diff --git a/.texpadtmp/main.aux b/.texpadtmp/main.aux index 4bc1719..8aed3c3 100644 --- a/.texpadtmp/main.aux +++ b/.texpadtmp/main.aux @@ -95,5 +95,10 @@ \@writefile{toc}{\contentsline {subsection}{\numberline {15.3}Applications of Sound}{15}{subsection.15.3}} \@writefile{toc}{\contentsline {part}{V\hspace {1em}Electricity and Magnetism}{15}{part.5}} \@writefile{toc}{\contentsline {section}{\numberline {16}Static Electricity}{15}{section.16}} +\@writefile{toc}{\contentsline {subsection}{\numberline {16.1}Electric Fields}{15}{subsection.16.1}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {16.1.1}Isolated Charges}{15}{subsubsection.16.1.1}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {16.1.2}Attraction}{15}{subsubsection.16.1.2}} +\@writefile{toc}{\contentsline {subsubsection}{\numberline {16.1.3}Repulsion}{15}{subsubsection.16.1.3}} +\@writefile{toc}{\contentsline {subsection}{\numberline {16.2}Charging}{15}{subsection.16.2}} \@writefile{toc}{\contentsline {section}{\numberline {17}Current of Electricity}{15}{section.17}} -\@writefile{toc}{\contentsline {section}{\numberline {18}DC Circuits}{15}{section.18}} +\@writefile{toc}{\contentsline {section}{\numberline {18}DC Circuits}{16}{section.18}} diff --git a/.texpadtmp/main.log b/.texpadtmp/main.log index 3610121..b0284c8 100644 --- a/.texpadtmp/main.log +++ b/.texpadtmp/main.log @@ -1,4 +1,4 @@ -This is XeTeX, Version 3.14159265-2.6-0.99996 (TeX Live 2016) (preloaded format=xelatex 2017.3.5) 12 OCT 2018 01:20 +This is XeTeX, Version 3.14159265-2.6-0.99996 (TeX Live 2016) (preloaded format=xelatex 2017.3.5) 13 OCT 2018 00:53 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. @@ -1505,7 +1505,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 26--26 \EU1/STIXTwoText(0)/m/n/10 where $[][]$ is the specific latent heat of fu- [] -) (./content/chapter12.tex [11]) (./content/chapter13.tex [12] [13]) (./content/chapter14.tex) (./content/chapter15.tex [14]) (./content/chapter16.tex) (./content/chapter17.tex) (./content/chapter18.tex) [15] +) (./content/chapter12.tex [11]) (./content/chapter13.tex [12] [13]) (./content/chapter14.tex) (./content/chapter15.tex [14]) (./content/chapter16.tex) (./content/chapter17.tex [15]) (./content/chapter18.tex) [16] Package atveryend Info: Empty hook `BeforeClearDocument' on input line 134. 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set cntrparam levels 18; set contour; set table "main_contourtmp1.table"; splot "main_contourtmp1.dat"; diff --git a/content/chapter16.tex b/content/chapter16.tex index a0a772e..5a511e1 100644 --- a/content/chapter16.tex +++ b/content/chapter16.tex @@ -5,5 +5,83 @@ \begin{preamb} Static electricity is the study of charges at rest. In this chapter we will explore that very concept. \end{preamb} - + + \pdef{Charge}{Charge is measured in coulombs [\si{\coulomb}]. There are positive and negative charges.