Power is the instantaneous product of voltage across and current through a circuit element. Inductors and capacitors can store power applied for a time as energy, so when considering transient conditions, you need to distinguish between power that became stored energy, (or stored energy that became power), and power converted to heat (so-called ohmic losses). If you are calculating or simulating an AC circuit or a DC switching circuit, its important to calculate or measure the power over either N whole cycles (so it has returned to the same state) or very large number of cycles, so that the power used to change the stored energy is a negligible part of the total.
If you connect your charging circuit to a 50R load it will almost certainly NOT deliver or use the same power as it would while charging the capacitor. Depending on the level of detail and accuracy you need (and your budget), you could instrument your circuit with current and voltage probes and use a DSO that can do waveform arithmetic, or a data logger to measure the actual power while charging the capacitor or if you have enough component data you could model it in a SPICE simulator.
RMS is not meaningful for power! P=V*I or P=V2/R or P=I2*R all contain a square or equivalent product. Just integrate over time and divide by the time interval for Average power. If you have a RMS voltage and a RMS current and you *KNOW* they are always in phase, you can multiply them to get the Average Power. If they are not in phase the true power will be less and may even be zero.