Electric power
Describe the transfer of energy into, out of, or within an electric circuit, in terms of power.
The rate at which energy is transferred, converted, or dissipated by a circuit element depends on the current in the element and the electric potential difference across it. \[\begin{equation} P = I \delta V \end{equation}\] \[\begin{equation} P = I^2 R = \dfrac{\Delta V^2}{R} \end{equation}\]
The brightness of a lightbulb increases with power, so power can be used to qualitatively predict the brightness of lightbulbs in a circuit.
In addition to sources, a simple circuit might have passive components such as resistors, capacitors, and inductors.
Resistors
Resistors are devices that dissipate electrical energy. They are given the symbol \(R\) and are depicted on circuit diagrams as shown in figure \[fig:resistor\].
(0,2) to \[R=$R$,v=$e_R$, i=$i_R$\] (0,0);
The constitutive relationship for the resistor in figure \[fig:resistor\] is given by Ohm’s Law: \[\begin{equation} e_R = i_R R \quad \mbox{Ohm's Law} \end{equation}\] where \(R\) is a constant called the resistance. Resistance is measured in units of Ohms (Ω). Resistors are available in resistances from 1 Ω to several thousand (kΩ) or million (MΩ). The resistance value is marked as a series of colored bands (see figure \[fig:resistor-bands\]). Several colorful mnemonics (some dating to WWII and wildly inappropriate today) exist for learning the resistor color code. A meter may be used to check resistance values before installation, but the color bands are useful for quality assurance and verifying the correct resistors are installed in a circuit.
| black brown red orange yellow | 0 1 2 3 4 | green blue violet grey white | 5 6 7 8 9 |
| tolerances: no band silver gold | ± 20 % ± 10 % ± 5 % |
The power dissipated in a resistor (“Ohmic heating”) is given by the voltage times the current: \[\begin{equation} P = e i = \frac{e^2}{R} = i^2 R \end{equation}\]
A smal low-power resistor used as a discrete device on a circuit board might have a power rating of 1/8 or 1/4 W, while very large power resistors (often in tubular geometries with means for cooling) may be used for braking in motor drives and transport systems like electric-drive buses; or as heaters in plants or industrial processes.
See also
- list here