Transformers

Electromagnetic induction devices for transforming AC voltage levels while maintaining power.

Conceptual context

A transformer is a static device that transfers electrical energy between two circuits through mutual electromagnetic induction. Unlike generators and motors, it has no moving parts: energy transfer occurs entirely through the magnetic field in a shared ferromagnetic core.

Transformers are the backbone of worldwide electrical power systems. They allow voltage to be raised for transmission over large distances with minimal losses, and then reduced for domestic and industrial use. Every phone charger, every electrical substation and every distribution network depends on them. Understanding their operation is understanding how electrical energy travels from generating power stations to the sockets in our homes.

🟢 Essential level

A transformer consists of two wire windings wrapped around an iron core. When alternating voltage is applied to the primary winding, a varying magnetic field is generated that passes through the core. This varying field induces a voltage in the secondary winding, allowing energy transfer without direct electrical connection between the two circuits.

The relationship between input and output voltages depends only on the number of turns in each winding. If the secondary has more turns than the primary, the voltage increases. If it has fewer, the voltage decreases. Current behaves inversely: where voltage rises, current falls proportionally, maintaining constant transferred power.

This symmetry between voltage elevation and current reduction is the key to efficient electrical transport. Joule losses in transmission cables depend on the square of the current, so raising the voltage and reducing the current dramatically minimizes losses over long distances. That is precisely why power lines crossing a country run at hundreds of thousands of volts rather than at the voltage used inside a home.

🔵 Formal level

Basic formulas

The mathematical description of the ideal transformer starts from Faraday's law of electromagnetic induction. The alternating voltage applied to the primary of $N_1$ turns generates an alternating magnetic flux in the core. The relationship between primary $V_1$ and secondary $V_2$ voltages is directly proportional to the ratio between the number of turns:

Voltage transformation ratio

This equation reveals that voltage transformation is purely geometric, depending only on the turns ratio $N_1$/$N_2$. A step-up transformer has $N_2$ > $N_1$, while a step-down transformer has $N_2$ < $N_1$.

Power conservation in the ideal transformer implies that apparent power in the primary equals that in the secondary. Since power is the product of voltage and current, the currents must obey an inverse relationship:

Current transformation ratio

Real student questions

Why doesn't a transformer work with direct current? Because a varying magnetic field is needed to induce voltage in the secondary. With DC, the flux is constant and there is no induction.

Why does a transformer make noise? Due to magnetostriction: the iron core slightly changes dimensions when magnetized cyclically, generating mechanical vibrations.

Can a transformer increase power? No. The active power output is always less than the input due to losses. It only transforms the voltage-current product, maintaining approximately constant power.

What happens if I overload a transformer? Copper losses grow with the square of the current, generating excessive heat that can damage the insulation and cause internal short circuits.

Final synthesis

The transformer transfers electrical energy between circuits through mutual electromagnetic induction in a common ferromagnetic core. The transformation ratio between voltages is direct to the turns ratio, while between currents it is inverse, conserving power. Copper and iron losses reduce efficiency below 100%, although modern transformers achieve efficiencies above 98%. The absence of moving parts makes them robust and reliable, constituting the fundamental element of modern electrical power systems.