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 the source is changed to `omega/3` ( but maintaining the same voltage ) , then current in the circuit is found to be halved . Calculate the ratio of reactance to resistance at the original frequency `omega`.

Options

A. `sqrt(3/(5)`
B. `sqrt(5)/(3)`
C. 3//5
D. `sqrtR`

Answer

A

Explanation

According to given problem,`i=(V)/(Z)=V//[R^(2)+(1//Comega^(2))]^(1//2)`ldots(1)`
and`(1)/(2)=(V)/[[R^(2)+(3)//(Comega^(2))]^(1//2))` Idots(2),
substituting the value of Ifrom equation (1) in (2),`4(R^(2)+(1)/(C^(2)omega^(2)))=R^(2)+(9)/(C^(2)omega^(2))`i.e.,`(1)/(C^(2)omega^(2))=(3)/(5)R^(2)`
sothat`(X)/(R)=((1//Comega))/(R)=[(3//5)R^(2)]^(1//2)/(R)=sqrt(3)/(5)`