Expressions for Q-factor of inductor and capacitor

 

Define
Q-factor; Derive the expressions for Q-factor of inductor and capacitor.

(or)

Write
a note on figure of merit.

 

The resonance phenomenon is observed in
ac circuits consisting reactive elements such as inductor and capacitor. These
two elements are basic passive elements of energy storing type.

 

It is found convenient to express the
efficiency with which these elements store energy. It is also found simpler to
compare various inductors and capacitors in terms of efficiency while designing
such circuits. Such efficiency is measured as quality factor. It is also called
figure of merit.

The figure of merit or
Q-factor is defined as

 = 2pi – {Maximum energy stored
per cycle / Energy dissipated per cycle} 

Let us derive the expressions for the
quality factor of inductor and capacitor.

Consider that sinusoidal voltage V is applied to an
inductor with leakage resistance R in series as shown in fig.

 

The maximum energy
stored per cycle is given by

Where   Im = Peak or maximum value
of current in the circuit.

The average power dissipated in inductor is given by

The total energy
dissipated / cycle is given by

Energy dissipated / cycle =

Where,        f = frequency of
operation.

 

Thus by definition, the quality factor of inductor is given by,

Let us consider that sinusoidal voltage V is applied
too capacitor with a small resistance R is series as shown in fig.

 

The maximum energy
stored per cycle is given by

Where
Vm = peak or maximum value of applied voltage

The average power
dissipated in capacitor is given by

The
total energy dissipated per cycle is given by,

 

Energy dissipated
/cycle =

where

 

f
= frequency of operation,

Thus by definition, the
quality factor of capacitor is given by,