A charged capacitor discharges through a resistance `R` with time constant `tau`. The two are now placed in series across an `AC` source of angular frequency `omega =1/(tau)` . The impedance of the circuit will be

Options

A. `(R )/(sqrt2)`
B. R
C. `sqrt2R`
D. 2R

Answer

C

Explanation

The time constant of RC circuit is `tau = RC`
According to given problem , `omega = 1/tau = (1)/(RC) " or " R = (1)/(omega C)`
Impedance of the RC circuit is
` Z = sqrt(R^2 + X_C^2) = sqrt(R^2 + ((1)/(omega C))^2) = sqrt(R^2 + R^2) = sqrt2R`