When charge \( Q \), due to an applied voltage \( U \) is transported in the conductor, potential energy is converted into kinetic energy. The kinetic energy \( W \) that a charge gains (\(W\) positive)) or loses (\(W\) negative)) by passing through the voltage \(U\) is given by:
The power \(P\) is defined as the converted energy \(W\) per time period \(t\):
The electric power is obtained by substituting Eq.
The electric current \(I\), is the charge \(Q\) transported per time interval \(t\): \(I = Q/t \). The factor \(Q/t\) is in Eq.
3, so we replace it with \(I\) to eliminate the unknown and experimentally not easily accessible time \(t\). Thus, the electric power becomes:
For an Ohmic conductor (these are those conductors for which Ohm's law applies), Equation
4 can be rewritten using \( U = R \, I \). The power \(P\) can therefore be expressed by the resistance \(R\) of the conductor (or a load) and the applied voltage \(U\):
Of course you can also rearrange Ohm's law \( U = R\,I \) with respect to the current \( I = U/R \), and use it to rewrite the electric power: