An L-C-R series circuit with R = 100`Omega` is connected to a 200 V, 50 Hz A.C. source when only the capacitance is removed, the current lags the voltage by `60^@`. When only the inductance is removed, the current leads the voltage by `60^@`. Find the current in the circuit.

Options

A. `4 A`
B. `2 A`
C. `6 A`
D. `8 A`

Answer

B

Explanation

Removing capacitor, L - R circuit is prepared where phase difference `delta=60^@`
`therefore` tan `60^@ =X_L/R=sqrt3 rArr X_L=sqrt3R`….(1)
Removing inductor C-R circuit is prepared where phase difference `|delta|=60^@`
`therefore tan 60^@ = X_C/R = sqrt3 rArr X_C=sqrt3R`....(2)
From (1) and (2) `X_L = X_C rArr omegaL=1/(omegaC)`
means resonance circuit is prepared
`therefore Z=R rArr I_(rms) = V_(rms)/R`
`=200/100`=2A