Question

In a series $LCR$ resonance circuit, if we change the resistance only, from a lower to higher value:

• A. The resonance frequency will increase.
• B. The quality factor will increase.
• C. The quality factor and the resonance frequency will remain constant.
• D. The bandwidth of resonance circuit will increase.

Answer 1

The correct option is D The bandwidth of resonance circuit will increase.

The resonance frequency for a series $LCR$ circuit is given by,
$f=\frac{1}{\sqrt{LC}}$
Here the value of $L$ and $C$ is constant, hence the resonance frequency will not change.

The quality factor is,
$Q=\frac{\omega L}{R}$
Hence if $R\uparrow$ the $Q\downarrow$

Now the band width of resonance circuit;
$\Delta \omega =\frac{R}{L}$
$\Delta \omega \propto R$, since the value of $L$ is constant

Thus if $R\uparrow$ the $\Delta \omega \uparrow$
Hence bandwidth of the resonance circuit will increase.