I the inductance and the capacitance both double in an LRC series circuit,the resonate frequency of that circuit will
A) decrease by a factor of 1/2.
B) decrease by a factor of 1/4.
C) increase by a factor of 2.
D) increase by a factor of 4.

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 new frequency becomes $ f' = \frac{1}{2\pi\sqrt{2L \cdot 2C}} = \frac{1}{2\pi\sqrt{4LC}} = \frac{1}{2} \cdot \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2}f $. Thus, the frequency decreases by a factor of 1/2.

I the Inductance and the Capacitance Both Double in an LRC