# 10.9: The Transformer

Two coils are wound on a common iron core. The primary coil is connected to an AC (alternating current) generator of (RMS) voltage \(V_1\). If there are \(N_1 \) turns in the primary coil, the primary current will be proportional to \(V_1 /N_1\) and, provided the core is not magnetically saturated, the magnetic field will also be proportional to this. The voltage \(V_2\) induced in the secondary coil (of \(N_2\) turns) will be proportional to \(N_2\) and to the field, and so we have

\[\dfrac{V_2}{V_1}=\dfrac{N_2}{N_1}.\]

We shall give a more detailed analysis of the transformer in a later chapter. However, one aspect which can be noted here is that the rapidly-changing magnetic field induces *eddy* *currents* in the iron core, and for this reason the core is usually constructed of thin laminated sheets (or sometimes wires) insulated from each other to reduce these energy-wasting eddy currents. Sometimes these laminations vibrate a little unless tightly bound together, and this is often responsible for the "hum" of a transformer.

**Figure 10.9.1**: Idealized single-phase transformer also showing the path of magnetic flux through the core.Magnetic flux is produced by the primary winding, and contained by the high permeability core, links the secondary winding. The mutual inductance between the two windings results in an induced voltage on the secondary side, whose magnitude is determined by the ratio of turns between the two windings. Image used with permission (CC SA-BY 3.0; BillC).