32.11 : Transformers

A device that transforms voltages from one value to another using induction is called a transformer. A transformer consists of two separate coils, or windings, wrapped around the same soft iron core. However, they are electrically insulated from each other.

The iron core has a substantial relative permeability. Therefore, the magnetic field lines generated due to the current in one winding are almost entirely confined within the core, such that the same magnetic flux permeates each turn of both the primary and the secondary windings, maximizing the mutual inductance of the two windings.

The primary winding has N_P loops, or turns, and is connected to an alternating voltage source. The secondary winding has N_S turns and is connected to a load resistor. In an ideal transformer, the alternating voltage applied to the primary winding generates magnetic flux, which induces an emf in the secondary winding. Therefore, the output voltage delivered to the load resistor must equal the emf induced across the secondary winding. Consequently, the ratio of the secondary emf to the primary emf equals the ratio of secondary to primary turns. If the windings have zero resistance, the induced emfs are equal to the terminal voltages across the primary and the secondary windings, respectively, and are given by:

This equation is often abbreviated as the transformer equation. In an ideal case, energy losses to magnetic hysteresis, ohmic heating in the windings, and ohmic heating of the induced eddy currents in the core are also ignored.

The induced emf in the secondary winding gives rise to an alternating current that delivers energy to the device to which it is connected. All currents and emfs have the same frequency as the ac source.