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`
B. `f=250 p Hz`
C. current through R is `2A`
D. `V_(1)=V_(2)=1000V`

Answer

A, C, D

Explanation

`V_(1)=V_(2)implies XL=XC`
`implies f=(1)/(2 pi sqrt(LC))=125 Hz`
`I_(rms)=(V)/(R)=(200)/(100)=2A` `( :. Z=R)`
`V_(1)=V_(2)= IXL = L(omega L)=1000` volt.