An $LCR$ series circuit is connected to an external $emf$,$e = 200 \sin(100 \pi t) \ V$. The values of capacitance and resistance in the circuit are $1 \ \mu F$ and $100 \ \Omega$ respectively. The amplitude of current in the circuit is maximum when the inductance is (in henry):

The resonant frequency of a circuit is $f$. If the capacitance is made $4$ times the initial value,then the resonant frequency will become

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:

In a series $LCR$ circuit,the voltage leads the current when (Given that $\omega_0$ is the resonant angular frequency):

Power delivered by the $ac$ source of the circuit becomes maximum when

Power factor is maximum in an $LCR$ circuit when