In a simple $L-R$ circuit with $A.C$. source the potential difference at any instant across inductor and resistance are $V_L$ and $V_R$ respectively and $A.C.$ souree has potential difference $V_{Ac}$ at the same instant. Then

What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved ?

A coil of inductance $0.50\;H$ and resistance $100 \;\Omega$ is connected to a high frequency supply $(240\; V, 10 \;k\,Hz)$

$(a)$ What is the maximum current in the coil?

$(b)$ What is the time lag between the voltage maximum and the current maximum?

Hence, explain the statement that at very high frequency, an inductor in a circuit nearly amounts to an open circuit. How does an inductor behave in a $dc$ circuit after the steady state?

A resistor of $200 \;\Omega$ and a capacitor of $15.0 \;\mu \,F$ are connected in series to a $220\; V , 50\; Hz$ $ac$ source.

$(a)$ Calculate the current in the circuit;

$(b)$ Calculate the voltage $(rms)$ across the resistor and the capacitor. Is the algebraic sum of these voltages more than the source voltage? If yes, resolve the paradox.

The adjoining figure shows an $AC$ circuit with resistance $R$, inductance $L$ and  source voltage $V_s$. Then