An inductance of `(200/pi)` mH, a capacitance of `(10^(-3)/pi)F` and a resistance of 10`Omega` are connected in series with an a.c. source 220 V, 50Hz. Then what is the phase angle of the circuit ?

Options

A. `pi/4` rad
B. `pi/3` rad
C. `pi/2` rad
D. `pi/6` rad

Answer

A

Explanation

Here , f=50 Hz
`L=200/pi` mH
`C=10^(-3)/pi`F
`R=10 Omega`
`rArr X_L =2pifL=2pixx50xx200/pixx10^(-3)`
`=20Omega`
`rArr X_C =1/(2pifC)=1/(2pixx50xx10^(-3)/pi)`
`therefore X_C=10Omega`
`rArr tan theta =(X_L-X_C)/R`
`=(20-10)/10`
`=10/10`
`tan theta =1`
`therefore theta = tan^(-1) (1)`
`therefore theta =pi/4`
Here, `X_L gt X_C` so, current lags behind by voltage by `pi/4` rad .