Question

A series $R-C$ combination is connected to an ac voltage of angular frequency $\omega =500rad/s$. If the impedance of the R-C circuit is $R\sqrt{1.25}$, the time constant (in millisecond) of the circuit is

Answer 1

As we know that the time constant is given as, $\tau =RC$, so we have to calculate resistance as well as capacitance.
Impedance is given, $Z=R\sqrt{1.25}$ and we know the phase difference between $R$ and $X_C$ is $\frac{\pi }{2}$.
$(R\sqrt{1.25}{)}^2=R^2+X_C^2$
$0.25R^2=X_C^2$
$X_C=0.5R$
as we know,
$X_C=\frac{1}{\omega C}$
$C=\frac{1}{500\times 0.5R}=\frac{1}{250R}$
$RC=\frac{1}{250}=4\times {10}^{-3}s$
$\tau =RC=4ms$