If the power factor is $1/2$ in a series $RL$ circuit with $R = 100\,\Omega$ connected to an $ac$ mains $(50\,Hz)$,find the value of $L$.

Two resistors are connected in series across a $5\,V\,rms$ source of alternating potential. The potential difference across the $6\,\Omega$ resistor is $3\,V$. If $R$ is replaced by a pure inductor $L$ of such magnitude that the current remains the same,then the potential difference across $L$ is.......$V$.

$A$ series $RLC$ circuit is connected to an $ac$ source of voltage $V_S$ and variable angular frequency $\omega$,as shown in the figure. $V_{RL}$ and $V_C$ are the potential drops across the $RL$ combination and the capacitor $C$,respectively. Select the correct statement.

$A$ coil of $200 \, \Omega$ resistance and $1.0 \, H$ inductance is connected to an $ac$ source of frequency $200/2\pi \, Hz.$ The phase angle between potential and current will be.....$^o$

For the $AC$ circuit shown, the phase difference between emf and current is $\frac{\pi}{4} \text{ rad}$ as shown in the graph. If the impedance of the circuit is $1414 \Omega$, then the values of $P$ and $Q$ are:

In a series $L-C-R$ circuit,the current in the circuit is $11 \, A$ when the applied voltage is $220 \, V$. The voltage across the capacitor is $200 \, V$. If the value of the resistor is $20 \, \Omega$,then the voltage across the unknown inductor is.......$V$