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Question 14

To increase the resonant frequency in series LCR circuit,

We need to determine how to increase the resonant frequency in a series LCR circuit.

Recall that the resonant frequency of a series LCR circuit is given by: $$f_0 = \frac{1}{2\pi\sqrt{LC}}$$

To increase $$f_0$$, we need to decrease either $$L$$ or $$C$$ (or both).

Evaluating the options, Option A: Increasing source frequency does not change the resonant frequency; it only changes the operating frequency.

Option B: Adding resistance does not affect the resonant frequency, since $$f_0$$ is independent of $$R$$.

Option C: Adding another capacitor in series with the first capacitor. For capacitors in series:

$$\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2}$$

This gives $$C_{eq} < C_1$$, so the equivalent capacitance decreases. Since $$f_0 \propto \frac{1}{\sqrt{C}}$$, decreasing $$C$$ increases $$f_0$$. This is correct.

Option D: Decreasing source frequency does not change the resonant frequency.

Hence, the correct answer is Option C.

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