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 `Rsqrt(1.25)`, the time constant (in millisecond) of the circuit is

Options

A. 2
B. 3
C. 4
D. 5

Answer

C

Explanation

Here, `omega = 500` radian/s
The capacitive reactance is
`X_(C )=(1)/(omega C)`
The impedance of the circuit is
`Z=sqrt(R^(2)+(X_(C ))^(2))=sqrt(R^(2)+((1)/(omega C))^(2))`
`R sqrt((5)/(4))=sqrt(R^(2)+((1)/(omega C))^(2))` or `(5)/(4)R^(2)=R^(2)+((1)/(omega C))^(2)`
`(1)/(4)R^(2)=((1)/(omega C))^(2)` or `R^(2)C^(2)=4((1)/(omega))^(2)`
or `RC=(2)/(omega)=(2)/(500)s=0.4xx10^(-2)s=4` millisecond
`therefore` The time constant of RC circuit, `tau = RC = 4 ms`