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

$A$ $ 100 \,W $ bulb is connected to an $ AC $ source of $ 220 \,V, 50 \,Hz $. Then the current flowing through the bulb is

An alternating power supply of $220 \,V$ is applied across a series circuit of resistance $10 \sqrt{3} \,\Omega$,capacitive reactance $40 \,\Omega$,and inductive reactance $30 \,\Omega$. The respective currents in the circuit for zero and infinite frequencies are

Assertion : In the purely resistive element of a series $LCR$ $AC$ circuit,the maximum value of $rms$ current increases with an increase in the angular frequency of the applied $e.m.f$.
Reason : $I_{\max} = \frac{\varepsilon_{\max}}{Z}$,where $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$ and $I_{\max}$ is the peak current in a cycle.

In a series $LCR$ circuit,$R = 200 \, \Omega$ and the voltage and frequency of the main supply are $220 \, V$ and $50 \, Hz$ respectively. On taking out the capacitance from the circuit,the current lags behind the voltage by $30^\circ$. On taking out the inductor from the circuit,the current leads the voltage by $30^\circ$. The power dissipated in the $LCR$ circuit is......$W$.

An $LCR$ circuit is equivalent to a damped oscillator. $A$ capacitor is charged to a charge $Q_0$ as shown and then connected to $L$ and $R$. If a student plots graphs of the square of the maximum charge on the capacitor $(Q^2_{max})$ versus time for two different values of inductors $L_1$ and $L_2$ $(L_1 > L_2)$, which of the following graphs will correctly represent it? (The diagram is schematic and not drawn to scale.)