Power

Electric power

• Electric power is the rate of transfer of electrical energy within a circuit
• $P=\frac{dE}{dt}=\frac{dE}{dq}\frac{dq}{dt}=VI$
  • $E$ is electrical energy (in joules)
  • $t$ is time (in seconds)
  • $P$ is power (in watts)
  • $V$ is voltage (in volts)
  • $I$ is current (in amperes)
  • $q$ is charge (in coulombs)
• $P=I^{2}R=\frac{V^2}{R}$
  • $P$ is the power dissipated by the resistor (in $\mathsf{W}$)
  • $R$ is the resistance of the resistor (in $\mathsf{\Omega }$)
  • $I$ is the current through the resistor (in $\mathsf{A}$)

Passive sign convention

todo

• Components of an electrical circuit
  • Voltage source
    • Terminals:
      • Positive voltage terminal (higher voltage)
      • Negative voltage terminal (lower voltage)
• Passive sign convention (PSC)
  • electric power is positive if it flows out of the circuit into an electrical component
  • electric power is negative if it flows into the circuit out of a component
  • Passive components (loads) will have positive power dissipation ($P>0$) and positive resistance ($r>0$)
  • Active components (sources) will have negative power dissipation ($P<0$) and negative resistance ($r<0$)
  • The conventional current variable $I$:
    • If $i$ is defined such that positive current enters the device through the positive voltage terminal:
      • $P=VI$ and $R=\frac{V}{I}$
    • If $i$ is defined such that positive current enters the device through the negative voltage terminal:
      • $P=-VI$ and $R=-\frac{V}{I}$

\usepackage{color,graphicx,circuitikz}
\begin{document}
\begin{circuitikz}[american]
\draw (0,0) to [V, l={$v$}](2,0) to[short, =>, i=$i$](3,0);
\end{circuitikz}
\end{document}