If the inductance and the capacitance both double in an LRC series circuit, the resonant frequency of that circuit will
A) decrease to one-half its original value.
B) increase to four times its original value.
C) increase to twice its original value.
D) decrease to one-fourth its original value.
E) decrease to one-eighth its original value.

Question

Quizplus · Accepted Answer

The resonant frequency of an LRC circuit is given by $ f = \frac{1}{2\pi\sqrt{LC}} $. If both L and C double, the resonant frequency becomes $ \frac{1}{2\pi\sqrt{2L \cdot 2C}} = \frac{1}{2\pi\sqrt{4LC}} = \frac{1}{2} \times \frac{1}{2\pi\sqrt{LC}} $, which is half the original frequency.

If the Inductance and the Capacitance Both Double in an LRC