Question

A series resonant circuit consists of inductor L' of negligible resistance and a capacitor' C' which produces resonant frequency' f'. If L is changed to 3 L and' C'is changed to 6 C, the resonant frequency will become.

Answer 1

The new resonant frequency is $\frac{f}{3\sqrt{2}}$.

Answer 2

The resonant frequency for an LC circuit is given by:

$$f = \frac{1}{2\pi\sqrt{LC}}$$

For the modified circuit:

$$L' = 3L \quad \text{and} \quad C' = 6C$$

So the new resonant frequency $f'$ is:

$$f' = \frac{1}{2\pi\sqrt{(3L)(6C)}} = \frac{1}{2\pi\sqrt{18LC}} = \frac{1}{2\pi \cdot 3\sqrt{2}\sqrt{LC}}$$ $$f' = \frac{1}{3\sqrt{2}} \cdot \frac{1}{2\pi\sqrt{LC}} = \frac{f}{3\sqrt{2}}$$