Question
(i) Find the value of the phase difference between the current and the voltage in the series LCR circuit shown below. Which one leads in phase: current or voltage?
(ii) Without making any other change, find the value of the additional capacitor C, to be connected in parallel with the capacitor C, in order to make the power factor of the circuit unity.
Solution
Given V = Vosin (1000 +Φ)
ω = 1000s-1
L = 100 mH
C =2μF
R = 400Ω
Phase difference 
XL = ωL = 1000 x100 x10-3 = 100Ω
=
(ii) For power factor to be unity, R = Z
or XL = XC
For two capacitance in parallel, resultant capacitance C'=C + C1
10-5 = 0.2 x 10-5 + C1
⇒ C1 = 8μF
