$A$ resonance circuit having inductance and resistance $2 \times 10^{-4} \ H$ and $6.28 \ \Omega$ respectively oscillates at $10 \ MHz$ frequency. The value of the quality factor of this resonator is .........
$[\pi = 3.14]$

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

$A$ series $LCR$ circuit containing $5.0 \, H$ inductor,$80 \, \mu F$ capacitor,and $40 \, \Omega$ resistor is connected to a $230 \, V$ variable frequency $AC$ source. The angular frequencies of the source at which the power transferred to the circuit is half the power at the resonant angular frequency are likely to be:

In a series $LCR$ circuit,at resonance,the peak value of current will be [where $E_0$ is peak emf,$R$ is resistance,$\omega L$ is inductive reactance,and $1/\omega C$ is capacitive reactance].

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 $: 1$)?

At an airport,a person is made to walk through the doorway of a metal detector,for security reasons. If she/he is carrying anything made of metal,the metal detector emits a sound. On what principle does this detector work?