POWER IN AC CIRCUITS
You know that in a direct current circuit the power is equal to the voltage times the
current, or P = E X I. If a voltage of 100 volts applied to a circuit produces a current
of 10 amperes, the power is 1000 watts. This is also true in an ac circuit when the
current and voltage are in phase; that is, when the circuit is effectively resistive. But,
if the ac circuit contains reactance, the current will lead or lag the voltage by a
certain amount (the phase angle). When the current is out of phase with the voltage, the
power indicated by the product of the applied voltage and the total current gives only
what is known as the APPARENT POWER. The TRUE POWER depends upon the phase angle between
the current and voltage. The symbol for phase angle is q
(Theta).

When an alternating voltage is impressed across a capacitor, power is taken from the
source and stored in the capacitor as the voltage increases from zero to its maximum
value. Then, as the impressed voltage decreases from its maximum value to zero, the
capacitor discharges and returns the power to the source. Likewise, as the current through
an inductor increases from its zero value to its maximum value the field around the
inductor builds up to a maximum, and when the current decreases from maximum to zero the
field collapses and returns the power to the source. You can see therefore that no power
is used up in either case, since the power alternately flows to and from the source. This
power that is returned to the source by the reactive components in the circuit is called
REACTIVE POWER.

In a purely resistive circuit __all of the power is consumed and none is returned to
the source;__ in a purely reactive circuit __no power is consumed and all of the power
is returned to the source.__ It follows that in a circuit which contains both resistance
and reactance there must be some power dissipated in the resistance as well as some
returned to the source by the reactance. In figure 4-9 you can see the relationship
between the voltage, the current, and the power in such a circuit. The part of the power
curve which is shown below the horizontal reference line is the result of multiplying a
positive instantaneous value of current by a negative instantaneous value of the voltage,
or vice versa. As you know, the product obtained by multiplying a positive value by a
negative value will be negative. Therefore the power at that instant must be considered as
negative power. In other words, during this time the reactance was returning power to the
source.

Figure 4-9. - Instantaneous power when current and voltage are out of phase.

The instantaneous power in the circuit is equal to the product of the applied voltage
and current through the circuit. When the voltage and current are of the same polarity
they are acting together and taking power from the source. When the polarities are unlike
they are acting in opposition and power is being returned to the source. Briefly then, in
an ac circuit which contains reactance as well as resistance, the apparent power is
reduced by the power returned to the source, so that in such a circuit the net power, or __true
power__, is always less than the apparent power.

Calculating True Power in AC Circuits

As mentioned before, the true power of a circuit is the power actually used in the
circuit. This power, measured in watts, is the power associated with the total resistance
in the circuit. To calculate true power, the voltage and current associated with the
resistance must be used. Since the voltage drop across the resistance is equal to the
resistance multiplied by the current through the resistance, true power can be calculated
by the formula:

For example, find the true power of the circuit shown in figure 4-10.

Figure 4-10. - Example circuit for determining power.

Since the current in a series circuit is the same in all parts of the circuit:

Q.19 What is the true power in an ac circuit?

Q.20 What is the unit of measurement of true power?

Q.21 What is the formula for calculating true power?