In an $LCR$ circuit,the resonance frequency of the circuit increases to two times its initial value by changing the capacitance from $C$ to $C^{\prime}$ and the resistance from $100 \ \Omega$ to $400 \ \Omega$,while the inductance $L$ is kept constant. The ratio $C / C^{\prime}$ is:

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:

The current in resistance $R$ at resonance is

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:

Which of the following combinations should be selected for better tuning of an $L-C-R$ circuit used for communication?

In the given circuit,the voltmeter reads $75 \ V$. The value of $C$ is $.... \mu F$. (Given: $\pi^2 = 10$)