Physics - EMI/AC Question with Solution | TestHub

In the given circuit, two condensors and the inductor are in series. $\therefore {\mathrm{L}}_{\mathrm{s}}=\mathrm{L}+\mathrm{L}=2\mathrm{L}$ and $\frac{1}{{\mathrm{C}}_{\mathrm{s}}}=\frac{1}{\mathrm{C}}+\frac{1}{\mathrm{C}}=\frac{2}{\mathrm{C}}\Rightarrow {\mathrm{C}}_{\mathrm{s}}=\frac{\mathrm{C}}{2}$ $\therefore$ Natural frequency of the circuit $\begin{array}{l}\mathrm{v}=\frac{1}{2\pi \sqrt{{\mathrm{L}}_{\mathrm{s}}{\mathrm{C}}_{\mathrm{s}}}}=\frac{1}{2\pi \sqrt{2\mathrm{L}}\times \sqrt{\mathrm{C}/2}}\\ =\frac{1}{2\pi \sqrt{\mathrm{LC}}}\end{array}$