A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as =2 U . A similar capacitor with no dielectric is charged to U₀=78 ~V . It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.

Step-by-step solution

Let C₀ be the capacitance of the capacitor without the dielectric. The charge on this capacitor is Q₀ = C₀ U₀ , where U₀ = 78 V. When the two capacitors are connected in parallel, the total charge Q₀ is shared between them. Let U be the final common voltage. The charge on the first capacitor is Q₁ = C₀ U . The second capacitor has a dielectric with relative permittivity = 2U . The capacitance of this capacitor is C = C₀ = (2U) C₀ . The charge on this capacitor is Q₂ = C U = (2U) C₀ U = 2 C₀ U^2 . By the principle o