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

Answer

4

Explanation

Impedance of `R - C` circuit is
`Z = sqrt(R^(2) + ((1)/(omega C))^(2)) :. R sqrt(1.25) = sqrt(R^(2) + ((1)/(omega C))^(2))`
or `R^(2) xx (5)/(4) + ((1)/(omega C))^(2)` or `(R^(2))/(4) = ((1)/(omega C))^(2)`
or `(R )/(2) = (1)/(omega C)` or `RC = (2)/(omega) = (2)/(500) = 4 xx 10^(-3) s`
`tau = RC = 4 xx 10^(-3) s = 4 ms`