AC Electrics - Introduction to AC 11

Summary

•The Voltage and Current phase relationship in reactive circuits can be remembered using the following mnemonic:

C I V I L

In a Capacitive circuit, I current leads Voltage leads I current in an L inductive circuit.

•The effect of frequency variation on inductive and capacitive reactance is shown in the following graph.

AC Electrics - Introduction to AC 11

Figure 11.14

Power in AC Circuits

The power absorbed in a DC circuit, according to Ohm’s Law, is the product of the Voltage and the Current. So it is in AC circuits. However, due to the change in phase relationship between voltage and current in reactive circuits, the actual power absorbed is not necessarily the same as the power apparently supplied.

Once again the Resistive, Inductive and Capacitive circuits need to be examined separately and then a practical circuit having a combination of all three is considered.

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11 AC Electrics -Introduction to AC

Power in a Purely Resistive Circuit

AC to Introduction - Electrics AC 11

The power in a resistive circuit is the average value of all of the instantaneous values of power for a complete cycle. The instantaneous power value is found by multiplying the instantaneous values of current and voltage. If this process is carried out over a full cycle, it will give the power curve shown in Figure 11.15.

	6
	5
Voltage	4	Average power
Current	3	(True power)
Power		RMS Volts ×
	2	RMS Amps
	1	Watts or kW
	0
Voltage and Current	-1
	-2
‘in phase’ = Real power
	-3
	-4
	-5
	-6

Figure 11.15 Power in a purely resistive circuit

Notice that the power curve is always positive because the voltage and current are in phase and its frequency is twice that of the voltage and current.

This positive power is known as the True Power, Real Power or Wattfull Power and its value is the product of the RMS current and the RMS voltage. It is measured in watts or kilowatts (kW).

The average power over a complete cycle is the average value of the power curve and can be represented by a line drawn halfway between the minimum and maximum values.

Power in a Purely Inductive Circuit

Figure 11.16 shows a purely inductive circuit where the current ‘lags ‘the voltage by 90°. It can be seen that by plotting instantaneous values of current × voltage we can obtain the waveform of instantaneous power.

The axis of that power waveform is the same as that of the voltage and current but its frequency is double.

If the axis of all the waveforms is the same, then the positive power is equal to the negative power. The positive cycle represents power given to the circuit to generate the magnetic field, and the negative cycle is power given back by the circuit in generating the Back EMF.

Thus in a circuit that contains only inductance, the true power is zero and only the power required that is necessary to overcome the inductive reactance is absorbed. This called reactive power and is the product of the voltage and current that is 90° out of phase. It is measured as Volts × Amps Reactive VAR or kVAR.

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AC Electrics - Introduction to AC 11

The product of the RMS voltage and the RMS current in this circuit is known as the apparent power and is measured in VA or KVA.

Positive power

Phase angle 90° current lags voltage

True power = 0

Negative power

Power = Volts × Amps Reactive. VAR or kVAR (No real power generated when current 90° out of phase with voltage)

Figure 11.16 Power in a purely inductive circuit

Power in a Capacitive Circuit

Power in a purely capacitive circuit is very similar to the inductive circuit, because the current is also out of phase with the voltage, but this time leading. Refer to Figure 11.17, once again the positive power is equal to the negative power thus no real power is absorbed. The power required is only overcoming the capacitive reactance. When the voltage and current are 90° out of phase the power required is all reactive power (VAR or kVAR).

As before the RMS volts × RMS amps is apparent power (VA or kVA)

Power = Volts × Amps Reactive. VAR or kVAR (No real power developed when current 90° out of

phase with voltage)

Positive power

True power = 0

Phase angle 90° current leads voltage

Negative power

Figure 11.17 Power in a purely capacitive circuit

AC Electrics - Introduction to AC 11

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11 AC Electrics -Introduction to AC

Power in a Practical AC Circuit

AC to Introduction - Electrics AC 11

A practical AC circuit will always have some resistance and some inductance, and the amounts of each will depend on the construction of that circuit. An AC circuit may also have capacitance if capacitors are fitted.

Calculating power, therefore, depends on the ratio of resistance in a circuit to the inductance or capacitance (remember that inductance has the opposite effect to capacitance so if both are present in a circuit, the effects of one will cancel out some of the other leaving the circuit more inductive or capacitive depending on which one is more dominant, the resistance will always be there).

Figure 11.18 shows a circuit having equal resistance and inductance; notice the phase angle is 45° and that the amounts of positive power and negative power are not equal.

A line dividing the power curve into two equal areas would show the average power consumed in that circuit. The “average power” in a circuit with both resistance and inductance is the true power (kW) consumed in that circuit.

The apparent power (kVA) is the RMS volts × amps and the reactive power (kVAR) is the amount of power required to overcome the inductive reactance.

More positive power than negative power. True power axis now above the zero axis.

Phase angle of 45° current ‘lags’ voltage

Positive power

True

power

(kW)

Negative power

true power (kW) Power factor = apparent power (kVA)

Figure 11.18 Power in a circuit having equal amounts of resistance and inductance

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