Question

What is meant by resonance in an LCR circuit?

Answer 1

The resonance of a series LCR circuit occurs when the inductive and capacitive reactances are equal in magnitude but cancel each other because they are 180 degrees apart in phase.

In LCR circuit, the impedance is given by:

$Z=\sqrt{R^2+(X_L-X_C{)}^2}$

where $R$ is resistance, $X_L$ is inductive resistance and $X_C$ is capacitive resistance.

At Resonance in LCR circuit,

$X_L=X_C$

$\omega L=\frac{1}{\omega C}$

$\therefore \omega =\frac{1}{\sqrt{LC}}$ which is known as resonance frequency.

Further, impedance is minimum at resonance, $Z_{min}=R$ which means that the current becomes maximum, $I_{max}=\frac{V_{rms}}{R}$.