The resonant frequency of an $L-C$ circuit is

$A$ 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 $\mu F$)

The tuning circuit of a radio receiver has a resistance of $50\,\Omega$,an inductor of $10\,mH$ and a variable capacitor. $A$ $1\,MHz$ radio wave produces a potential difference of $0.1\,mV$. The value of the capacitor to produce resonance is.......$pF$ (Take $\pi^2 = 10$).

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 . . . . . . .

For a series $LCR$ circuit,the power loss at resonance is

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 $V$)