In a parallel plate capacitor the separation between plates is \(3 x\). This separation is filled by two layers of dielectrics, in which one layer has thickness \(x\) and dielectric constant \(3 k\), the other layer is of thickness \(2 x\) and dielectric constant \(5 k\). If the plates of the capacitor are connected to a battery, then the ratio of potential difference across the dielectric layers is

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.