AIIMS 2019 Physics L-C Circuits MCQ Question

In an L⁻C circuit, the natural frequency $f_1$ is given by $f_1 = \frac{1}{2\pi\sqrt{LC}}$. When a resistance $R$ is added, the frequency $f_2$ is modified to $f_2 = \frac{1}{2\pi\sqrt{L(C - \frac{R^2}{4L})}}$. The ratio $\frac{f_2}{f_1}$ simplifies to $\sqrt{1 - \frac{R^2C}{4L}}$, which corresponds to option B. Other options are incorrect as they either incorrectly add or misrepresent the relationship between resistance, capacitance, and inductance in determining the modified frequency.