Generators and electrical energy transmission

A turbine turns a generator, and voltage is raised before energy enters a long transmission line. What does rotation do, and why does raising voltage help the wires heat up less?

A loop rotates in a magnetic field, continuously changing its orientation. Even with constant B, the flux through the loop changes and a periodic emf arises. This is a simple generator model: a device that converts mechanical work into electrical energy by induction. A magnet can also rotate relative to the windings; what matters is a change in their linked flux. A strong stationary magnet alone cannot provide a continuous energy output.

After half a turn, the flux changes in the opposite sense and the induced voltage reverses. A simple closed circuit with a load therefore carries alternating current. When the generator supplies energy, the induced action opposes rotation. A turbine or another motor must therefore keep driving the shaft. Once the mechanical energy input stops, the previous rotation cannot power the load forever.

A transformer changes voltage. Alternating current in its primary winding creates a changing magnetic flux in a shared core. This flux also passes through the secondary winding, inducing an emf there. The windings need not have any conducting contact: their coupling is magnetic. Electrons therefore do not need to move from one coil to the other for energy to reach a load connected to the secondary.

Replace the alternating current with steady direct current. At switch-on the field changes, so a brief effect is possible; then the flux becomes constant. An ordinary transformer no longer sustains a secondary voltage by this mechanism. Moreover, an unsuitable DC voltage supply can cause excessive current and overheating in the primary winding. A core and two coils therefore cannot replace the requirement for changing flux.

Each turn linked by the same changing flux contributes to the winding voltage. In the ideal model these contributions add: U₁/U₂ = N₁/N₂. Voltages U₁ and U₂ are measured in V; turn counts N₁ and N₂ are dimensionless. At fixed U₁, doubling N₂/N₁ doubles U₂; equal turn counts give equal voltages. The model neglects losses and voltage drops in the windings; it does not promise to create energy.

How can one number describe voltage that changes continuously? Mains problems usually use the root mean square (RMS) value: a constant voltage of that size would produce the same average heating power in the same resistor. It is not the maximum instantaneous value. A transformer's voltage ratio must compare values of the same kind, such as two RMS values. Otherwise the ratio would silently mix different measurement conventions.

The transmission line also has resistance Rлинии. At a given current it dissipates power I²Rлинии that does not reach the consumer. In a simple resistive-load model, transmitted power is UI. Keeping power fixed while raising U reduces I and therefore wire heating. Simply raising the voltage across the same unchanged resistor would instead increase current. The benefit applies specifically to transmitting the same power.

Reduce line current by a factor of 10 at unchanged resistance: (I/10)²R = I²R/100. Losses become 100 times smaller. A transformer matches a higher voltage with a smaller current for the same power; it adds no energy. Input and output powers are equal in an ideal transformer; a real one loses some energy. Voltage cannot be raised without limit: line construction and insulation are designed for specified conditions.

The consumer needs the voltage specified for the equipment, so transformers reduce it near the point of use. The conversion chain is: mechanical work → generator → voltage change → line → voltage reduction → appliance. Domestic mains voltage is still dangerous to touch. It is reduced to suit the equipment, not to make touching conductors permissible.

An ideal transformer has N₁ = 100, N₂ = 500 and RMS U₁ = 12 В. Find RMS U₂.

The secondary has 500 turns compared with 100: N₂/N₁ = 5. With the shared flux, its voltage is five times greater.

From U₁/U₂ = N₁/N₂ we obtain U₂ = U₁·N₂/N₁ = 12·5 = 60 В. Both the given voltage and the voltage sought are RMS values.

Five times the voltage does not mean five times the power. In an ideal transformer, output energy comes from input energy; at a given power, the available current is correspondingly smaller.

U₂ = 60 В. This is the RMS secondary voltage of an ideal transformer with a fivefold turns ratio.

A generator transfers energy supplied by mechanical work to a load through changing magnetic flux.

A transformer couples its windings through a changing field; their voltage ratio is set by their turns ratio.

For the same transmitted power, raising voltage reduces current and lowers line losses according to the square of current.

Light can also carry energy. We will begin optics with light sources and how objects become visible.