A tunable capacitor & Resistor?
A tunable capacitor (with variable capacitance) is charged by a U_0=12 V battery and then is connected in parallel to a R=3 Ω 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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Since the capacitor is precharged by the 12 VDC battery, when it is connected to the resistor, it will disspiate the enegy that is stored in it across the resistor.
The time that it takes to decay is known as the RC time constant and can be calculated from a known capacitance.
http://en.wikipedia.org/wiki/RC_time_constant
The current will not remain constant as the charge it being reduced, therefore the voltage is dropping and therefore the current is also decaying as the voltage is dropping.
Theoretically if the voltage stayed constant on the capacitor, then it would operate at the same voltage to which it was charged initally (12 VDC) and therefore operate as if it was a 12 VDC battery too ! The power that would be consumed is P = V^2 / R = (12)^2 / 3 = 144 / 3 = 48 Watts.
Super Capacitors or Ultra Capacitors operate somewhat like what you are trying to describe, but they too also have a voltage decay as their charge drops.
http://en.wikipedia.org/wiki/Super_capacitor
BTW, there is not alot of work to vary the distance beween the plates with air gap rotating variable capacitors:
http://en.wikipedia.org/wiki/Variable_capacitor
Its just that for the power consumed, you couldn't adjust the plates fast enough. Also even if you could increase capacitance instantaneously, you cannot increase charge instantaneously without a voltage or current source.
Also there are electrically variable capacitors, called varactor diodes that change capacitance baed upon the voltage across it and are used for RF tuning and Phase Lock Loop (PLL) Voltage Controlled Oscillator (VCO) circuits, but are only a few picoFarads.
http://en.wikipedia.org/wiki/Varicap