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

$A$ series $LCR$ circuit is connected to an ac source of $220\,V, 50\,Hz$. The circuit contains a resistance $R=100\,\Omega$ and an inductor of inductive reactance $X_L=79.6\,\Omega$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be $..........\mu F$.

In the given $LCR$ circuit,the voltage across the terminals of the resistance and the current in the circuit will be:

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?

$A$ $100 \, \Omega$ resistance,a $0.1 \, \mu \text{F}$ capacitor,and an inductor are connected in series across a $250 \, \text{V}$ supply at variable frequency. Calculate the value of inductance of the inductor at which resonance will occur. Given that the resonant frequency is $60 \, \text{Hz}$. (In $\text{H}$)

$A$ telegraph line of length $100 \, km$ has a capacity of $0.01 \, \mu F/km$ and it carries an alternating current at $0.5 \, kHz$. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is . . . . . . $mH$. (Take $\pi = \sqrt{10}$)