Transformers and Power Transmission

A transformer changes the voltage of an alternating current using electromagnetic induction between two coils wound on a common iron core; the voltage ratio equals the turns ratio, V_s ÷ V_p = N_s ÷ N_p, and for an ideal transformer V_pI_p = V_sI_s. In brief: a step-up transformer (N_s > N_p) raises the voltage and lowers the current; a step-down transformer does the opposite. Power is transmitted at high voltage because the power lost in the lines, I²R, falls steeply when the current is reduced. Transformers work only with AC, since induction requires a changing flux.

Phone chargers, power stations and electrical grids rely on transformers. This guide explains how transformers work, the losses and efficiency, why the grid uses high voltages, compares step-up and step-down transformers in a table, works through numerical examples and corrects common mistakes.

How does a transformer work?

A transformer has a primary coil (N_p turns) connected to the AC supply and a secondary coil (N_s turns) connected to the load, both wound on a laminated soft-iron core. The alternating current in the primary produces a changing magnetic flux in the core, which links the secondary coil and induces an alternating emf in it (Faraday’s law). Since the same flux change goes through each turn of both coils, the emf per turn is the same, so

V_s ÷ V_p = N_s ÷ N_p.

For an ideal (100 percent efficient) transformer, the power in equals the power out: V_pI_p = V_sI_s, so I_s ÷ I_p = N_p ÷ N_s. A step-up transformer increases voltage but reduces current by the same factor. A transformer cannot increase power. If a DC voltage is applied, the flux is constant and no emf is induced in the secondary, so DC cannot be transformed (and the primary may overheat).

What are the losses in real transformers?

Large power transformers reach efficiencies of 98 to 99.5 percent, while small ones are less efficient. The energy is lost as thermal energy in:

• Resistance of the coils (copper losses, I²R): reduced by thick wire of low resistance.
• Eddy currents induced in the core: reduced by using a core made of thin laminated sheets, insulated from each other.
• Hysteresis, the energy needed to repeatedly magnetize and demagnetize the core: reduced by using soft iron or silicon steel.
• Flux leakage: not all the flux from the primary links with the secondary. It is reduced by winding the coils on top of one another on a closed core.

The efficiency is (P_out ÷ P_in) × 100 percent.

Why is power transmitted at high voltage?

Power stations generate electricity at about 10 to 25 kV. The power to be sent is P = VI. The power lost as heat in the transmission lines of resistance R is P_loss = I²R. For a given power, raising the voltage by a factor of ten reduces the current ten times and the line loss a hundred times. For this reason, step-up transformers raise the voltage to 132 kV, 275 kV or 400 kV (or higher) for long-distance lines. Near the consumers, step-down transformers reduce it in stages, to about 11 kV for local distribution and to 230 V (or 120 V) for homes. This system is the main reason why AC was preferred to DC in the “war of the currents” at the end of the 19th century; modern high-voltage DC lines use power electronics for very long links.

Step-up and step-down transformers compared

Worked example: turns, currents and line losses

1. Charger. A transformer reduces 230 V to 12 V. The primary has 1,000 turns. N_s = N_p × V_s ÷ V_p = 1,000 × 12 ÷ 230 = 52 turns.
2. Currents. The secondary supplies 2.0 A at 12 V (24 W). For an ideal transformer, I_p = P ÷ V_p = 24 ÷ 230 = 0.104 A. With an efficiency of 90 percent, the input power is 24 ÷ 0.90 = 26.7 W, and I_p = 26.7 ÷ 230 = 0.116 A.
3. Step-up. 10 MW is transmitted through a line with a total resistance of 5.0 Ω. At 10 kV: I = P ÷ V = 10 × 10⁶ ÷ 10 × 10³ = 1,000 A, and the line loss is I²R = 1,000² × 5.0 = 5.0 MW (50 percent of the power!).
4. At 100 kV: I = 100 A, loss = 100² × 5.0 = 50,000 W = 50 kW, which is 0.5 percent of the power. A tenfold increase in voltage reduces the loss a hundredfold.
5. Efficiency. A transformer takes 5.0 kW and delivers 4.9 kW: efficiency = 4.9 ÷ 5.0 = 98 percent, and 100 W is lost as heat.

How were transformers and the grid developed?

Michael Faraday and Joseph Henry demonstrated the principle in 1831 to 1832. Lucien Gaulard and John Dixon Gibbs developed an early practical transformer for AC distribution in 1881 to 1883, and Ottó Bláthy, Miksa Déri and Károly Zipernowsky of Hungary invented the closed-core transformer in 1885. William Stanley built a commercial system for Westinghouse in 1886 in Great Barrington, Massachusetts. The first large AC power transmission was from Niagara Falls to Buffalo in 1896.

Which mistakes are common?

Mistake 1: Thinking that a step-up transformer gives more power

It raises the voltage and reduces the current. The output power cannot exceed the input.

Mistake 2: Using a transformer with DC

Induction needs a changing flux, so DC gives no output.

Mistake 3: Putting the turns ratio the wrong way round

V_s ÷ V_p = N_s ÷ N_p, but I_s ÷ I_p = N_p ÷ N_s.

Mistake 4: Saying that high voltage reduces the loss because voltage is lower resistance

The loss falls because the current is lower for the same power. The line resistance is unchanged.