Electrical Engineering BMT & UFC › Electrical Fundamentals

Electrical Power and Energy

Separating charge requires a force. Once charge has been separated, the electrical energy in the system has increased. The process of charge separation corresponds to an electrical power that caused the change in energy. For charge separation, the following applies:

\[ \begin{gathered} P_{\mathrm{el}}(t) = U(t) \cdot I(t) \\[6pt] P_{\mathrm{el}}(t) = \frac{dW_{\mathrm{el}}(t)}{dt} \\[6pt] W_{\mathrm{el}}(t) = W_0 + \int P_{\mathrm{el}}(t)\,dt \\[6pt] \text{Special case } P(t) = \text{constant and } W_0 = 0\text{:} \\[6pt] W_{\mathrm{el}}(t) = P_{\mathrm{el}}(t) \cdot t = U(t) \cdot I(t) \cdot t \\[6pt] \text{With } I(t) = \frac{Q(t)}{t} \\[6pt] W_{\mathrm{el}}(t) = Q(t) \cdot U(t) \end{gathered} \]

Integration is the inverse of differentiation. So the energy after charge separation corresponds to the time integral of the power. We can also describe the energy as the product of voltage and charge.

So we calculate electrical power as voltage times current. The energy is the integral of the power over time. We achieve an effect when electrical power is used to convert electrical energy into, for example, kinetic energy. In electrical engineering, there is only power when voltage and current are present at the same time.

A voltage is always present at a socket. A full battery also always has a voltage at its terminals. As long as we do not connect a load through which current flows, the power is 0. Only when, for example, an LED is connected to the battery does current flow through the LED. Then voltage and current, and thus power, are present at the same time. Now electrical energy is converted into light energy. The amount of energy change per unit of time corresponds to the power.

A voltage without current is like a stone lying on a table and not moving. It is attracted by the Earth, so a force acts on it. But nothing happens. Only when we remove the table and force and movement are present at the same time do the energies in the system change.

Further information

Leifi-Physik (in German)