AC Electrics -Introduction to AC — Page 180, Lesson 184

I want to walk you through power in AC circuits, starting with the simplest case: a purely resistive circuit. In a purely resistive circuit, the power we care about is the average value of all the instantaneous power values over one complete cycle. To get an instantaneous power value, you multiply the instantaneous current by the instantaneous voltage at that same moment. If you do that multiplication for every point across a full cycle, you get a power curve — and that's what Figure 11.15 shows you. Let me describe what that curve looks like. The voltage and current waveforms are in phase — they rise and fall together. Because of that, when you multiply them, the resulting power curve is always positive. It never dips below the zero line. And its frequency is twice that of the voltage and current — so if your AC supply is 50 Hz, the power waveform is pulsing at 100 Hz. This positive power has several names. It's called True Power, Real Power, or Wattfull Power. Its value is simply the product of the RMS voltage and the RMS current — RMS meaning Root Mean Square, which is the effective DC-equivalent value. True power is measured in watts or kilowatts (kW). Now, the average power over a complete cycle is just the average value of that power curve. You can represent it as a straight line drawn halfway between the minimum and maximum values of the curve. --- Now let's move to the opposite case: a purely inductive circuit. This is shown in Figure 11.16. In a purely inductive circuit, the current lags the voltage by exactly 90°. If you plot the instantaneous values of current times voltage, you get the instantaneous power waveform. That power waveform has the same axis — the same zero line — as the voltage and current waveforms, but again its frequency is double. Here's the key difference from the resistive case. Because the axis of all three waveforms is the same, the positive power and the negative power are exactly equal. The positive half-cycle represents power being given to the circuit to build up the magnetic field in the inductor. The negative half-cycle represents power being given back by the circuit as the collapsing magnetic field generates a Back EMF — that's the voltage the inductor produces trying to keep current flowing when the supply tries to change it. So in a circuit that contains only inductance, the true power — the average power over a full cycle — is zero. The only power that's absorbed is the power needed to overcome the inductive reactance. That power is called Reactive Power. It's the product of the voltage and current that are 90° out of phase. Reactive power is measured in Volts × Amps Reactive, abbreviated as VAR or kVAR for kilovolt-amps reactive. So to summarise what we've covered: in a purely resistive circuit, voltage and current are in phase, the power curve is always positive, and we get True Power measured in watts or kW. In a purely inductive circuit, current lags voltage by 90°, the positive and negative power cancel out over a cycle, so True Power is zero, and we only have Reactive Power measured in VAR or kVAR.