170 lines
4.4 KiB
TeX
Executable File
170 lines
4.4 KiB
TeX
Executable File
\documentclass[
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solutions,
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hidewarning,
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singlenumbering,
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nopagenumber
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]{../../resources/ormc_handout}
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\usepackage{../../resources/macros}
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% We put nodes in a separate layer, so we can
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% slightly overlap with paths for a perfect fit
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\pgfdeclarelayer{nodes}
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\pgfsetlayers{main,nodes}
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% Layer settings
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\tikzset{
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% Layer hack, lets us write
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% later = * in scopes.
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layer/.style = {
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execute at begin scope={\pgfonlayer{#1}},
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execute at end scope={\endpgfonlayer}
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}
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}
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\title{The Electrician's Warm-Up}
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\uptitler{\smallurl{}}
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\subtitle{Prepared by Mark on \today}
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\begin{document}
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\maketitle
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Ivan the electician is working in an apartment. He has a box of switches, which come in three types:
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\begin{center}
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\begin{minipage}[t]{0.3\textwidth}
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\begin{center}
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Plain switch
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\end{center}
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\begin{center}
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\begin{tikzpicture}
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% A state
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\node at (0.375, -1.25) {A};
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\draw[line width=1mm] (0, 0) -- (0.75, 0);
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\draw[fill=white] (0, 0) circle (1mm);
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\draw[fill=white] (0.75, 0) circle (1mm);
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% B state
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\node at (2.375, -1.25) {B};
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\draw[line width=1mm,cap=round] (2, 0) -- (2.6, 0.4);
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\draw[fill=white] (2, 0) circle (1mm);
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\draw[fill=white] (2.75, 0) circle (1mm);
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\end{tikzpicture}
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\end{center}
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\end{minipage}
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\begin{minipage}[t]{0.3\textwidth}
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\begin{center}
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Three-way switch
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\end{center}
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\begin{center}
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\begin{tikzpicture}
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% A state
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\node at (0.375, -1) {A};
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\draw[line width=1mm] (0, 0) -- (0.75, 0.5);
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\draw[fill=white] (0, 0) circle (1mm);
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\draw[fill=white] (0.75, 0.5) circle (1mm);
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\draw[fill=white] (0.75, -0.5) circle (1mm);
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% B state
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\node at (2.375, -1) {B};
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\draw[line width=1mm] (2, 0) -- (2.75, -0.5);
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\draw[fill=white] (2, 0) circle (1mm);
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\draw[fill=white] (2.75, 0.5) circle (1mm);
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\draw[fill=white] (2.75, -0.5) circle (1mm);
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\end{tikzpicture}
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\end{center}
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\end{minipage}
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\hfill
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\begin{minipage}[t]{0.3\textwidth}
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\begin{center}
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Four-way switch
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\end{center}
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\begin{center}
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\begin{tikzpicture}
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% A state
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\node at (0.375, -0.5) {A};
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\draw[line width=1mm] (0, 0) -- (0.75, 1);
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\draw[line width=1mm] (0, 1) -- (0.75, 0);
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\draw[fill=white] (0, 0) circle (1mm);
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\draw[fill=white] (0.75, 0) circle (1mm);
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\draw[fill=white] (0, 1) circle (1mm);
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\draw[fill=white] (0.75, 1) circle (1mm);
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% B state
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\node at (2.375, -0.5) {B};
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\draw[line width=1mm] (2, 0) -- (2.75, 0);
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\draw[line width=1mm] (2, 1) -- (2.75, 1);
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\draw[fill=white] (2, 0) circle (1mm);
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\draw[fill=white] (2.75, 0) circle (1mm);
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\draw[fill=white] (2, 1) circle (1mm);
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\draw[fill=white] (2.75, 1) circle (1mm);
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\end{tikzpicture}
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\end{center}
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\end{minipage}
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\end{center}
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A switch is always in the \say{A} or \say{B} state. Its state changes when you toggle the switch on the wall. Each circle represents a terminal on the switch, and lines represent electrical connections. \par
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The two crossing wires in the A state of the four-way switch are \textbf{not} connected.
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\example{}
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First, Ivan wires a simple light in the kitchen: one switch, one lamp. The result is the following circuit:
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\begin{center}
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\begin{tikzpicture}
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\begin{scope}[layer = nodes]
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\draw[fill=white] (-1.5, 0) circle (1mm);
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\node (h) at (-2, 0) {\texttt{Hot}};
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\draw[fill=white] (0, 0) circle (1mm);
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\draw[fill=white] (0.75, 0) circle (1mm);
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\node[
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circle,
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draw = black,
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fill = white,
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label = below:\texttt{Lamp}
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] (l) at (2,0) {$\circledast$};
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\draw[fill=white] (3.5, 0) circle (1mm);
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\node (n) at (4.5, 0) {\texttt{Neutral}};
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\end{scope}
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\draw[line width=1mm,cap=round] (-1.5, 0) -- (0, 0);
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\draw[line width=1mm,cap=round] (0, 0) -- (0.6, 0.4);
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\draw[line width=1mm,cap=round] (0.75, 0) -- (l);
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\draw[line width=1mm,cap=round] (l) -- (3.5,0);
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\end{tikzpicture}
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\end{center}
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\problem{}
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Ivan now needs to wire a hallway. It has two switches, one at each end. \par
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Toggling either switch should toggle the single lamp in the middle. \par
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Which switches should Ivan use, and how should he connect their terminals? \par
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\hint{There are two solutions. One is clever, the other is deadly.}
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\vfill
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\problem{}
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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?
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\vfill
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\problem{Bonus}
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Is it possible to do the same with four or more switches? If so, how?
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\end{document} |