$A$ $10 \Omega$ resistance,$5 \ mH$ coil,and $10 \ \mu F$ capacitor are joined in series. When an alternating current source of suitable frequency is joined to this combination,the circuit resonates. If the resistance is halved,the resonant frequency is

In a series $LCR$ circuit,the capacitance is changed from $C$ to $4C$. To keep the resonance frequency unchanged,the new inductance should be:

$A$ series $LCR$ circuit is connected to an ac voltage source. When $L$ is removed from the circuit,the phase difference between current and voltage is $\frac{\pi}{3}$. If instead $C$ is removed from the circuit,the phase difference is again $\frac{\pi}{3}$ between current and voltage. The power factor of the circuit is:

For a series $LCR$ circuit with $L=2 \ H, C=18 \ \mu F$ and $R=10 \ \Omega$. What is the value of the $Q$ factor of this circuit?

An $AC$ circuit consists of an inductor of inductance $0.5 \, H$ and a capacitor of capacitance $8 \, \mu F$ in series. The current in the circuit is maximum when the angular frequency of the $AC$ source is

In an $LCR$ circuit,at resonance