} + Like charges repel, unlike charges attract. + \begin{center} + \begin{tikzpicture} + \draw [line width=0.5mm, ->] (-2,0) -- (-3,0); + \draw [line width=0.5mm, ->] (2,0) -- (3,0); + \filldraw [fill=white] (-2,0) circle (0.25) node {\(+\)}; + \filldraw [fill=white] (2,0) circle (0.25) node {\(+\)}; + \end{tikzpicture} + \end{center} + \begin{center} + \begin{tikzpicture} + \draw [line width=0.5mm, ->] (-2,0) -- (-3,0); + \draw [line width=0.5mm, ->] (2,0) -- (3,0); + \filldraw [fill=white] (-2,0) circle (0.25) node {\(-\)}; + \filldraw [fill=white] (2,0) circle (0.25) node {\(-\)}; + \end{tikzpicture} + \end{center} + \begin{center} + \begin{tikzpicture} + \draw [line width=0.5mm, ->] (-2,0) -- (-1,0); + \draw [line width=0.5mm, ->] (2,0) -- (1,0); + \filldraw [fill=white] (-2,0) circle (0.25) node {\(+\)}; + \filldraw [fill=white] (2,0) circle (0.25) node {\(-\)}; + \end{tikzpicture} + \end{center} + + \subsection{Electric Fields} + + \pdef{Electric Field}{An electric field is a region of space whereby a charge experiences an electric force.} + + \begin{center} + \begin{tikzpicture} + \foreach \x in {1,...,9} + \node [color=blue, anchor=south] at (0.5*\x,2) {\(-\)}; + \foreach \x in {1,...,9} + \node [color=red, anchor=north] at (0.5*\x,0) {\(+\)}; + \node at (5,1) {\(\vec{\mathbf{E}}\)}; + \draw (0,0) -- (5,0); + \draw (0,2) -- (5,2); + \foreach \x in {1,...,9} + \draw [->] (0.5*\x,0) -- (0.5*\x,2); + \end{tikzpicture} + \end{center} + + \subsubsection{Isolated Charges} + Field lines are the path a test charge would take within that electric field. The tighter the field lines are, the stronger the electric field at that area, which means that the test charge would experience a stronger force. + \begin{center} + \begin{tikzpicture} + \foreach \x in {0,...,7} + \draw [->] (0,0) -- (45*\x:1); + \filldraw [fill=white] (0,0) circle (0.25) node {\(+\)}; + \end{tikzpicture} + \end{center} + Field lines extend out from positive charges. + \begin{center} + \begin{tikzpicture} + \foreach \x in {0,...,7} + \draw [<-] (45*\x:0.25) -- (45*\x:1); + \filldraw [fill=white] (0,0) circle (0.25) node {\(-\)}; + \end{tikzpicture} + \end{center} + Field lines go in to negative charges. + + If a charge is stronger, it gets more field lines (e.g. this one has twice the charge as the one above, so it should get more) + \begin{center} + \begin{tikzpicture} + \foreach \x in {0,...,15} + \draw [->] (0,0) -- (22.5*\x:1); + \filldraw [fill=white] (0,0) circle (0.25) node {\(+\)}; + \end{tikzpicture} + \end{center} + + \subsubsection{Attraction} + + \subsubsection{Repulsion} + + \subsection{Charging} \end{document} diff --git a/content/chapter17.tex b/content/chapter17.tex index 3f7bca3..5d6bb85 100644 --- a/content/chapter17.tex +++ b/content/chapter17.tex @@ -4,5 +4,65 @@ \section{Current of Electricity} \begin{preamb} Current is the rate of flow of charge. When charges move there is current and hence we name this current electricity. In this chapter we will explore the fundamentals that govern current electricity. - \end{preamb} + \end{preamb} + + \pdef{Current}{Current is the rate of flow of charge. \[I = \frac{Q}{t}\] The SI unit of current is ampere [\si{\ampere}].