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In an LCR circuit, the capacitance is changed from \(C\) to \(2C\). For the resonant frequency to remain unchanged, the inductance should be changed from \(L\) to:

1. 4L
2. 2L
3. L/2
4. L/4

Correct answer: L/2

Solution

The resonant frequency of an LCR circuit is \(f_0 = \frac{1}{2\pi\sqrt{LC}}\). If capacitance doubles, inductance must halve so that the product \(LC\) remains the same and the resonant frequency does not change.

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