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 = 125 Hz`
B. `f = 250 Hz`
C. Current through `R` is `2A`
D. `V_(1) = V_(2) = 1000` volt

Answer

A,C,D

Explanation

`v_(1) = v_(2) implies x_(L) = x_(c )`
`implies f = (1)/(2pi sqrt(LC)) = 125 Hz`
`I_(0) = (v_(0))/(R ) = (200)/(100) = 2A`
`v_(1) = v_(2) = IX_(L) = L (omega L) = IL. (1)/(LC)`
`= 1 sqrt((L)/(C )) = 2 sqrt(((2 // pi))/((8 xx 10^(-6) // pi))) = 1000` volt