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Alternating Current — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsAlternating Current3 Marks
Question
A series 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:
  1. In which case is the resonance sharper and why?
  2. In which case is the power dissipation more and why?
✓

Answer

  1. Sharper for $R = R_2​​​​​​​$​​​​​​​
Sharpness of resonance $ = \frac{\omega_{\circ}\text{L}}{\text{R}}\propto\frac{1}{\text{R}}.$
  1. 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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