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Added electrician's warm-up

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2023-01-08 10:34:53 -08:00
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Misc/Warm-Ups/electician.tex Executable file
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% 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}