The resonant frequency of a circuit is $f$. If the capacitance is made $4$ times the initial value,then the resonant frequency will become

At what angular frequency $\omega$ does the following circuit consume maximum power? (in $rad/s$)

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

The capacitor of an oscillatory circuit is enclosed in a container. When the container is evacuated,the resonance frequency of the circuit is $10\, kHz$. When the container is filled with a gas,the resonance frequency changes by $50\, Hz$. The dielectric constant of the gas is

For an $R-L-C$ circuit,driven with voltage of amplitude $V_m$ and frequency $\omega_0 = \frac{1}{\sqrt{LC}}$,the current exhibits resonance. The quality factor $Q$ is

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: