Question

In a series resonant LCR circuit, if L is increased by 25% and C is decreased by 20%, then the resonant frequency will

• A. Increase by 10%
• B. Decrease by 10%
• C. Remain unchanged
• D. Increase by 2.5 %

Answer 1

Answer: (C)

Remain unchanged

Answer 2

$\nu_{0} = \frac{1}{2\pi\sqrt{LC}}$ ⇒ In this question $L' = L + 25\%$ of

$L = L + \frac{L}{4} = \frac{5L}{4}$ and $C' = C -$20% of C $= C - \frac{C}{5} = \frac{4C}{5}$

Hence $\nu_{0}^{'} = \frac{1}{2\pi\sqrt{L'C'}} = \frac{1}{2\pi\sqrt{\frac{5L}{4} \times \frac{4C}{5}}} = \frac{1}{2\pi\sqrt{LC}} = \nu_{0}$