A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as ε = αU where α = 2V-1. 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.
Since the capacitors are connected in parallel, the potential difference across the capacitors is the same. The final voltage is assumed to be U. C is the capacitance of the capacitor without dielectric, then the charge is given as Q1 = CU
The initial charge is given as
Q0 = CU0
The conversion of charges is
Q0 = Q1 + Q2
CU0 = CU + αCU2
αU2 + U – U0 = 0
Solving the equation, we get U = 6V
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