Preface
This tutorial was made solely for the purpose of education and it was designed for students taking Applied Math 0330. It is primarily for students who have very little experience or have never used Mathematica before and would like to learn more of the basics for this computer algebra system. As a friendly reminder, don't forget to clear variables in use and/or the kernel.
Finally, the commands in this tutorial are all written in bold black font, while Mathematica output is in regular fonts. This means that you can copy and paste all commands into Mathematica, change the parameters and run them. You, as the user, are free to use the scripts to your needs for learning how to use the Mathematica program, and have the right to distribute this tutorial and refer to this tutorial as long as this tutorial is accredited appropriately.
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Return to Part I of the course APMA0330
Electric Circuits
The resistor element can be plotted assawgraph = Graphics[sawline]
1.1.7. Electric Circuits
display[Table[rcElement // at[{i, 0}], {i, 0, 17, 3}]]
(* The following line adds a connecting wire for a list of points within a framework defined by the Map. The Map is defined by the text and point list. The Text is defined by the Style. *)
connect[pointList_] := {Line[pointList], Map[Text[Style["", FontSize -> 18]] &, pointList[[{1, -1}]]]}
(*The following segment of code is to instantiate each of the elements that will be used in the circuit. If you wanted to include a
switch or any other new element, this would be the section to add it.*)
gap[l_: 1] := Line[l {{{0, 0}, {1/3, 0}}, {{2/3, 0}, {1, 0}}}]
resistor[l_: 1, n_: 3] :=
Line[Table[{i l/(4 n), 1/3 Sin[i Pi/2]}, {i, 0, 4 n}]]
coil[l_: 1, n_: 3] := Module[{
scale = l/(5/16 n + 1/2),
pts = {{0, 0}, {0, 1}, {1/2, 1}, {1/2, 0}, {1/2, -1}, {5/
16, -1}, {5/16, 0}} },
Append[Table[BezierCurve[scale Map[{d 5/16, 0} + # &, pts]], {d, 0,
n - 1}],
BezierCurve[scale Map[{5/16 n, 0} + # &, pts[[1 ;; 4]]]]]]
(*This portion of the code dictates the specifics of the display of
the circuit. In particular, I have a grid with dotted lines.*)
capacitor[l_: 1] := {gap[l],
Line[l {{{1/3, -1}, {1/3, 1}}, {{2/3, -1}, {2/3, 1}}}]}
battery[l_: 1] := {gap[
l], {Rectangle[l {1/3, -(2/3)}, l {1/3 + 1/9, 2/3}],
Line[l {{2/3, -1}, {2/3, 1}}]}}
contact[l_: 1] := {gap[l],
Map[{EdgeForm[Directive[Thick, Black]], FaceForm[White],
Disk[#, l/30]} &, l {{1/3, 0}, {2/3, 0}}]}
Options[display] = {Frame -> True, FrameTicks -> None,
PlotRange -> All, GridLines -> Automatic,
GridLinesStyle -> Directive[Orange, Dashed],
AspectRatio -> Automatic};
display[d_, opts : OptionsPattern[]] :=
Graphics[Style[d, Thick],
Join[FilterRules[{opts}, Options[Graphics]], Options[display]]]
(*This line sets up the framework for adding components to the
circuit at specific positions.*)
at[position_, angle_: 0][obj_] :=
GeometricTransformation[obj,
Composition[TranslationTransform[position],
RotationTransform[angle]]]
(*This generates the specific circuit, which all prior code was \
designed to allow us to do. This is the only part that needs to be \
changed to alter the circuit, providing no new unique elements need \
to be added.*)
label[s_String, color_: RGBColor[.3, .5, .8]] :=
Text@Style[s, FontColor -> color, FontFamily -> "Geneva",
FontSize -> Large];
display[{
battery[] // at[{0, 0}, Pi/2],
connect[{{0, 1}, {0, 2}, {2, 2}}],
resistor[] // at[{2, 2}],
connect[{{3, 2}, {4, 2}, {4, 1}}],
coil[] // at[{4, 0}, Pi/2],
connect[{{4, 0}, {4, -1}, {3, -1}}],
capacitor[] // at[{2, -1}],
connect[{{2, -1}, {0, -1}, {0, 0}}]}]
