$A$ virtual current of $4 \, A$ and $50 \, Hz$ flows in an $AC$ circuit containing a coil. The power consumed in the coil is $240 \, W$. If the virtual voltage across the coil is $100 \, V$,its inductance will be:

In a circuit,a metal filament lamp is connected in series with a capacitor of capacitance $C \mu F$ across a $200 V, 50 Hz$ supply. The power consumed by the lamp is $500 W$ while the voltage drop across it is $100 V$. Assume that there is no inductive load in the circuit. Take $rms$ values of the voltages. The magnitude of the phase-angle (in degrees) between the current and the supply voltage is $\varphi$.
Assume,$\pi \sqrt{3} \approx 5$.
$(1)$ The value of $C$ is . . . . . .
$(2)$ The value of $\varphi$ is
Give the answers of the questions $(1)$ and $(2)$:

What will be the reading in the voltmeter and ammeter of the circuit shown?

In an $LCR$ series circuit,the source voltage is $120 \ V$,the voltage across the inductor is $50 \ V$,and the voltage across the resistor is $40 \ V$. Determine the voltage across the capacitor.

With an alternating voltage source of frequency $f$,an inductor $L$,a capacitor $C$,and a resistor $R$ are connected in series. The voltage leads the current by $45^{\circ}$. The value of $L$ is $(\tan 45^{\circ} = 1)$.

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 $\omega/3$ (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 $\omega$.