$A$ coil of negligible resistance is connected in series with a $90 \Omega$ resistor across a $120 \text{ V}, 60 \text{ Hz}$ supply. $A$ voltmeter reads $36 \text{ V}$ across the resistor. The inductance of the coil is: (in $\text{ H}$)

An ideal inductor of $\left(\frac{1}{\pi}\right) H$ is connected in series with a $300 \Omega$ resistor. If a $20 \ V, 200 \ Hz$ alternating source is connected across the combination,the phase difference between the voltage and current is

When an inductor $L$ and a resistor $R$ in series are connected across a $12 \, V, 50 \, Hz$ supply, a current of $0.5 \, A$ flows in the circuit. The current differs in phase from the applied voltage by $\frac{\pi}{3}$ radian. Then the value of $R$ is (in $\Omega$)

$A$ resistance of $200 \ \Omega$ and an inductor of $\frac{1}{2 \pi} \ H$ are connected in series to an a.c. voltage of $40 \ V$ and $100 \ Hz$ frequency. The phase angle between the voltage and current is

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$(a)$ Phase difference between current and voltage in a purely resistive $AC$ circuit	$(i)$ $\frac{\pi}{2}$; current leads voltage
$(b)$ Phase difference between current and voltage in a pure inductive $AC$ circuit	$(ii)$ zero
$(c)$ Phase difference between current and voltage in a pure capacitive $AC$ circuit	$(iii)$ $\frac{\pi}{2}$; current lags voltage
$(d)$ Phase difference between current and voltage in an $LCR$ series circuit	$(iv)$ $\tan^{-1}\left(\frac{X_C - X_L}{R}\right)$

Choose the most appropriate answer from the options given below:

$A$ $220\, V$,$50\, Hz$ $ac$ source is connected to an inductance of $0.2\, H$ and a resistance of $20\, \Omega$ in series. What is the current in the circuit (in $, A$)?