Answer :

Given

Dielectric of capacitor 2 = ε = αU

Value of constant a=2 V^{-1}

Voltage applied to capacitor 1 = U_{0}=78 V

We know that the charge stored in a capacitor and the voltage applied across are related by the equation

Where C is the capacitance of the capacitor and V is the applied voltage. Let the final voltage of the capacitors be U, and capacitance of the capacitor with no dielectric be C, then the capacitance of the capacitor with dielectric is then εC, then the final charges stored in these capacitors after being connected will be,

and

respectively.

Now from conservation of electric charge we have:

Where Q is the total charge distributed among the capacitors, which comes from the original capacitor charged by a voltage of 78V. Thus,

Solving for U we get

Thus, the final voltage is 6 V on each capacitor.

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