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Question

A sinusoidal voltage of peak value 283V and frequency 50Hz is applied to a series LCR circuit in which R=3Ω,L=25.48mH and C=786μF.
Find :
a) Impedance of the circuit
b) The phase difference between the voltage across the source and the current
c) The power factor.

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Solution

Angular frequency of the ac signal w=2πν
w=2π(50)=100π
Capacitive reactance Xc=1wC
Xc=1100π×786×106=4Ω
Inductive reactance XL=wL
XL=100π×(25.48×103)=8Ω
(a) Impedance of the circuit Z=R2+(XLXc)2
Z=32+(84)2=5Ω
(b) Phase difference ϕ=tan1(XLXcR)
Or ϕ=tan1(843)=tan1(43)
ϕ=53.13o
(c) Power factor cosϕ=cos53.13o=0.6

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