To reduce the resonant frequency in an `LCR` series circuit with a generator

At resonance frequency the impedance in series LCR circuit is

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 ohm.

Obtain the resonant frequency and Q – factor of a series LCR circuit with L = 3H, C = 27muF, " " R = 7.4Omega . It is desired to improve the sharpness of resonance of circuit by reducing its full width at half maximum by a factor of 2. Suggest a suitable way.

Keeping the source of frequency equal to the resonating frequency of the series LCR circuit, if the three elements L, C and R in are arranged in parallel , show that the total current in the parallel LCR circuit is a minimum at this frequency. Obtain the r.m.s. value of current in each brach of the circuit for the elements and source specified in for this frequency.

Compute the resonant frequency and the Q factor of a series LCR circuit having L = 4.0 H, C = 36 mu F and R = (10)/(3) Omega . How can sharpness of resonance of the circuit be improved by a factor of 2 by reducing its full width at half maximum ?

The resonant frequency of a series LCR circuit with L=2.0 H,C =32 muF and R=10 Omega is