# Derivation Electric Power

**Level 2**requires school mathematics. Suitable for pupils.

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:

**Electrical energy**

The **power** \(P\) is defined as the converted energy \(W\) per time period \(t\):

**Definition of power quantity**

The electric power is obtained by substituting Eq. 1

into 2

:

**Electric power using charge, voltage and time**

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:

**Electric power (with U, I)**

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 \(U\):

**Electric power (with U, R)**

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:

**Electric power (with I, R)**