$A$ resistor of $500 \Omega$ and an inductor of $0.5 \ H$ are connected in series with an $AC$ source given by $V = 100 \sqrt{2} \sin(1000 t)$. The power factor of the combination is:

$A$ light bulb and an open coil inductor are connected to an $AC$ source through a key as shown in the figure. The switch is closed and after some time,an iron rod is inserted into the interior of the inductor. Does the glow of the light bulb $(a)$ increase,$(b)$ decrease,or $(c)$ remain unchanged? Give your answer with reasons.

In an $LR$-circuit,the inductive reactance is equal to the resistance $R$ of the circuit. An e.m.f. $E = E_0 \cos(\omega t)$ is applied to the circuit. The power consumed in the circuit is:

In a series $LCR$ circuit,the voltages across the capacitor,resistor,and inductor are in the ratio $2:3:6$. If the voltage of the ac source in the circuit is $240 \ V$,then the voltage across the inductor is (in $V$)

When an inductor $L$ and a resistor $R$ in series are connected across a $12 \, V, 50 \, Hz$ supply, a current of $0.5 \, A$ flows in the circuit. The current differs in phase from the applied voltage by $\frac{\pi}{3}$ radian. Then the value of $R$ is (in $\Omega$)

$A$ coil has self-inductance $L = 0.04 \ H$ and resistance $R = 12 \ \Omega$. When it is connected to a $220 \ V, 50 \ Hz$ supply,what will be the current flowing through the coil (in $A$)?