$A$ series $AC$ circuit consists of an inductor and a capacitor. The inductance and capacitance are $1 \ H$ and $25 \ \mu F$ respectively. If the current is maximum in the circuit,then the angular frequency will be:

Obtain the resonant frequency and $Q$-factor of a series $LCR$ circuit with $L=3.0\; H$,$C=27\; \mu F$,and $R=7.4\; \Omega$. It is desired to improve the sharpness of the resonance of the circuit by reducing its 'full width at half maximum' by a factor of $2$. Suggest a suitable way.

The resonant frequency of a series $LCR$ circuit is $f$. The circuit is now connected to a sinusoidally alternating e.m.f. of frequency $2f$. The new reactance $X_{L}^{\prime}$ and $X_{C}^{\prime}$ are related as:

In an $LCR$ circuit,the capacitance is changed from $C$ to $2C$. For the resonant frequency to remain unchanged,the inductance should be changed from $L$ to:

In an $LCR$ series resonant circuit,at resonance,the voltage across $L$ and $C$ will cancel each other because they are:

What is resonance in an $LCR$ series circuit?