In the circuit shown, `R` is a pure resistor, `L` is an inductor of negligible resistance (as compared to `R`) and `S` is a`100V,50 Hz AC` source of negligible resistance. With eigther key `k_(1)` alone or `k_(2)` alone closed, the current is `I_(0)`. if the source is changed to `100 V, 100 Hz`, the current with `k_(1)` alone closed and with `k_(2)` alone closed will be respectively

Options

A. `I, (1)/(2)`
B. `I, 2 I`
C. `2 I, I`
D. `2 I, (1)/(2)`

Answer

A

Explanation

In first case , `X_(L) = omegaL = 2 pi xx 50 L = 10 pi L`
In second case `X'_(L) = omega'L =2 pi xx 100 L = 200 piL = 2X_(L)`
`i_(L) = (100)/(X_(L)) =I, I'_(L) = (100)/(X'_(L)) = (100)/(2X_(L)) = (1)/(2) `
`In R current remains same .