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?

When a coil is connected to a $d.c.$ source of $e.m.f.$ $12 \ V$,the current of $4 \ A$ flows in it. If the same coil is connected to a $12 \ V, 50 \ Hz$ $a.c.$ source,the current flowing in it is $2.4 \ A$. The self-inductance of the coil will be:

An electric bulb rated $100 \,W - 300 \,V$ is connected to an $AC$ supply of $500 \,V$ and $\frac{150}{\pi} \,Hz$. The required inductance to save the electric bulb is .......... $H$.

The current $I$,potential difference $V_L$ across the inductor,and potential difference $V_C$ across the capacitor in the circuit as shown in the figure are best represented vectorially as:

$A$ series combination of resistor $R$ and capacitor $C$ is connected to an a.c. source of angular frequency $\omega$. Keeping the voltage same, if the frequency is changed to $\omega/3$, the current becomes half of the original current. Then the ratio of capacitive reactance and resistance is

In a circuit,$L, C$ and $R$ are connected in series with an alternating voltage source of frequency $f$. The current leads the voltage by $45^o$. The value of $C$ is