The impedance of a circuit,when a resistance $R$ and an inductor of inductance $L$ are connected in series in an $AC$ circuit of frequency $f$ is

When a coil is connected to a $d.c.$ source of $e.m.f.$ $12 \ V$,the current of $4 \ A$ flows in it. If the same coil is connected to a $12 \ V, 50 \ Hz$ $a.c.$ source,the current flowing in it is $2.4 \ A$. The self-inductance of the coil will be:

An ideal choke draws a current of $8 \, A$ when connected to an $AC$ supply of $100 \, V, 50 \, Hz$. $A$ pure resistor draws a current of $10 \, A$ when connected to the same source. The ideal choke and the resistor are connected in series and then connected to the $AC$ source of $150 \, V, 40 \, Hz$. The current in the circuit becomes

To light a $50\,W, 100\,V$ lamp,it is connected in series with a capacitor of capacitance $C = \frac{50}{\pi \sqrt{x}} \mu F$ to a $200\,V, 50\,Hz$ $AC$ source. The value of $x$ is........

$A$ coil of inductance $0.50 \; H$ and resistance $100 \; \Omega$ is connected to a $240 \; V, 50 \; Hz$ $AC$ supply.
$(a)$ What is the maximum current in the coil?
$(b)$ What is the time lag between the voltage maximum and the current maximum?

If $i$ is the current in an $L-C-R$ series $AC$ circuit,what are the formulas for:
$(i)$ Voltage across resistance.
$(ii)$ Voltage across inductor.
$(iii)$ Voltage across capacitor.