Circuit Equations:Transformer

The application of the voltage law to both primary and secondary circuits of a transformer gives:

The transformer is the most common application of the concept of mutual inductance. In the transformer, the effect of the mutual inductance is to cause the primary ciruit to take more power from the electrical supply in response to an increased load on the secondary. For example, if the load resistance in the secondary is reduced, then the power required will increase, forcing the primary side of the transformer to draw more current to supply the additional need.

Circuit Equations: Transformer

The secondary circuit equation is that of an RC circuit driven by a voltage source: The primary circuit current is given by:

Note that the effective impedance of the primary circuit contains not only the coupling of the mutual impedance, but contains terms dependent upon the secondary load resistor R. When R is smaller (greater load) , ZP becomes smaller and more resistive, taking more power from the primary source. For ideal coupling, the mutual inductance becomes

There is a practical midrange of load resistances for the operation of a transformer. In the example above, you can see that maximum output power is obtained with a load resistance between 15 and 20 ohms. When too heavy a load is drawn from the secondary, the primary coil heats up and the amount of audible "hum" that you hear from the transformer increases. My brother, Edgar Nave, worked in commercial electrical construction and wired many large transformers. He reports incidents when the secondary of a transformer was shorted, and says that the transformer would "squawl" like a wounded beast before it burned up the primary coil.