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A 10 \(\Omega\) resistor, a 0.5 mH coil, and a 10 \(\mu\)F capacitor are connected in series. When a suitable frequency of an alternating current source is applied, the circuit resonates. If the resistance is halved, the resonance frequency:

1. is halved
2. is doubled
3. remains unchanged
4. is quadrupled

Correct answer: remains unchanged

Solution

The resonant frequency of a series LCR circuit is \(f_0 = \frac{1}{2\pi\sqrt{LC}}\). It depends only on inductance and capacitance, not on resistance. Therefore, halving the resistance does not change the resonance frequency.

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