Power transmission

Power stations generate electricity at a few thousand volts. To transmit it over long distances:

• A step-up transformer at the station raises the voltage to hundreds of kilovolts. For the same power P = VI, the current I is correspondingly smaller, and the power lost in the line, I²R, falls by the square of the voltage ratio. If the current is reduced to one-hundredth, the loss is reduced to one ten-thousandth.
• Step-down transformers at the distribution areas reduce the voltage (finally to 220 V for homes).
• Transformers are also found in doorbells, chargers, refrigerators and other appliances.

Example 9. A line of resistance 10 Ω transmits 100 kW. At 10 kV: I = 10 A, loss = 1 kW. At 100 kV: I = 1 A, loss = 10 W (a hundred times smaller).

Example 9a. A power of 200 kW is sent through a line of total resistance 0.5 Ω. At 400 V the current is 500 A and the loss is 500² × 0.5 = 125 kW (63% of the power!). At 20 kV the current is 10 A and the loss is 10² × 0.5 = 50 W. The voltage was multiplied by 50, so the loss fell by 50² = 2500 times.