A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as \(\epsilon=2 U\). A similar capacitor with no dielectric is charged to \(U_0=78 \mathrm{~V}\). It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.

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.