How does the resonant frequency of an alternating current RLC series circuit change if the inductance and the capacitance of the circuit are both doubled simultaneously?

💡 Solution & Explanation

The resonant frequency of a series RLC circuit is inversely proportional to the square root of the product of inductance and capacitance. When both inductance and capacitance are doubled, their product increases by a factor of four, and taking the square root of four yields a factor of two in the denominator. Therefore, the overall resonant frequency is reduced by half. Incorrect reasoning assumes additive changes or linear scaling with parameters. Resonance occurs when inductive reactance equals capacitive reactance.