Electricity is often generated a long way from where it is used, and is transmitted long distances through power lines. Although the resistance of a short length of power line is relatively low, over a long distance the resistance can become substantial. A power line of resistance R causes a power loss of I²R ; this is wasted as heat. By reducing the current, therefore, the I²R losses can be minimized.

Power companies use step-up transformers to boost the voltage to hundreds of kV before it is transmitted down a power line, reducing the current and minimizing the power lost in transmission lines. Step-down transformers are used at the other end, to decrease the voltage to the 120 V used in household circuits.

Example

Let's say a power company generates electricity with a voltage of 2400 V and a current of 1000 A. This is a 2.4 MW power plant.
(a) How much power is lost by sending this current through a 10 W transmission line?
(b) If the voltage is boosted to 240 kV before the current is sent through the transmission line, how much power is lost now? Assume the transformer is ideal (i.e., no energy is lost in the transformer).
(c) At the other end of the transmission line the voltage is transformed to 120 V. How much current is available?

(a) The power dissipated in the transmission line is I²R = 10 MW. This doesn't make any sense, seeing as that's more than we had to start with...but we'd essentially lose all of it.

(b) With an ideal transformer, if the voltage is increased by a factor of 100 the current is decreased by a factor of 100, so the current is 10 A. The power lost now is:
I²R = 1000 W, basically negligible compared to the 2.4 MW we started with.

(c) Ignoring the 1000 W lost in transmission, transforming the voltage to 120 V gives:

I

=

2.4 x 106 120

=

20000 A, enough to meet the needs of a few hundred homes.