$A$ series $RLC$ circuit is shown here. The source frequency $f$ is varied, but the current is kept unchanged. Which of the curves showing changes of $V_C$ and $V_L$ with frequency would be valid for the circuit under consideration?

Find the peak current and resonant frequency of the following circuit (as shown in the figure).

In the circuit shown in the figure, the source frequency is $\omega = 2000 \, rad/s$. The current in the circuit will be:

In a series $LR$ circuit with $X_L = R$. Power factor is $P_1$. If a capacitor of capacitance $C$ with $X_c = X_L$ is added to the circuit the power factor becomes $P_2$. The ratio of $P_1$ to $P_2$ will be :

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$A$. $AC$ generator	$I$. Detects the presence of current in the circuit
$B$. Galvanometer	$II$. Converts mechanical energy into electrical energy
$C$. Transformer	$III$. Works on the principle of resonance in $AC$ circuit
$D$. Metal detector	$IV$. Changes an alternating voltage for smaller or greater value

Choose the correct answer from the options given below:

In an $LCR$ series circuit,when $L$ is removed from the circuit,the phase difference between voltage and current is $\frac{\pi}{3}$. If $C$ is removed from the circuit instead of $L$,the phase difference is again $\frac{\pi}{3}$. The power factor of the circuit is $(\tan 60^{\circ}=\sqrt{3})$.