using two significant figures.

Explanation / Answer

a)

Z = R = 29.1 ohm

P = (Vrms)2/Z = 26*26/29.1 = 23.2 W

b)

fo = 1/2LC = 1/2/3.1416/(343e-3*42.4e-6) = 41.7339 Hz

f = 2*fo = 2 * 41.7339 = 83.4678 Hz

XL = 2*3.1416*83.4678*343e-3 = 179.88 ohm

XC = 1/(2*3.1416*83.4678*42.4e-6) = 44.9712 ohm

Z = (29.1*29.1+(179.88-44.9712)*(179.88-44.9712)) = 138.012 ohm

P = (Vrms)2/Z = 26*26/138.012 = 4.90 W

c)

fo = 1/2LC = 1/2/3.1416/(343e-3*42.4e-6) = 41.7339 Hz

f = fo/2 = 41.7339/2 = 20.867 Hz

XL = 2*3.1416* 20.867*343e-3 = 44.9712 ohm

XC = 1/(2*3.1416* 20.867*42.4e-6) = 179.88 ohm

Z = (29.1*29.1+(179.88-44.9712)*(179.88-44.9712)) = 138.012 ohm

P = (Vrms)2/Z = 26*26/138.012 = 4.90 W

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