One of the main uses of transformers is in increasing or step up the voltage supplied by power stations for transmission over long distances by power lines. The power is transmitted at high rather than low voltages for the following chain of reasoning.
The typical output from a power station is about 1000 MW. If this were transmitted at ordinary domestic voltages, a high current will be required because of the equation
In this case V is the voltage at which voltage is supplied to the line.
The wires do not have zero resistance so some power will be dissipated because of the equation
V in this derivation is the drop in voltage along the power line, and is not the same as the voltage supplied to the line. Because the current,
is squared, if the current is large then the
and the power dissipated will be very large.
The power dissipated will be proportional to the resistance, and hence proportional to the distance over which transmission takes place because resistance is proportional to length of wire (
).
If the supply voltage is increased then the current will be reduced, again because of the equation P=IV, then the current will be squared and multiplied by the resistance to give the power dissipated, so if the current is reduced by a factor
the power dissipated will be reduced by a factor
High voltages are not without advantages however. High voltages are dangerous. Trespassers inside substations where the power is transformed down to the safer voltage of the domestic supply are regularly electrocuted.