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 difference
is applied along a conductor, causing it to carry a current
heat 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 for
gives
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 is
the power dissipated is then
