FIGURE 30.36 shows two coils wrapped on an iron core. The left coil is called the primary coil. It has $N_1$ turns and is driven by an oscillating voltage $V_1\text{cos}\omega t$. The magnetic field of the primary follows the iron core and passes through the right coil, which has $N_2$ turns and is called the secondary coil. The alternating current through the primary coil causes an oscillating magnetic flux through the secondary coil and, hence, an induced emf. The induced emf of the secondary coil is delivered to the load as the oscillating voltage $V_2\text{cos}\omega t$.

FIGURE 30.36 A transformer.

The changing magnetic field inside the iron core is inversely proportional to the number of turns on the primary coil: $B\propto 1\text{/}{N}_1$. (This relation is a consequence of the coil’s inductance, an idea discussed in the next section.) According to Faraday’s law, the emf induced in the secondary coil is directly proportional to its number of turns: ${\epsilon }_{\text{sec}}\propto N_2$. Combining these two proportionalities, the secondary voltage of an ideal transformer is related to the primary voltage by

Depending on the ratio $N_2\text{/}{N}_1$, the voltage $V_2$ across the load can be transformed to a higher or a lower voltage than $V_1$. Consequently, this device is called a transformer. Transformers are widely used in the commercial generation and transmission of electricity. A step-up transformer, with $N_2\gg N_1$, boosts the voltage of a generator up to several hundred thousand volts. Delivering power with smaller currents at higher voltages reduces losses due to the resistance of the wires. High-voltage transmission lines carry electric power to urban areas, where step-down transformers $(N_2\ll N_1)$ lower the voltage to 120 V.