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 $\Omega$)

An inductor and a resistor are connected in series to an ac source of variable frequency. When the frequency of the applied ac is $50 \ Hz$,the power factor of the circuit is $\frac{\sqrt{3}}{2}$. If the frequency of the ac is increased by $200 \%$,the power factor of the circuit is . . . . . . .

In an $RL$ circuit,the current is $i = 100 \sin(314t) \ A$ and the voltage is $e = 200 \sin(314t + \pi/3) \ V$. If the resistance is $1 \ \Omega$,what is the reactance?

In the $A$.$C$. circuit shown,keeping switch $K$ closed,if an iron rod is inserted into the coil,the bulb in the circuit:

An alternating current source of frequency $100\, Hz$ is connected to a combination of a resistor,a capacitor,and an inductor in series. The potential difference across the inductor,the resistor,and the capacitor is $46\, V$,$8\, V$,and $40\, V$ respectively. The electromotive force $(EMF)$ of the alternating current source in volts is:

In a series $L-C$ circuit,if $L=10^{-3} \,H$ and $C=3 \times 10^{-7} \,F$ is connected to a $100 \,V, 50 \,Hz$ a.c. source,the impedance of the circuit is ...........