What happens to the resonant frequency of a series LCR alternating current circuit when both the capacitance of the capacitor and the inductance of the inductor are simultaneously decreased to one-fourth of their original values?

💡 Solution & Explanation

The resonant frequency of a series LCR circuit is inversely proportional to the square root of the product of inductance and capacitance. When both LC parameters are reduced by a factor of sixteen combined, their product decreases by a factor of sixteen, and taking the inverse square root results in a fourfold increase in frequency. Halving or maintaining frequency occurs under different scaling ratios. The quality factor of the circuit also shifts proportionally during such simultaneous parameter modifications. Resonance occurs when inductive reactance equals capacitive reactance.