An e.m.f. $E = 4 \cos(1000t) \, V$ is applied to an $LR$-circuit of inductance $3 \, mH$ and resistance $4 \, \Omega$. The amplitude of current in the circuit is:

For a series $LCR$ circuit, inductive reactance $X_L$ is equal to resistance $R$ and also equal to twice the capacitive reactance $X_C$. The impedance of the circuit and the phase difference between voltage $V$ and current $i$ are respectively

In the circuit shown below,the $ac$ source has voltage $V = 20\cos (\omega t)$ volts with $\omega = 2000 \,rad/sec$. The amplitude of the current will be nearest to:

$A$ sinusoidal voltage $V_0 \sin \omega t$ is applied across a series combination of resistance $R$ and inductance $L$. The amplitude of the current in this circuit is

An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega/4$, (keeping the voltage unchanged) the current is found to be $I/3$. The ratio of resistance to reactance at frequency $\omega$ is

$A$ coil has resistance $30\,\Omega$ and inductive reactance $20\,\Omega$ at $50\,Hz$ frequency. If an $AC$ source of $200\,V, 100\,Hz$ is connected across the coil,the current in the coil will be ......$A$