Question

A $10\Omega$ resistor, $10\text{mH}$ coil and $10\mu \text{F}$ capacitor are connected in series across an AC supply. For a certain frequency of the source, the circuit resonates. If the resistance of the resistor is halved, the resonant frequency will -

• A. be halved.
• B. be doubled.
• C. remain the same.
• D. Either option $\left(A\right)$ or $\left(B\right)$

Answer 1

The correct option is C remain the same.

The resonant frequency is given by,

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

As the resonant frequency is independent of the resistance $\left(R\right)$ of the resistor, any change in the resistance will not affect the resonant frequency.

Hence, option $\left(C\right)$ is the correct answer.