In an $RL$ circuit,the resistance is $\pi \sqrt{3} \,\Omega$. The phase difference between the current and the voltage is $30^\circ$. The $ac$ frequency is $50 \,Hz$. The inductance is . . . . . . $Henry$.

In a series $LCR$ circuit,the $rms$ voltage across the resistor and the capacitor are $30 \ V$ and $90 \ V$ respectively. If the applied voltage is $V = 50 \sqrt{2} \sin \omega t$,then the peak voltage across the inductor is

An $ac$ source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current registered is $I$. If the frequency of the source is changed to $\omega/3$ (while maintaining the same voltage),the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$.

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:

The power factor of an $RL$ circuit is $1/2$. If $R = 100 \, \Omega$,what is the value of $L$? The frequency of the $AC$ source is $50 \, Hz$.

For the series $LCR$ circuit,$R = \frac{X_L}{2} = 2 X_C$. The impedance of the circuit and the phase difference between $V$ and $I$ will be