A series LCR circuit is connected across an a.c. source of variab… - Vidyadip

Question

A series $\text{LCR}$ circuit is connected across an $a.c.$ source of variable angular frequency $' \omega'$. Plot a graph showing variation of current $‘i\ ’$ as a function of $' \omega'$ for two resistances $R_1$ and $R2 \ (R_1 > R_2).$
Answer the following questions using this graph:

In which case is the resonance sharper and why?
In which case is the power dissipation more and why?

✓

Answer

Sharper for $R = R_2$
Sharpness of resonance $ = \frac{\omega_{\circ}\text{L}}{\text{R}}\propto\frac{1}{\text{R}}.$
More power dissipation for $\text{R} = \text{R}_{2}$
At Resonance, power dissipation $ = \frac{\text{V}^{2}}{\text{R}}\propto\frac{1}{\text{R}} ($for same $V).$

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