$A$ tuned amplifier circuit is used to generate a carrier frequency of $ 2 \text{ MHz} $ for amplitude modulation. The value of $ \sqrt{LC} $ is

$A$ series $LCR$ circuit of $R=5 \, \Omega, L=20 \, \text{mH}$ and $C=0.5 \, \mu \text{F}$ is connected across an $AC$ supply of $250 \, \text{V}$,having variable frequency. The power dissipated at resonance condition is $..... \times 10^{2} \, \text{W}$.

An inductor of inductance $2\,\mu\text{H}$ is connected in series with a resistance,a variable capacitor,and an $AC$ source of frequency $7\,\text{kHz}$. The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{x}\text{ F}$,where the value of $x$ is $.........$. (Take $\pi = \frac{22}{7}$)

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

The current in a series $LCR$ circuit will be maximum when $\omega$ is

The quality factor of an $LCR$ circuit having resistance $(R)$ and inductance $(L)$ at resonance frequency $(\omega)$ is given by: