An R L C circuit with R = 25.6 , L = 361 mH , and C = 48.9 F is connected to an
ID: 1648249 • Letter: A
Question
An RLC circuit with R = 25.6 , L = 361 mH , and C= 48.9 F is connected to an ac generator with an rms voltage of 26 V .
A.) 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.
B.)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.
C.)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
P = Vrms^2/Z
Pavg = P/2
Z = sqrt (R^2 + (XL - Xc)^2)
1.
at resonance frequency
Z = R
P = 26^2/25.6 = 26.41 W
Pavg = P/2 = 13.205 W
2.
resonance frequency will be
fr = 1/(2*pi*sqrt (LC))
fr = 1/(2*pi*sqrt (361*10^-3*48.9*10^-6))
fr = 37.88 Hz
f1 = 2*fr = 75.76 Hz
XL = w*L = 2*pi*f*L = 2*pi*75.76*361*10^-3 = 171.84 ohm
Xc = 1/wC = 1/(2*pi*f*C) = 1/(2*pi*75.76*48.9*10^-6) = 42.96 ohm
Z = sqrt (25.6^2 + (171.84 - 42.96)^2) = 131.40 ohm
P = 26^2/131.40 = 5.14 W
Pavg = P/2 = 2.57 W
C.
f2 = fr/2 = 37.88/2 = 18.94 Hz
XL = w*L = 2*pi*f*L = 2*pi*18.94*361*10^-3 = 42.96 ohm
Xc = 1/wC = 1/(2*pi*f*C) = 1/(2*pi*18.94*48.9*10^-6) = 171.84 ohm
Z = sqrt (25.6^2 + (42.96 - 171.84)^2) = 131.40 ohm
P = 26^2/131.40 = 5.14 W
Pavg = P/2 = 2.57 W