In the figure shown `R = 100 Omega L = (2)/(pi) H` and `C = (8)/(pi) mu F` are connected in series with a.c source of 200 volt and frequency `'f'`. `V_(1)` and `V_(2)` are two hot-wire voltmeters. If the readings of `V_(1)` and `V_(2)` are same then:

Options

A. `f=125Hz, (v_(1))/(v_(2))=1`
B. `f=250 pi Hz, (v_(1))/(v_(2))=1`
C. current through R is 1A, `(v_(1))/(v_(2))=1`
D. current through R is `2A,(v_(1))/(v_(2))=2`

Answer

A

Explanation

`V_(1)=V_(2)rArr x_(L)=x_(c)`
`rArr f=1/(2pisqrt(LC)) =125 Hz`
`I_(0)=(v_(0))/R =200/100 ( :' X=0 :. Z=R)`
=2A
`V_(1)=V_(2)=IX_(L) =I.(omegaL)=2xx2pixx125xx2//pi`
=100 volt
=1000 volt