## Power Dissipation in a Conductor

When a conductor carries a current, the process is not 100% efficient. The conductor heats up so some of the energy used to drive the current through the wire is wasted as heat. We can find an expression for the amount of energy so wasted.

We can write this as

We can write this as

Multiply these together to obtain

This means that when a potential differenceis applied along a conductor, causing it to carry a currentheat is generated in the conductor at a rate,

We can obtain other expression for the power consumed using Ohm's law,

Substituting this directly into the equation forgives

Alternatively we can write

Hence

It is important to realise that V above is the potential difference (also called the voltage drop) across the conductor, and not the voltage applied to one ened. For instance, a power cable may have a voltage applied at one end of 4000 V, but the voltage drop may be only 40V across the entire length of the conductor. If the resistance of the conductor isthe power dissipated is then