# Derivation: Electric Power 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:

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The power $$P$$ is defined as the converted energy $$W$$ per time period $$t$$:

Definition of power quantity
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The electric power is obtained by substituting Eq. 1 into 2:

Electric power using charge, voltage and time
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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:

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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 $$U$$:

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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:

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