A
series *LCR *circuit
with *L *=
0.12 H, *C *=
480 nF, *R *=
23 Ω is connected to a 230 V variable frequency supply.

**(a) ** What
is the source frequency for which current amplitude is maximum.
Obtain this maximum value.

**(b) ** What
is the source frequency for which average power absorbed by the
circuit is maximum. Obtain the value of this maximum power.

**(c)** For
which frequencies of the source is the power transferred to the
circuit half the power at resonant frequency? What is the current
amplitude at these frequencies?

**(d)
** What is the *Q*-factor
of the given circuit?

Inductance, *L* =
0.12 H

Capacitance, *C* =
480 nF = 480 × 10^{−9} F

Resistance, *R* =
23 Ω

Supply voltage, *V*
= 230 V

Peak voltage is given as:

*V*_{0} =
=
325.22 V

**(a)** Current flowing in the circuit is given by the relation,

Where,

*I*_{0}
= maximum at resonance

At resonance, we have

Where,

ω_{R
}*= *Resonance angular frequency

∴Resonant frequency,

And, maximum current

**(b)** Maximum
average power absorbed by the circuit is given as:

Hence, resonant frequency () is

**(c)** The power
transferred to the circuit is half the power at resonant frequency.

Frequencies at which power transferred is half, =

Where,

Hence, change in frequency,

∴

And,

Hence, at 648.22 Hz and 678.74 Hz frequencies, the power transferred is half.

At these frequencies, current amplitude can be given as:

**(d)** *Q*-factor of the given circuit can be obtained using
the relation,

Hence, the Q-factor of the given circuit is 21.74.

**
**