Physics - EMI/AC Question with Solution | TestHub

In LCR series circuit, resonance frequency ${\mathrm{f}}_0$ is given by $$\begin{array}{c}L\omega =\frac{1}{\mathrm{C}\omega }\Rightarrow {\omega }^2=\frac{1}{\mathrm{LC}}\therefore \omega =\sqrt{\frac{1}{\mathrm{LC}}}=2\pi {\mathrm{f}}_0\\ \therefore {\mathrm{f}}_0=\frac{1}{2\pi \sqrt{\mathrm{LC}}}\text{ or }{\mathrm{f}}_0\alpha \frac{1}{\sqrt{\mathrm{C}}}\end{array}$$ When the capacitance of the circuit is made 4 times, its resonant frequency become ${\mathrm{f}}_0^{\prime }$ $$\therefore \frac{{\mathrm{f}}_0^{\prime }}{{\mathrm{f}}_0}=\frac{\sqrt{\mathrm{C}}}{\sqrt{4\mathrm{C}}}\text{ or }{\mathrm{f}}_0^{\prime }=\frac{{\mathrm{f}}_0}{2}$$