Ah now we are getting to the core of your concern.Thanks, though if it was a constant current recharging every second, then that would be a high ESR, as the frequency of the current would be very low.
A capacitor has ESR (effective series resistance) and SR (series resistance). SR is normally lower than ESR.
The dissipation with a constant current (Ik) and low dV/dt (rate of voltage change) will be Ik^2 * SR
Incidentally, as you no doubt know, the rate of voltage change is, dV/dt = C * I
Where
V: Voltage across the capacitor in Volts.
C: Capacitance in Farads.
I: Current flowing into the capacitor in Amps.
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