Question

In an LCR circuit the capacitance is changed from C to C/2. To keep the same resonance frequency, L should be changed to

• A. L/2
• B. 2L
• C. 4L
• D. L/4

Answer 1

Answer: (B)

2L

Answer 2

The resonance frequency ($f_0$) of an LCR circuit is given by the formula:

$f_0 = \frac{1}{2\pi\sqrt{LC}}$

Where L is the inductance and C is the capacitance. To maintain the same resonance frequency when capacitance is halved (C to C/2), the product LC must remain constant. If C becomes C/2, then L must become 2L for the product $L \times C$ to remain the same ($L \times C = (2L) \times (C/2)$).