An RLC circuit with R = 28.1 Ohm, L = 362 mH, and C = 48.0 mu F is connected to
ID: 1648980 • Letter: A
Question
An RLC circuit with R = 28.1 Ohm, L = 362 mH, and C = 48.0 mu F is connected to an ac generator with an rms voltage of 28 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
part A:
when the frequency is equal to resonance frequency, then total impedance =resistance =R=28.1 ohms
average power delivered=rms voltage^2/resistance
=28^2/28.1
=27.9 W
part B:
resonant angular frequency=1/sqrt(L*C)
=239.8972 rad/s
give frequency is double the resonant frequency.
then angular frequency=w=2*239.8972=479.7944 rad/s
then capacitive reactance=Xc=1/(w*C)=43.4124 ohms
inductive reactance=Xl=w*L=173.6856 ohms
then total impedance=Z=R+j*(Xl-Xc)=28.1 + j130.2642 ohms
magnitude of Z=sqrt(28.1^2+130.2642^2)=133.2605 ohms
rms current magnitude=rms voltage/magnitude of Z=28/133.2605=0.21 A
then power delivered=rms current^2*resistance
=0.21^2*28.1= 1.2392 W
part C:
when freqeuncy is half the resonant frequency, frequency=239.8972/2=119.9486 rad/s
then capacitive reactance=Xc=1/(w*C)=173.6855 ohms
inductive reactance=Xl=w*L=43.4214 ohms
then total impedance=Z=R+j*(Xl-Xc)=28.1 - j130.2641 ohms
magnitude of Z=sqrt(28.1^2+130.2641^2)=133.2605 ohms
rms current magnitude=rms voltage/magnitude of Z=28/133.2605=0.21 A
then power delivered=rms current^2*resistance
=0.21^2*28.1= 1.2392 W
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