} + + Conventional current is where current flows from a higher voltage to a lower voltage. + \begin{center} + \begin{circuitikz} + \draw (2,2) to[battery1, i^>=\(I\)] (4,2) -- (6,2) -- (6,0) -- (4,0) to[european resistor, i=\(I\)] (2,0) -- (0,0) -- (0,2) -- (2,2); + \end{circuitikz} + \end{center} + + Electron flow is the opposite of that. + \begin{center} + \begin{circuitikz} + \draw (2,2) to[battery1, i<=\(e^-\)] (4,2) -- (6,2) -- (6,0) -- (4,0) to[european resistor, i<=\(e^-\)] (2,0) -- (0,0) -- (0,2) -- (2,2); + \end{circuitikz} + \end{center} + + \pdef{Electromotive Force}{Electromotive force (e.m.f.) is the work done by a source in driving unit charge around a complete circuit. \[E = \frac{W}{Q}\] The SI unit of electromotive force is volt [\si{\volt}].} + + \peqn{Electromotive Forces in Series}{If multiple electromotive force sources are arranged in series + \begin{center} + \begin{circuitikz} + \draw (0,0) to[battery1, v=\(E_1\)] (1,0) to[battery1, v=\(E_2\)] (2,0) to[open] (3,0) to[battery1, v=\(E_n\)] (4,0); + \draw [dashed] (2,0) -- (3,0); + \end{circuitikz} + \end{center} + then the net electromotive force is}{E_\mathrm{net} = E_1 + E_2 + \cdots + E_n} + + + \pdef{Potential Difference}{The potential difference (p.d.) (or voltage) across a component in a circuit as the work done to drive unit charge through the component. \[V = \frac{W}{Q}\] The SI unit of potential difference is volt [\si{\volt}].} + + \pdef{Resistance}{The resistance of a component is the ratio of the potential difference across it to the current flowing through it. \[R = \frac{V}{I}\] The SI unit of resistance is ohm [\si{\ohm}].} + + \peqn{Resistance in Series}{If multiple resistors are arranged in series + \begin{center} + \begin{circuitikz} + \draw (0,0) to[european resistor, l=\(R_1\)] (2,0) to[european resistor, l=\(R_2\)] (4,0) to[open] (5,0) to[european resistor, l=\(R_n\)] (7,0); + \draw [dashed] (4,0) -- (5,0); + \end{circuitikz} + \end{center} + then the net resistance is}{R_\mathrm{net} = R_1 + R_2 + \cdots R_n} + + \peqn{Resistance in Parallel}{If multiple resistors are arranged in parallel + \begin{center} + \begin{circuitikz} + \draw (0,0) to[european resistor, l=\(R_1\)] (2,0) -- (2,-1); + \draw (0,0) -- (0,-1) to[european resistor, l=\(R_2\)] (2,-1) -- (3,-1); + \draw (-1,-1) -- (0,-1) -- (0,-1.25); + \draw (0,-1.75) -- (0,-2); + \draw [dashed] (0,-1.25) -- (0,-1.75); + \draw (2,-1) -- (2,-1.25); + \draw (2,-1.75) -- (2,-2); + \draw [dashed] (2,-1.25) -- (2,-1.75); + \draw (0,-2) to[european resistor, l=\(R_n\)] (2,-2); + \end{circuitikz} + \end{center} + then the effective resistance is}{R_\mathrm{net} = \left(R_1^{-1} + R_2^{-1} + \cdots + R_n^{-1}\right)^{-1}} + + \pdef{Ohm's Law}{Ohm's Law states that the current passing through a metallic conductor is directly proportional lo the potential difference across it, provided that physical conditions (such as temperature) remain constant. \[ V = IR\]} + \end{document} diff --git a/main.pdf b/main.pdf index d68bee8..c461422 100644 Binary files a/main.pdf and b/main.pdf differ diff --git a/main.tex b/main.tex index 25c90b6..f956520 100644 --- a/main.tex +++ b/main.tex @@ -101,7 +101,7 @@ \end{multicols} \newpage -\begin{multicols}{2} +\begin{multicols*}{2} \part{Measurement} \subfile{content/chapter01} @@ -129,6 +129,6 @@ \part{Electricity and Magnetism} \subfile{content/chapter16} \subfile{content/chapter17} \subfile{content/chapter18} -\end{multicols} +\end{multicols*} \end{document}