Why Power Lines Use High Voltage
A power station sends electricity to a town through a long cable. The cable has resistance, so it heats up and wastes power. See how much is lost, and why raising the voltage fixes it.
The power lost in the line is I2R. The current is I = P / V, so a higher voltage means a much smaller current.
Show the physics and the notes
The problem. A power station makes electrical power P = VI. The power is carried to the town by long cables. A cable is not a perfect conductor, so it has a resistance R (about 0.1 Ω per kilometre for a typical power line). The current I in the cable heats it up, and the power that is turned into heat in the cable, which is wasted, is
Plost = I2R
The solution. The power sent is fixed by what the town needs, P = VI, so the current in the line is I = P/V. Put that into the formula for the power lost:
Plost = (P/V)2 R
The power lost is proportional to 1/V2. If the voltage is doubled, the current is halved, and the power lost is four times smaller. Raising the voltage from 11 kV (from the generator) to 330 kV (a factor of 30) cuts the loss by a factor of 900. That is why power stations use a step-up transformer to raise the voltage for the long journey, and then step-down transformers near the town to bring it down to a safe 240 V for homes. A transformer only works with alternating current (AC), which is the reason mains electricity is AC.
Why not just use thicker cable? A thicker cable has a lower resistance, but it is heavier, more expensive, and needs stronger towers (try the resistance slider). Using high voltage costs only the insulation and the transformers, so it is cheaper. There are limits to going higher: at very high voltages the air breaks down and sparks (corona discharge), and the insulators must be bigger.
What the model leaves out. I treat the line as one resistance R that carries the whole current and the power P is the power that enters the line (so the power that is delivered is P − I2R). Real systems use three phases, the line also has inductance and capacitance (which matter for long AC lines), power factor, and the losses in the transformers (about 1% each). If the loss would be more than the power sent, the line cannot do the job: in that case the picture shows that no power is delivered.
Things to try. (1) Set the voltage to 11 kV and the power to 100 MW. What happens? (2) Find the voltage that makes the loss about 2%. (3) Double the voltage. How does the loss change? (4) Double the length of the line. (5) A thick cable has half the resistance. How could you get the same effect by changing the voltage?
Learn more in the Electrical power lesson. Built for Physics High.