When a coil is connected to an $AC$ supply of frequency $50 \, Hz$, a current of $4 \, A$ flows in it and it consumes $240 \, W$ power. If the potential difference across the coil is $100 \, V$, then the inductance value of the coil is

$A$ current of $4 \, A$ flows in a coil when connected to a $12 \, V$ d.c. source. If the same coil is connected to a $12 \, V, (25/\pi) \, Hz$ a.c. source, a current of $2.4 \, A$ flows in the circuit. The inductance of the coil is: (in $ \, mH$)

Draw the effective equivalent circuit of the circuit shown in the figure at very high frequencies and find the effective impedance.

An $AC$ voltage source of variable angular frequency $\omega$ and fixed amplitude $V_0$ is connected in series with a capacitance $C$ and an electric bulb of resistance $R$ (inductance zero). When $\omega$ is increased,

When alternating current is passed through an $L-R$ series circuit,the power factor is $\frac{\sqrt{3}}{2}$ and $R=50 \ \Omega$. If the frequency of the source is $50 \ Hz$,then the value of $L$ is (Assume $\pi \approx 3.14$):
$\left[\cos \frac{\pi}{6}=\frac{\sqrt{3}}{2}, \quad \sin \frac{\pi}{6}=\frac{1}{2}, \quad \tan \frac{\pi}{6}=\frac{1}{\sqrt{3}}\right]$

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: