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Using Everyday Examples in Engineering (E3)
Power in an AC Circuit
Perlekar Tamtam
Wichita State University
Physical analogy:
Active power = useful drink (which is in the liquid form)
Reactive power = foam
Apparent power = whole bottle (liquid + foam)
Take a Pepsi or Coca-Cola half-filled bottle, Active power is the liquid in that bottle which is
useful to drink, same as active power which is useful to produce light and heat
When we shake the bottle, useful drink is converted into useless foam, same as converting active
power into reactive power because of the property of an inductive load. More than 80% of the
entire load in the world is inductive load (motor). It is hard to transmit reactive power in a longer
transmission line, same as foam does not flow freely like water in the bottle.
Active Power (P) = Apparent Power (S)
Reactive Power (Q) = 0
This material is based upon work supported by the National Science Foundation (NSF) under Grant No. 083306. Any
opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not
necessarily reflect the views of NSF.
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Reactive power (Q)
Apparent power (S) = P+jQ
Active power (P)
In DC circuits, there is only one power, which is active power, since an inductor acts like a short
circuit and a capacitor acts like an open circuit in DC circuits. When it comes to the AC circuit,
inductors delay the rate of change of current, and capacitors delay the rate of change of voltage.
So AC circuits have active power, reactive power and apparent power.
Active power (P):
Active power is the power that produces heat and light. Active power is represented with ‘P’ and
measured in Watt or KW. Active power has the only real part in a complex number, and active
power is always consumed by the resistive elements of the load.
Active Power (P) = Real power =
Where
V = voltage across the load
I = current flowing in the load
= power factor
= angle between the voltage and current
Reactive Power (Q):
Reactive Power (Q) is the Imaginary power which is consumed by the inductive load and
supplied by the capacitive load. Reactive power is represented with ‘Q’ and measured in Volt
Ampere Reactive (VAR) or KVAR.
Reactive Power (P) = Imaginary power =
Apparent power (S):
Apparent power is the vector sum of active power and reactive power, represented with ‘S’ and
measured in Volt Ampere.
S= P+ jQ VA or KVA
Reference:
Fundamentals of Electric Circuits by Charles Alexander and Matthew Sadiku
© 2014 Perlekar Tamtam. All rights reserved. Copies may be downloaded from
www.EngageEngineering.org. This material may be reproduced for educational purposes.
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