Circuit Phasor Diagram for Transformers

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This Demonstration shows the equivalent circuit phasor diagram for a transformer.


A power source supplies a voltage that is some combination of sine waves, represented by a phasor diagram. For , the phasor diagram would be a unit vector rotating about the origin. A more complex circuit gives a combination of these, representing the changes in electromagnetic quantities as circuit parameters are varied.


Contributed by: Anping Zeng (May 2012)
(Sichuan Chemical Technical College)
Open content licensed under CC BY-NC-SA



The resistances and are the physical resistances of the primary and the secondary windings.

The reactances and , known as leakage reactances, account for the magnetic coupling between the primary and the secondary.

is the excitation resistance.

The reactance , known as the magnetizing reactance, allows for the current required to magnetize the core when the reluctance is not zero.

is iron core resistance with .

is the load resistance on the secondary winding.

The reactance is the load reactance on the secondary winding.

is the load resistance.

is the primary current and the secondary current.

is the no load current in the primary turns, is the watt current, and and is the reactive current.

is the primary voltage and is the secondary voltage.

is the primary electromotive force and is the secondary electromotive force.

is the primary leakage inductance electromotive force and is the secondary leakage inductance electromotive force.

is the ratio of primary-to-secondary turns.


[1] Wikipedia. "Transformer." (May 28, 2012)

[2] S. Chapman, Electric Machinery Fundamentals, 4th ed., New York: McGraw–Hill, 2005.

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