An inductor and a resistor are connected in series to an $AC$ source of $10 \ V$. If the potential difference across the inductor is $6 \ V$,then the potential difference across the resistor is: (in $V$)

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 $L$.

An $A.C.$ circuit contains a resistance of $12 \ \Omega$ and an inductive reactance of $5 \ \Omega$. The phase angle between the current and the potential difference will be

An $AC$ circuit has an inductor and a resistor of resistance $R$ in series,such that $X_L = 3R$. Now,a capacitor is added in series such that $X_C = 2R$. The ratio of the new power factor to the old power factor of the circuit is $\sqrt{5} : x$. The value of $x$ is ...... .

$A$ coil of resistance $450 \Omega$ and self-inductance $1.5 \text{ H}$ is connected to an $A$.$C$. source of frequency $\frac{150}{\pi} \text{ Hz}$. The phase difference between voltage and current is

$A$ bulb and a capacitor are connected in series to a source of alternating current. If its frequency is increased,while keeping the voltage of the source constant,then