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((5)/(3))`
C. `(3)/(5)`
D. `(5)/(3)`

Answer

1

Explanation

at frequency `omega, X_(C ) = 1//omega C`
frequency `omega//3, X'_(C ) = (3)/(omega C) = 3 X_(C )`
`I = (V)/(sqrt(R^(2) + X_(C )^(2))) , I/(2) = (V)/(sqrt(R^(2) + 9 X_(C )^(2))) , (X_(C ))/(R ) = sqrt((3)/(5))`