RESONANT CIRCUITS

INTRODUCTION:

In many of the electrical circuits resonance circuits is a very important phenomenon.In study of resonance circuits is very useful,particularly in the field of communication.Resonant circuits best example is radio receivers.here radio receiver has ability to select certain desired frequency transmitted by station.The radio receives the all unwanted frequencies transmitted by other station.

What is resonance ?

Resonance is defined as a phenomenon in which applied voltage and resulting current are in phase which means an a.c circuits is said to be in resonance if it is exhibits unity power factor condition,that means applied voltage and resulting current are in phase.

resonance in series circuits is referred as series resonance or simply resonance.

resonance in parallel circuits is referred as parallel resonance or antiresonance.

Q-factor

Q-factor is also known as the quality factor.In this phenomenon is observed in a.c circuits consisting of reactive elements such as inductor and capacitor.these two elements are basic passive elements of energy storing type.

The figure of merit or Q-factor is defined as 

Thus the expression for the quality factor of inductor and capacitor
I.quality factor of Inductor :
considered that sinusoidal voltage V is applied to an inductor with leakage resistance R in series

from above fig resistance R and inductance L is connected in series and I current flows through it.

Thus by definition quality factor of inductor is given by,

II.quality factor of capacitor:

considered that sinusoidal voltage V is applied yo capacitor with a small resistance R in series.

 thus by definition,quality factor of capacitor is given by,

In the resonant of circuits,the quality factor of the inductor or coil is the controlling factor.so,when the Q of a resonant circuits is stated,the frequency of the circuit is used for the measurement.