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. Calculate the ratio of the reactance to resistance at the original frequency `omega`.

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)/(omegaC))^(2)))`
or `I = (V)/(sqrt(R^(2) + (1)/(omega^(2)C^(2))))` "...(i)
and `(I)/(2) = (V)/(sqrt(R^(2) + (omega^(2)C^(2))/(9))`....(ii)On simplifying above equations, we get
`(X_(L))/(R) = (omegaL)/(R) = sqrt((3)/(5))`