# How to calculate reactive power of a capacitor with a current waveform which consists of a sum of sinusoids?

Assume that there is a current which consists of a sum of sinusoids flowing through a capacitor with capacitance C.
How to calculate its reactive power?
It is quite simple with a pure sine wave but I wonder how would you do it for the waveform of multiple sine waves as above as the superpostion is not allowed to use here.
If you use RMS current, Q = IRMS^2*Xc then how would you calculate reactance as it is frequency dependent?

• Complex power (and therefore reactive power) is only well-defined for a single sinusoidal frequency since it's defined via phase angles. You can only calculate it for each frequency individually; adding them would furthermore be meaningless. Therefore there is no single "reactive power" number in a multi-frequency system. What are you supposed to calculate exactly? The apparent power, maybe? Jan 3 at 21:06
• @JonathanS. the question is to calculate the reactive power of the capacitor. Jan 3 at 21:08
• "Reactive power," or reactive volt-amperes is not a very useful concept for waveforms other than un-distorted sine waves. It may be somewhat useful to calculate the reactive VA for the fundamental current in an AC power system that has some harmonic distortion, but the effects of the harmonic components need to be considered separately. Jan 3 at 21:09
• I assume this is university homework... Reactive power is simply not defined in this context so you can't calculate it either. You should ask your professor to clarify. Jan 3 at 21:21
• I think that reactive power in this context could be defined as the rate of energy transfer for a charge-discharge cycle. If the series of currents have frequencies that are a fundamental and a series of harmonics, I think that the energy transfer could be calculated for one cycle of the fundamental. Normally the angles given would be the angles between the current and voltage. Are a corresponding series of voltages given? Jan 3 at 21:41