An R L C circuit with R = 21.8 ? , L = 364 mH , and C = 40.1 ? F is connected to

Question

An RLC circuit with R = 21.8 ? , L = 364 mH , and C = 40.1 ?F is connected to an ac generator with an rms voltage of 21 V .

Item 1 Part A An RLC circuit with R = 21.8 ·L-364 mH and C 40.1 F is connected to an ac generator with an rms voltage of 21 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. Submit My Answers Give Up Part 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. Submit My Answers Give Up Part 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. Submit My Answers Give Up

Explanation / Answer

A)Average power delivered to the ckt, Pavg = Vrms^2/R

= 21^2/21.8

= 20.23 Watts

B)
resosnant frquency, fo = 1/(2*pi*sqrt(L*C))

= 1/(2*pi*sqrt(0.364*40.1*10^-6))

= 41.66 Hz

at f = 2*fo = 2*41.66 = 83.32 Hz

inductive reactance, XL = 2*pi*f*L = 2*pi*83.32*0.364 = 190.56 ohms

Capacitive reactance, XC = 1/(2*pi*f*C) = 1/(2*pi*83.32*40.1*10^-6) = 47.64 ohms

imedance of the ckt, z = sqrt(R^2 + (XL - XC)^2)

= sqrt(21.8^2 + (190.56 - 47.64)^2)

= 144.57 ohms

Irms = Vrms/z

= 21/144.57

= 0.145 A

power delivered to the ckt, Pavg = Irms*R

= 0.145*21.8

= 3.17 W

c) at f = fo/2 = 41.66/2 = 20.83 Hz

inductive reactance, XL = 2*pi*f*L = 2*pi*20.83*0.364 = 47.64 ohms

Capacitive reactance, XC = 1/(2*pi*f*C) = 1/(2*pi*20.83*40.1*10^-6) = 190.54 ohms

imedance of the ckt, z = sqrt(R^2 + (XL - XC)^2)

= sqrt(21.8^2 + ( 47.64 - 190.56)^2)

= 144.57 ohms

Irms = Vrms/z

= 21/144.57

= 0.145 A

power delivered to the ckt, Pavg = Irms*R

= 0.145*21.8

= 3.17 W

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