14, A series RLC circuit with R-100 ?, L-0.5 H, and C-5x105 F, is connected to a

Question

14, A series RLC circuit with R-100 ?, L-0.5 H, and C-5x105 F, is connected to an AC voltage source. The frequency of the AC source is 60 Hz and its maximum voltage AVmax is 170 V. (a) Calculate the impedance Z. (4 points) (b) Calculate the rms (root-mean-square) current in the circuit. (4 points) (c) Calculate the maximum voltage across the resistor. (4 points) (d) If the frequency of the AC source is changed, what must the new frequency be so that the circuit is in resonance? What is the rms current when the circuit is in resonance? (4 poi

Explanation / Answer

a)

Inductive reactance

XL=2pifL=2pi*60*0.5 =188.5 ohms

Capacitive reactance

XC=1/2pifC =1/2pi*60*(5*10-5)=53.05 ohms

Impedance is

Z=sqrt[R2+(XL-XC)2]=sqrt[1002+(188.5-53.05)2]

Z=168.36 ohms

b)

rms current

Irms=Vrms/Z =(170/sqrt(2))/168.36

Irms=0.714 A

c)

Maximum current

Imax=sqrt(2)*0.714=1.01 A

Maximum voltage across resistor

VR=1.01*100=100.1 V

d)

Resonance frequency

fr =1/2pisqrt(LC) =1/2pisqrt(0.5*5*10-5)

fr =31.83 Hz

Rms Current at resonance

Irms =(170/sqrt(2))/100 =1.202 A

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