Chapter 5 · Induction: how motion becomes electricity
Generators, transformers and the grid
Induction
In 1831 Michael Faraday pushed a magnet into a coil and the needle of a meter jumped; pulling it out made the needle jump the other way. The American Joseph Henry saw the same effect independently. A changing magnetic field creates a voltage. The size of it is EMF = N·ΔΦ / Δt, where N is the number of turns, ΔΦ the change of magnetic flux in webers and Δt the time in seconds. A coil of 200 turns with the flux changing by 0.002 Wb in 0.1 s gives 200 × 0.002 / 0.1 = 4 V. Hold the magnet still and nothing happens.
The turbine hall
A generator is induction on repeat. A coil spins in a strong magnetic field and the voltage swings back and forth. In coal, gas and nuclear stations, heat boils water into steam that blows on turbine blades; in a dam falling water does the job; in a wind farm, the wind. For N turns of area A in a field B turning at angular speed ω, the peak voltage is N·B·A·ω. With N = 100, B = 0.5 T, A = 0.02 m² and 50 turns per second (ω = 2π × 50 ≈ 314 rad/s), the peak is 100 × 0.5 × 0.02 × 314 ≈ 314 V. The effective value is the peak divided by √2: about 222 V.
AC and the war of currents
The voltage from a spinning coil alternates, so we call it alternating current, AC. Batteries give direct current, DC. Mains in Europe and Russia alternates 50 times a second (50 Hz) at 230 V; in the USA it is 60 Hz at 120 V. In the 1880s Edison's DC systems competed with AC systems backed by George Westinghouse and Nikola Tesla, and AC won because a transformer can change its voltage. A transformer has two coils on one iron core: V₂ / V₁ = N₂ / N₁. With 230 V on 1,000 turns and 50 turns on the other side, the output is 230 × 50 / 1,000 = 11.5 V.
Why the lines use high voltage
Long lines waste energy as heat: P_loss = I²R. Send 10 MW through a line of 5 Ω. At 10 kV the current is 10,000,000 / 10,000 = 1,000 A, and the loss is 1,000² × 5 = 5 MW, half of everything sent. Step up to 100 kV and the current falls to 100 A, so the loss is 100² × 5 = 50 kW, only 0.5 percent. Ten times the voltage gives a hundred times less loss. That is why the pylons in the scene carry hundreds of kilovolts. Stay far away from pylons, substations and fallen wires.
From station to socket
Follow the electricity through the scene. A transformer at the station steps the voltage up, lines carry it across the country, substations step it down in stages, and a last transformer on your street brings it to 230 V. The grid must match supply to demand every second. Your meter counts energy in kilowatt-hours: power in kW times time in hours. A 2 kW kettle running for 3 minutes uses 2 × 0.05 = 0.1 kWh. One kWh is 1,000 W × 3,600 s = 3.6 MJ, so the kettle used 360 kJ.
Light into current
A solar panel has no moving parts. Light knocks electrons loose at the junction between two layers of silicon and that creates a voltage: the photovoltaic effect, noticed by Edmond Becquerel in 1839. Bell Labs made the first practical silicon cell in 1954. In full sun, about 1,000 W per square metre, a 1.7 m² panel with 20 percent efficiency gives 1.7 × 1,000 × 0.20 = 340 W. In the scene the panels face the Sun, and the current they make runs through an inverter that turns DC into AC for the grid.
Catching the wind
A wind turbine catches P = ½·ρ·A·v³ of the wind, where ρ ≈ 1.2 kg/m³ is the density of air, A the area swept by the rotor and v the wind speed. For a rotor 100 m across, A = π × 50² ≈ 7,850 m². At 10 m/s the wind carries ½ × 1.2 × 7,850 × 10³ ≈ 4.7 MW, and a real turbine captures about 40 percent, roughly 1.9 MW. The cube matters: double the wind speed and the power grows eight times. Use the sandbox to turn the turbine and change the magnet's strength.
In numbers
- 1831
- Faraday discovers electromagnetic induction
- 50 / 60 Hz
- mains frequency in Europe and Russia / the USA
- × 100
- less line loss when the voltage rises ten times