diff --git a/Misc/Warm-Ups/electician.tex b/Misc/Warm-Ups/electician.tex new file mode 100755 index 0000000..f360d40 --- /dev/null +++ b/Misc/Warm-Ups/electician.tex @@ -0,0 +1,160 @@ +% https://git.betalupi.com/Mark/latex-packages +% use [nosolutions] flag to hide solutions. +% use [solutions] flag to show solutions. +% Last built with version 1.1.0 +\documentclass[ + nosolutions, + singlenumbering +]{ormc_handout} + +% We put nodes in a separate layer, so we can +% slightly overlap with paths for a perfect fit +\pgfdeclarelayer{nodes} +\pgfsetlayers{main,nodes} + +% Layer settings +\tikzset{ + % Layer hack, lets us write + % later = * in scopes. + layer/.style = { + execute at begin scope={\pgfonlayer{#1}}, + execute at end scope={\endpgfonlayer} + } +} + +\begin{document} + + \maketitle + {The Electrician's Warm-Up} + {Prepared by Mark on \today} + + Ivan the electician is working in an apartment. He has a box of switches, which come in three types: + \begin{center} + \begin{minipage}[t]{0.3\textwidth} + \begin{center} + Plain switch + \end{center} + \begin{center} + \begin{tikzpicture} + % A state + \node at (0.375, -1.25) {A}; + \draw[line width=1mm] (0, 0) -- (0.75, 0); + + \draw[fill=white] (0, 0) circle (1mm); + \draw[fill=white] (0.75, 0) circle (1mm); + + % B state + \node at (2.375, -1.25) {B}; + \draw[line width=1mm,cap=round] (2, 0) -- (2.6, 0.4); + + \draw[fill=white] (2, 0) circle (1mm); + \draw[fill=white] (2.75, 0) circle (1mm); + \end{tikzpicture} + \end{center} + \end{minipage} + \begin{minipage}[t]{0.3\textwidth} + \begin{center} + Three-way switch + \end{center} + \begin{center} + \begin{tikzpicture} + % A state + \node at (0.375, -1) {A}; + \draw[line width=1mm] (0, 0) -- (0.75, 0.5); + + \draw[fill=white] (0, 0) circle (1mm); + \draw[fill=white] (0.75, 0.5) circle (1mm); + \draw[fill=white] (0.75, -0.5) circle (1mm); + + % B state + \node at (2.375, -1) {B}; + \draw[line width=1mm] (2, 0) -- (2.75, -0.5); + + \draw[fill=white] (2, 0) circle (1mm); + \draw[fill=white] (2.75, 0.5) circle (1mm); + \draw[fill=white] (2.75, -0.5) circle (1mm); + \end{tikzpicture} + \end{center} + \end{minipage} + \hfill + \begin{minipage}[t]{0.3\textwidth} + \begin{center} + Four-way switch + \end{center} + \begin{center} + \begin{tikzpicture} + % A state + \node at (0.375, -0.5) {A}; + \draw[line width=1mm] (0, 0) -- (0.75, 1); + \draw[line width=1mm] (0, 1) -- (0.75, 0); + + \draw[fill=white] (0, 0) circle (1mm); + \draw[fill=white] (0.75, 0) circle (1mm); + \draw[fill=white] (0, 1) circle (1mm); + \draw[fill=white] (0.75, 1) circle (1mm); + + % B state + \node at (2.375, -0.5) {B}; + \draw[line width=1mm] (2, 0) -- (2.75, 0); + \draw[line width=1mm] (2, 1) -- (2.75, 1); + + \draw[fill=white] (2, 0) circle (1mm); + \draw[fill=white] (2.75, 0) circle (1mm); + \draw[fill=white] (2, 1) circle (1mm); + \draw[fill=white] (2.75, 1) circle (1mm); + \end{tikzpicture} + \end{center} + \end{minipage} + \end{center} + + When a switch is pointing up, it is in the \say{A} state. When it is pointing down, it is in the \say{B} state. Each circle represents a terminal on the switch, and lines represent electrical connections. + + \example{} + First, Ivan wires a simple light in the kitchen: one switch, one lamp. The result is the following circuit: + + \begin{center} + \begin{tikzpicture} + + \begin{scope}[layer = nodes] + + \draw[fill=white] (-1.5, 0) circle (1mm); + + \node (h) at (-2, 0) {\texttt{Hot}}; + + \draw[fill=white] (0, 0) circle (1mm); + \draw[fill=white] (0.75, 0) circle (1mm); + + \node[ + circle, + draw = black, + fill = white, + label = below:\texttt{Lamp} + ] (l) at (2,0) {$\circledast$}; + + \draw[fill=white] (3.5, 0) circle (1mm); + + \node (n) at (4.5, 0) {\texttt{Neutral}}; + + \end{scope} + + \draw[line width=1mm,cap=round] (-1.5, 0) -- (0, 0); + \draw[line width=1mm,cap=round] (0, 0) -- (0.6, 0.4); + \draw[line width=1mm,cap=round] (0.75, 0) -- (l); + \draw[line width=1mm,cap=round] (l) -- (3.5,0); + \end{tikzpicture} + \end{center} + + \problem{} + Ivan now needs to wire a hallway. It has two switches, one at each end. Toggling either switch should toggle the single lamp in the middle. Which switches should Ivan use, and how should he connect their terminals? + + \vfill + + + \problem{} + Next, Ivan goes to the bedroom. There is one switch by the door and one on each side of the bed. How can he make these three switches control one lamp? + + \vfill + + \problem{Bonus} + Is it possible to do the same with four or more switches? If so, how? +\end{document} \ No newline at end of file