A parallel plate capacitor is completely immersed in a liquid of resistivity \(0.25 \Omega \mathrm{m}\) and relative permittivity 80 . If the plates of the capacitor are connected to an alternating voltage source of \(\mathrm{V}_0 \sin (\omega \mathrm{t})\) volt at a frequency of \(0.4 \mathrm{GHz}\), then the ratio of the amplitudes of the displacement current and conduction current is ____
\(\left(\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-2}\right)\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.