Project Alexandria

2.1f.1 Resistor

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Resistor

A resistor is a circuit component that represents any material tending to resist the flow of current. It follows Ohm’s Law, or .

\usepackage{circuitikz}
\begin{document}
\begin{circuitikz}[american voltages]
 \node at (0,3.75) {Symbol};
 \draw
   (0,0) to [R, v<=$V_{elem}$, i<=$I_{elem}$, l=$R$] (0,3);

\end{circuitikz}
\hspace{1cm}
\begin{tikzpicture}[domain=0:4]
\node at (0,2.25) {IV Relationship};
\draw[<->] (-1.5,0)—(1.5,0) node[below]{};
\draw[<->] (0,-1.5)—(0,1.5) node[left]{};
\draw[<->, color=red] (-1,-1)—(1,1);
\end{tikzpicture}
\hspace{1cm}
\begin{tikzpicture}
\node at (0,2.25) {};
\node at (0,1.75) {};
\node at (0,0){};
\end{tikzpicture}
\end{document}

The SI unit of resistance is called the Ohm ($\Omega$). Resistance can alternatively be calculated using the formula
$$R = \frac{\ell}{\sigma A},$$
where $\ell$ is the length of the object, $A$ is its cross-sectional area, $\sigma$ is its resistivity, and $\rho = \frac{1}{\sigma}$ is its conductivity:
```tikz
\usepackage{tikz}
\usetikzlibrary{3d,calc}

\begin{document}

\begin{tikzpicture}[scale=0.75]

   % Parameters
   \def\R{0.75} % Radius of the cylinder (small size)
   \def\L{12}   % Length of the cylinder (long size)
   \def\A{0.25} % Opacity for transparency effect
   
   % Draw the back face of the cylinder
   \shade[ball color=blue!30, opacity=\A] (\L,0) circle (\R); % Back circle
   \draw[dashed] (\L,0) circle (\R); % Dashed line for transparency
   
   % Draw the sides of the cylinder
   \draw[fill=blue!30, opacity=\A] (0,-\R) -- (\L,-\R) arc[start angle=-90, end angle=90, radius=\R] -- (0,\R) arc[start angle=90, end angle=-90, radius=\R];
   
   % Draw the front face of the cylinder
   \shade[ball color=blue!30, opacity=\A] (0,0) circle (\R); % Front circle
   \draw (0,0) circle (\R); % Front edge
   
   % Draw the wires connected to the cylinder
   \draw[thick] (-1.5,0) -- (0,0); % Left wire
   \draw[thick] (\L,0) -- (\L+1.5,0); % Right wire
   
   % Labels for the cylinder
   \node at (\L/2, 0) {\huge $\sigma$}; % Sigma inside cylinder
   \draw[<->, thick] (-0.75,-2*\R) -- (\L+0.75,-2*\R) node[midway, below]{\huge $\ell$}; % Length indicator arrow across entire diagram
   
   % Label for the cross-sectional area A
   \draw[->, thick] (\L,0) -- ++(1.5,0);
   \node at (\L,0) {\huge $A$}; % Label for cross-sectional area
   
\end{tikzpicture}

\end{document}

The SI unit for conductance is the Siemen (S), given by .

Graph View