In a series $LCR$ circuit,the frequency of the source is half of the resonance frequency. The nature of the circuit will be:

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 a series $RLC$ circuit $(AC)$:
$L = 10 \, mH$
$C = 0.01 \, \mu F$
$R = 50 \, \Omega$
If the supply voltage is $V = 10 \sin \omega t$,find the power dissipated at resonance in $W$.

In a series $LR$ circuit with $X_L = R$, the power factor is $P_1$. If a capacitor of capacitance $C$ with $X_C = X_L$ is added to the circuit, the power factor becomes $P_2$. The ratio of $P_1$ to $P_2$ will be:

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

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