An alternating power supply of $220 V$ is applied across a series circuit of resistance $10\sqrt{3}\Omega$, capacitive reactance $40 \Omega$ and inductive reactance $30 \Omega$. The respective current in the circuit for zero and infinite frequencies are

Case I: When the frequency is zero.

$f=0$ implies $\omega = 0$

Therefore, the capacitive reactance becomes infinite

$X_C= \dfrac{1}{\omega C} \to \infty$

As a result the impedance(Z) of the circuit becomes infinite and the current becomes zero.

Case I: When the frequency is infinite.

$f \to \infty$ implies $\omega \to \infty$

Therefore, the inductive reactance becomes infinite

$X_L= \omega L \to \infty$

As a result the impedance(Z) of the circuit becomes infinite and the current becomes zero.