A series R-C combination is connected to an AC voltage of angular frequency `omega=500` radian/s. If the impedance of the R-C circuit is `R sqrt(1.25)`, the time constant (in millisecond) of the circuit is

Answer

4

Explanation

`omega=500 rad s^(-1)`
`Z=sqrt((1)/(omega C)^(2)+R^(2)) = Rsqrt(1.25)`
`(1)/(omega C)^(2)+R^(2)=R^(2)(1.25) implies ((1)/(omega C))^(2) =(R^(2))/(4)`
`implies CR=2/(omega)=(2)/(500) xx (10^3) ms = 4 ms`.