In an $L-C-R$ series circuit,the value of only capacitance $C$ is varied. The resulting variation of resonance frequency $f_0$ as a function of $C$ can be represented as

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 with $L = \frac{100}{\pi} \text{ mH}$,$C = \frac{10^{-3}}{\pi} \text{ F}$,and $R = 10 \ \Omega$ is connected across an $AC$ source of $220 \text{ V}, 50 \text{ Hz}$ supply. The power factor of the circuit would be . . . . . . .

In the circuit shown in the figure, the voltmeter reads $75 \, V$. The value of $C$ is ....... $\mu F$.

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

For a given series $LCR$ circuit,it is found that maximum current is drawn when the value of the variable capacitance is $2.5 \ nF$. If a resistance of $200 \ \Omega$ and a $100 \ mH$ inductor are being used in the given circuit,the frequency of the $AC$ source is $... \times 10^3 \ Hz$. (Given $\pi^2 = 10$)