For better tuning of a series $LCR$ circuit in a communication system,the preferred combination is

The resonant frequency of an $L-C$ circuit is

The power in an $AC$ circuit is given by $P = E_{rms}I_{rms} \cos \phi$. The value of $\cos \phi$ in a series $LCR$ circuit at resonance is:

$A$ resistor of $50 \Omega$,an inductor of self-inductance $(\frac{2}{\pi^2}) \text{ H}$,and a capacitor of unknown capacity are connected in series to an $A$.$C$. source of $100 \text{ V}, 50 \text{ Hz}$. When the voltage and current are in phase,the value of the capacitance is: (in $\mu \text{F}$)

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

The resonance frequency of an $L-C-R$ $AC$ circuit is $\nu_{0}$. If the capacitance is made $4$ times its initial value,then the new resonance frequency will become . . . . . . .