An `AC` source of angular frequency `omega` is fed across a resistor `R` and a capacitor `C` in series. The current registered is `I`. If now the frequency of source is changed to `omega//3` (but maintaining the same voltage), the current in the circuit is found to be halved. The ratio of reactance to resistance at the original frequency `omega` will be.

Options

A. `sqrt((3)/(5))`
B. `sqrt((2)/(5))`
C. `sqrt((1)/(5))`
D. `sqrt((4)/(5))`

Answer

A

Explanation

`I = (V)/(sqrt(R^(2) + (1)/(omega^(2)C^(2)))) = (V)/(sqrt(R^(2) + X_(C)^(2))) …(1)`
`1//2 = (V)/(sqrt(R^(2) + (9)/(omega^(2)C^(2)))) = (V)/(sqrt(R^(2) + (9X_(C)^(2)))) …(2)`