For an $LCR$ series $AC$ circuit, $L = 25 \, mH$, $R = 3 \, \Omega$, and $C = 62.5 \, \mu F$. What is the frequency of the source at which resonance occurs (in $Hz$)?

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?

In a series $RLC$ circuit,the resonance frequency is $12 \text{ kHz}$. If $R = 5 \text{ } \Omega$ and $X_L$ at resonance is $300 \text{ } \Omega$,the half-power frequencies will be:

In an $L-C-R$ circuit,the power factor at resonance is

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

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].