In an $LCR$ series circuit at resonance:

$A$ resistor of $100 \text{ } \Omega$, an inductor of self-inductance $(4/\pi^2) \text{ H}$, and a capacitor of unknown capacity are connected in series to an a.c. source of $200 \text{ V}$ and $50 \text{ Hz}$. When the current and voltage are in phase, the value of the capacity is: (in $\text{ } \mu\text{F}$)

An $AC$ voltage $V = 220 \sin(2 \times 10^3 t) \text{ V}$ is applied to a series $LCR$ circuit. The current amplitude in this circuit is: (Given: $L = 10 \text{ mH}$, $C = 25 \mu\text{F}$, $R = 100 \Omega$) (in $\text{ A}$)

$A$ 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 an $LCR$ circuit,at resonance

$A$ resistor of $2 \ \Omega$,an inductor of $100 \ \mu H$,and a capacitor of $400 \ pF$ are connected in series across an $A$.$C$. source of $e_{rms} = 0.1 \ V$. At resonance,the voltage drop across the inductor is: (in $V$)