🔄 Transformer — Mutual Induction

A transformer uses Faraday's law (ε = −N·dΦ/dt) and a shared iron core to couple two coils magnetically. The voltage ratio equals the turns ratio: V₂/V₁ = N₂/N₁. Step up or step down AC voltage by changing the number of primary (N₁) and secondary (N₂) turns.

Preset

Coils

Primary turns N₁ 100 Secondary turns N₂ 400

Source & Load

V₁ peak 120 V Load R 100 Ω Frequency 50 Hz

Output

Turns ratio N₂/N₁4.00

V₂ peak480 V

I₂ peak4.80 A

I₁ peak19.2 A

P₂1152 W

Physics

An AC current in the primary coil (N₁ turns) creates a time-varying magnetic flux Φ through the shared iron core. By Faraday's law, the secondary coil (N₂ turns) develops an EMF ε₂ = −N₂·dΦ/dt. For an ideal transformer the voltage ratio equals the turns ratio: V₂/V₁ = N₂/N₁, and energy conservation gives I₁/I₂ = N₂/N₁. Real transformers have core losses (eddy currents, hysteresis) and winding resistance, reducing efficiency below 100%.

Did you know?

The "War of Currents" (1880–1890s) between Edison (DC) and Tesla/Westinghouse (AC) was decided largely by the transformer: AC voltage can be stepped up for low-loss long-distance transmission and stepped down for safe household use — something DC could not easily do.