An R L C series circuit contains an AC source of emf for which Emax = 70.0 V , a

Question

An RLC series circuit contains an AC source of emf for which Emax = 70.0 V , a 4.00- resistor, a 7.00-mH inductor, and an 7.00-F capacitor.

Part A

What is the average rate at which energy is delivered by the source when the circuit is operated at the resonant frequency?

Express your answer with the appropriate units.

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Part B

What is the power factor when the circuit is operated at the resonant frequency?

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Part C

What is the average rate at which energy is delivered by the source when the circuit is operated at 1.00-kHz ?

Express your answer with the appropriate units.

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Part D

What is the power factor when the circuit is operated at 1.00-kHz ?

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no figure given

Explanation / Answer

at resonance condition phase = 0

Pav = Emax*Imax/2

Imax = Emax/R

Pav = Emax^2/2R

Pav = (70^2)/(2*4) = 612.5 W

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part(B)

power factor = cosphi = cos0 = 1

part(c)

XL = wL = 2*pi*f*L = 2*pi*1000*7*10^-3 = 44

Xc = 1/Wc = 1/2*pi*f*c = 1/(2*pi*1000*7*10^-6) = 22.73

tanphi = (XL-Xc)/R

phi = 79.34

Pav = Emax^2*cosphi/2R = 113.7

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part(d)

cosphi = 0.185

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