Power
Power indicates how quickly work is performed or energy is transferred. It is defined as the amount of energy converted per unit of time. The SI unit of power is the watt (W), where one watt corresponds to one joule per second. In other words, the work described above is the integral of power over time.
\begin {equation} W = \int P \cdot \mathrm {d}t \end {equation}
By rearranging the formula, we see that power \(P\) is the change in work over time.
\begin {equation} P = \frac {\mathrm {d}W}{\mathrm {d}t} \label {eq:PdWdt} \end {equation}
1 The electrical power
In the case of electrical power, assuming constant work over time after the onset of electrical work \(W_\mathrm {{el}}\), the following expression results from formula ??:
\begin {equation} P = \frac {W_\mathrm {{el}}}{t} = \frac {U \cdot I \cdot \cancel {\phantom {t}t\phantom {t}}} {\cancel {\phantom {t}t\phantom {t}}} = U \cdot I [P] = \text {1 Watt = 1 W} \end {equation}
2 The different power types
In addition to electrical power, there are other power quantities that result from the various forms of energy.
Furthermore to the forms of energy discussed in section ??, the corresponding power quantities are listed in
the following table. In each case, the potential quantity is multiplied by the flux quantity. The table only
applies to direct current.
| Types | Potential value | Flow rate | Formula |
| Electric | Voltage (\(U\)) | Current (\(I\)) | \(P_{\text {el}} = U \cdot I\) |
| Translatorical | Force (\(F\)) | Velocity (\(v\)) | \(P_{\text {tr}} = F \cdot v\) |
| Rotational | Moment (\(M\)) | Angular velocity (\(\omega \)) | \(P_{\text {rot}} = M \cdot \omega \) |
| Thermal | Temperature diff. (\(\Delta T\)) | Heat transfer (\(k\cdot A \)) | \(P_{\text {th}} = \Delta T \cdot k \cdot A\) |
| Fluidic | Pressure (\(p\)) | Volume flow (\(\mathrm{d}ot {V}\)) | \(P_\mathrm {f_{l}} = p \cdot \mathrm{d}ot {V}\) |
Key point:
Electrical work measures the energy transferred, while electrical power indicates the transfer speed.
The different types of power are relevant to the efficiency of a system. As a rule, in addition to the desired power, undesirable power also occurs, which should be avoided if possible. This is discussed in the following section on efficiency.
