The power factor in an $L-C-R$ circuit at resonance is

An $LCR$ circuit contains $R = 50 \, \Omega$,$L = 1 \, \text{mH}$,and $C = 0.1 \, \mu\text{F}$. The impedance of the circuit will be minimum for a frequency of:

The $Q$-factor of a resonant circuit is equal to

Using a variable-frequency a.c. voltage source, the maximum current measured in the given $LCR$ circuit is $50 \text{ mA}$ for $V = 5 \sin(100t)$. The values of $L$ and $R$ are shown in the figure. The capacitance of the capacitor $(C)$ used is . . . . . . $\mu\text{F}$.

What is the value of inductance $L$ in $mH$ for which the current is maximum in a series $LCR$ circuit with $C = 10 \, \mu F$ and $\omega = 1000 \, rad/sec$?

An inductor of inductance $2 \text{ } \mu\text{H}$ is connected in series with a resistance, a variable capacitor and an a.c. source of $10 \text{ kHz}$. The value of capacitance for which maximum current is drawn in the circuit is $\frac{1}{x} \text{ F}$, where the value of $x$ is (Take $\pi^2 = 10$).