An $AC$ circuit contains a resistance of $1 \text{ k}\Omega$, a capacitor of $0.1 \mu\text{F}$, and an inductor of $1 \text{ mH}$ connected in series. The resonance frequency of the circuit is approximately: (in $kHz$)

In a series $R-L-C$ circuit,the frequency of the source is half of the resonance frequency. The nature of the circuit will be

When you walk through a metal detector carrying a metal object in your pocket,it raises an alarm. This phenomenon works on

In a series $LCR$ circuit, $C = 2 \mu\text{F}$, $L = 1 \text{ mH}$, and $R = 10 \Omega$. What is the ratio of energies stored in the capacitor and inductor when maximum current flows through the circuit (in $: 1$)?

An $ac$ source of variable frequency $f$ is connected to an $LCR$ series circuit. Which one of the graphs represents the variation of current $I$ in the circuit with frequency $f$?

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