Power delivered by the source of the circuit becomes maximum,when

In an $LCR$ circuit,the inductance is changed from $L$ to $9 L$. For the same resonant frequency,the capacitance should be changed from $C$ to:

In the circuit shown,the $AC$ source has voltage $V=20 \cos (\omega t) \text{ V}$ with $\omega=2000 \text{ rad/s}$. The magnitude of the amplitude current will be nearly

$A$ series $LCR$ circuit driven by $300 \, V$ at a frequency of $50 \, Hz$ contains a resistance $R = 3 \, k\Omega$, an inductor of inductive reactance $X_{L} = 250 \pi \, \Omega$ and an unknown capacitor. The value of capacitance to maximize the average power should be: (Take $\pi^{2} = 10$) (in $\mu F$)

An inductor of $0.5 \ mH$,a capacitor of $20 \ \mu F$ and a resistance of $20 \ \Omega$ are connected in series with a $220 \ V$ a.c. source. If the current is in phase with the e.m.f.,the maximum current in the circuit is $\sqrt{x} \ A$. The value of '$x$' is

$A$ transmitting station releases waves of wavelength $960\, m$. $A$ capacitor of $2.56\, \mu F$ is used in the resonant circuit. The self-inductance of the coil necessary for resonance is $............ \times 10^{-8}\, H$.