Transformer voltage transformation

A transformer changes an alternating voltage using two coils of wire wound around a shared soft-iron core. The primary coil is connected to the input voltage; the secondary coil provides the output voltage.

The alternating voltage causes an alternating current in the primary coil. This current produces a changing magnetic field in the core. The changing field passes through the secondary coil and induces an alternating voltage across it.

Transformer voltage and turns ratios

The output voltage depends on the number of turns of wire in each coil. For an ideal transformer, the voltage ratio equals the turns ratio:

Here, $$V_{\mathrm{p}}$$ and $$V_{\mathrm{s}}$$ are the primary and secondary voltages, while $$N_{\mathrm{p}}$$ and $$N_{\mathrm{s}}$$ are the numbers of turns on the primary and secondary coils.

A step-up transformer has more turns on its secondary coil than on its primary coil, so the secondary voltage is greater than the primary voltage. A step-down transformer has fewer turns on its secondary coil, so the secondary voltage is lower.

For example, if the secondary coil has three times as many turns as the primary coil, its voltage is three times the primary voltage. An input of $$12\ \mathrm{V}$$ therefore gives an output of $$36\ \mathrm{V}$$.

High-voltage electricity transmission

Electricity is transmitted at high voltage so that the same power can be carried with a lower current. A lower current reduces heating in the transmission cables, so less energy is transferred to the surroundings and transmission is more efficient.

Voltage and current in transmission

Electrical power depends on voltage and current:

Here, $$P$$ is power, $$V$$ is voltage and $$I$$ is current. For a given power, increasing the voltage reduces the current. For example, doubling the voltage halves the current.

Heating in transmission cables

Transmission cables have electrical resistance. As current passes through them, energy is transferred by heating. The rate of this energy transfer is:

Here, $$R$$ is the resistance of the cables. Because the current is squared, reducing it has a large effect: if the current is halved and the resistance stays the same, the heating rate falls to one quarter of its original value. More of the transmitted energy is therefore available for use rather than being transferred to the surroundings.

Transformers in transmission

A step-up transformer raises the voltage before electricity is transmitted. This allows the power to be carried at a lower current, reducing cable heating. Step-down transformers then reduce the voltage for distribution and use.

Ideal transformer power

A transformer transfers electrical power from its primary side to its secondary side. An ideal transformer is 100% efficient: no power is lost, so the power supplied to the primary equals the power delivered by the secondary.

Electrical power is the product of voltage and current. For an ideal transformer:

Here, $$I_{\mathrm{p}}$$ and $$V_{\mathrm{p}}$$ are the primary current and voltage; $$I_{\mathrm{s}}$$ and $$V_{\mathrm{s}}$$ are the secondary current and voltage. Current is measured in amperes and voltage in volts, giving power in watts.

Calculating ideal transformer current

The power equation can be rearranged to find an unknown voltage or current. For example, dividing both sides by $$V_{\mathrm{s}}$$ gives the secondary current:

Suppose the primary voltage is $$120\ \mathrm{V}$$ and its current is $$2\ \mathrm{A}$$. The input power is $$240\ \mathrm{W}$$, so the secondary also delivers $$240\ \mathrm{W}$$. If the secondary voltage is $$240\ \mathrm{V}$$, its current is $$1\ \mathrm{A}$$.

For a given transferred power, stepping up the voltage reduces the current: in this example, doubling the voltage halves the current. Conversely, stepping down the voltage increases the current. The voltage and current change in opposite proportions so that their product remains the same.