(a) Determine the value of phase difference between the current and the voltage in the given series LCR circuit. (b) Calculate the value of the additional capacitor which may be joined suitably to the capacitor C that would make the power factor of the circuit unity.

(a)The phase difference between current and voltage φ is given by
tanφ = (XL - XC)/R
XC = 1/ωC = 500Ω
XL = ωL = 100Ω
R = 400Ω
Thus tanφ = (100 - 500)/400 = -1 ⇒ φ = -45°
(b) Power factor is given by cosφ = 1 ⇒ φ = 0° ⇒ tanφ = 0
⇒ XC = XL = 100Ω
⇒ C = 10µF
Hence an 8µF capacitor needs to be connected in parallel with the given capacitor.