Transformer Principle

Two coils of wire share an iron core. Send AC through one coil, and voltage appears in the other, even though they are not electrically connected. The ratio of input to output voltage equals the ratio of turns in each coil. This principle, discovered in the 1830s, is the reason electricity can travel hundreds of miles from a power plant to your home.

The transformer principle works through electromagnetic induction. AC in the primary coil creates a changing magnetic field in the shared iron core. That changing field induces a voltage in the secondary coil (Faraday's law). The voltage ratio equals the turns ratio: V_out / V_in = N_out / N_in. Power is conserved (minus small losses), so if voltage goes up, current goes down by the same factor: V_in x I_in = V_out x I_out.

A step-up transformer (more secondary turns) increases voltage and decreases current. A step-down transformer (fewer secondary turns) does the reverse. The grid uses step-up transformers at power plants (20 kV to 345-765 kV for transmission) and step-down transformers at substations and on utility poles (back to 120/240 V for homes).

Worked Example

A transformer has 200 primary turns and 10,000 secondary turns. Input: 20 kV at 1,000 A.

• Calculate output voltage. V_out = 20 kV x (10,000/200) = 20 kV x 50 = 1,000 kV.
• Calculate output current. I_out = 1,000 A / 50 = 20 A (power conserved).

If a second, identical transformer stepped that 1,000 kV output back down to 20 kV, what current would flow on the low side?

Power is conserved end to end: 1,000 kV x 20 A = 20 MW in, so 20 MW out at 20 kV means 20 MW / 20 kV = 1,000 A on the low side, the same current the line started with. The transformer changed voltage and current in each direction but never touched the power.

The transformer principle is a direct application of Faraday's law, and it is the physical reason the grid can exist at continental scale.

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