A transformer is one of the simplest yet most consequential electrical devices ever invented. It transfers electrical energy between two circuits through electromagnetic induction — no moving parts, no physical contact. Every wall charger, power grid substation, and welding machine relies on this principle.

How it works: Two coils of wire (the primary and secondary windings) are wrapped around a shared iron core. When AC current flows through the primary, it creates a changing magnetic field in the core, which induces a voltage in the secondary. DC won't work — the field must be changing to induce anything.

The turns ratio is the fundamental relationship:

V_s / V_p = N_s / N_p

where V is voltage and N is the number of turns on each winding. If the secondary has more turns, voltage goes up (step-up). Fewer turns, voltage goes down (step-down). Power is conserved (minus losses), so when voltage goes up, current goes down proportionally:

V_p × I_p ≈ V_s × I_s

Calculation example: You need to step 240V mains down to 24V for an industrial control circuit. The turns ratio is 240/24 = 10:1. If your primary winding has 500 turns, the secondary needs 50 turns. If the load draws 2A at 24V (48W), the primary side draws only 0.2A at 240V — same power, different voltage-current tradeoff.

Real-world application: This is exactly why power grids use high-voltage transmission (138kV–765kV). Transmitting 1MW at 500kV requires only 2A, meaning thin wires and minimal I²R resistive losses. Step-up transformers at the power plant boost voltage for transmission; step-down transformers at substations and on utility poles reduce it back to 120/240V for your outlets.

Core losses to know about:

• Hysteresis loss: Energy wasted reversing the magnetic domains in the core each cycle. Reduced by using silicon steel or ferrite cores.
• Eddy current loss: Circulating currents induced in the core itself. Reduced by laminating the core — stacking thin, insulated sheets instead of using a solid block.
• Copper loss (I²R): Resistive heating in the windings themselves. Reduced by using thicker wire.

Rule of thumb: Well-designed power transformers achieve 95–99% efficiency. Smaller transformers (like wall adapters) sit at the lower end; large utility transformers approach the upper end. If your transformer is running hot, suspect it's either overloaded, operating at the wrong frequency, or has shorted turns.