Tunable capacitor

A tunable capacitor (with variable capacitance) is charged by a \(U_{0}=12~\mbox{V} \) battery and then is connected in parallel to a \(R=3~\Omega \) resistor. The capacitance \(C(t)\) of the capacitor is controlled so that the current in the circuit remains constant at all times. What is the power (external) in Watts needed to keep the current in the circuit constant? Note that one possible way of controlling the capacitance could be varying the distance between the plates of the capacitor which, in general, requires some work.

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