True, Reactive and Apparent Power

True Power is also referred to as consumer power and is the amount of power, in watts (W), consumed. This can be read using or wattmeter.

P = I ² R

Reactive Power is represented by the letter Q and is expressed in terms of VAR (Voltage - Amp - Reactive)

Q = I ² X and Q = V ² / X Where X is the circuits reactance

Apparent Power is represented by the letter s and is expressed in terms of volt-amps (VA).

S = I ² Z
S = IV

where Z is the circuit's impedance

Although on electrical contractor's test will not require you to perform trigonometry calculation directly, it is important to know, for conceptual purposes how the three types of power relate for each other trigonometrically

Example 1:
You are deciding with a circuit with no reactance (resistance load only). The said circuit has a current of 3A, a resistance of 90 Ω and a Voltage of 120.
Find its true and apparent power
We can find its true power by using the formula below:

P = I ² R
P = (3) ² A x 90 Ω
P = 9A x 90 Ω
P = 810 W

We can find its apparent power by using the formula below:
S = I x V
S = 3A x 120V
S = 360 VA

Example 2:

Find the reactive and apparent power of the following circuit:

Let's find reactive power first:
the formula is listed below

Q = V ² / X
Q = 120 ² / 70.12
Q = 14,400/70.12
Q = 205.36 VAR (Voltage-Ampere-Reactive)

To find Apparent Power use

S = IV
S = 1.71A x 120V
S = 205.2 VA

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