$A$ coil has a resistance of $30\,\Omega$ and an inductive reactance of $20\,\Omega$ at a frequency of $50\,Hz$. If an $AC$ source of $200\,V$ and $100\,Hz$ is connected across the coil,the current in the coil will be.......$A$

$A$ 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$)

An inductor of inductive reactance $R$,a capacitor of capacitive reactance $2R$,and a resistor of resistance $R$ are connected in series to an $AC$ source. The power factor of the series $LCR$ circuit is

$A$ charged capacitor discharges through a resistance $R$ with time constant $\tau$. The two are now placed in series across an $AC$ source of angular frequency $\omega = \frac{1}{\tau}$. The impedance of the circuit will be

When an inductance $L$ and resistor $R$ are connected in series to $25 \ V$, $50 \ Hz$ supply, a current of $0.5 \ A$ flows in the circuit. The current lags behind in phase from applied voltage by $(\frac{\pi}{3})$ radian. The value of $R$ is $(\cos 60^{\circ} = \frac{1}{2})$ (in $\Omega$)

An alternating e.m.f. having voltage $V = V_0 \sin \omega t$ is applied to a series $L-C-R$ circuit. Given: $|X_L - X_C| = R$. The r.m.s. value of potential difference across the capacitor will be: