In a radio tuning $RLC$ circuit,the half-power frequencies are $100 \, MHz$ and $120 \, MHz$. Find the quality factor.

$A$ sinusoidal voltage of peak value $250\, V$ is applied to a series $LCR$ circuit,in which $R = 8\, \Omega$,$L = 24\, mH$ and $C = 60\, \mu F$. The value of power dissipated at resonant condition is $'x'\, kW$. The value of $x$ to the nearest integer is .............

In a series $LCR$ circuit, the voltage across $R$ is $100 \text{ V}$, $R = 1 \text{ k}\Omega$ and $C = 2 \mu\text{F}$. The angular frequency $\omega$ is $200 \text{ rad s}^{-1}$. At resonance, the voltage across '$L$' is (in $V$)

$A$ resistor of $50 \Omega$,an inductor of self-inductance $\left(\frac{3}{\pi^2}\right) H$,and a capacitor of unknown capacity are connected in series to an a.c. source of $100 \ V$ and $50 \ Hz$. When the voltage and current are in phase,the value of capacitance is (nearly):

In a series $RLC$ circuit $(AC)$:
$L = 10 \, mH$
$C = 0.01 \, \mu F$
$R = 50 \, \Omega$
If the supply voltage is $V = 10 \sin \omega t$,find the power dissipated at resonance in $W$.

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?