In a series $L-C-R$ circuit,$C = 10^{-11} \, F$,$L = 10^{-5} \, H$,and $R = 100 \, \Omega$. When a constant $D.C.$ voltage $E$ is applied to the circuit,the capacitor acquires a charge of $10^{-9} \, C$. The $D.C.$ source is replaced by a sinusoidal voltage source in which the peak voltage $E_0$ is equal to the constant $D.C.$ voltage $E$. At resonance,the peak value of the charge acquired by the capacitor will be:

Figure $(a)$ shows a plot of voltage across the capacitor as a function of the driving frequency for a sinusoidally driven electromagnetic $LCR$ circuit. Figure $(b)$ shows the phase angle $\phi$ (phase difference between voltage and current) vs $\omega / \omega_0$ graph for the same circuit,for three different quality factors corresponding to graphs $1, 2, 3$ of figure $(a)$. Each graph in figure $(a)$ can be matched by one of the graphs $a, b, c$ in figure $(b)$. Which of the following statements is correct?

An alternating e.m.f. of $0.2 \, V$ is applied across an $LCR$ series circuit having $R=4 \, \Omega$, $C=80 \, \mu F$, and $L=200 \, mH$. At resonance, the voltage drop across the inductor is (in $V$)

The self-inductance of the motor of an electric fan is $10\;H$. In order to impart maximum power at $50\;Hz$, it should be connected to a capacitance (in $\mu F$) of:

In an $L-C-R$ series $AC$ circuit,$L = 9 \ H$,$R = 10 \ \Omega$,and $C = 100 \ \mu F$. The $Q$-factor of the circuit is . . . . . . .

An $LCR$ series circuit with $100 \Omega$ resistance is connected to an $AC$ source of $200 V$ and angular frequency $300 \text{ rad/s}$. When only the capacitor is removed,the current lags behind the voltage by $60^{\circ}$. When only the inductor is removed,the current leads the voltage by $60^{\circ}$. The power dissipated in the $LCR$ circuit will be: