Commit a1c5ef6b authored by Timo Meinhof's avatar Timo Meinhof
Browse files

Initial commit

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\documentclass[a4paper]{article}
% tex/output imports
\usepackage[utf8]{inputenc}
\usepackage[unicode=true, hidelinks]{hyperref}
\usepackage{fancyhdr}
\usepackage{varwidth}
% math related imports
\usepackage[fleqn]{amsmath}
\usepackage{amssymb}
\usepackage{mathtools, geometry}
\usepackage[thinc]{esdiff}
% formatting imports
\usepackage{array}
\usepackage{lmodern}
\usepackage{float}
\usepackage{color}
% Images, graphs and code blocks
\usepackage{graphicx}
\usepackage{tikz}
\usepackage{listings}
% Setup header and footer style (fancy)
\fancyhf{} \pagestyle{fancy}
%
\hypersetup{%
pdfstartview=FitH,
pdfnewwindow,
pdfdisplaydoctitle
}
% Tikz setup
\usetikzlibrary{shapes.geometric, arrows}
\tikzstyle{arrow} = [thick,->,>=stealth]
% setup listings (code blocks)
\lstset{frame=tb,
language=python,
aboveskip=3mm,
belowskip=3mm,
showstringspaces=false,
columns=flexible,
basicstyle={\small\ttfamily},
numbers=left,
numberstyle=\tiny\color{gray},
keywordstyle=\color{blue},
commentstyle=\color{dkgreen},
stringstyle=\color{mauve},
breaklines=true,
breakatwhitespace=true,
tabsize=3
}
% Header and footer setup
\setlength{\headheight}{23pt}
\chead{GdS Formelsammlung \\ by Kathrin Maurer, Theresa Engelhardt, Timo Meinhof}
\cfoot{---~\thepage~---}
% Space for newcommands
\newenvironment{formblock}[1]
{
#1:
\begin{equation*}
\qquad
{
}
\end{equation*}
}
\newenvironment{formula}
{
\mathmakebox[0.3\textwidth][l]{
\begin{split}
{
}
% Here goes the input (In math mode)
% Q &= \pm N \cdot e,\; N \in \mathbb{N} \\
% Q &= I \cdot t \\
\end{split}
}
\mathmakebox[0.1\textwidth][l]{}
}
\newenvironment{variables}
{
\mathmakebox[0.45\textwidth][l]{
\begin{split}
{
}
% Here goes the input (In math mode)
% N &: \text{ Anzahl der elemenatar Ladungen}\\
% e &: \text{ Elementarladung} \\
% I &: \text{ Stromstärke} \\
% t &: \text{ Zeit} \\
\end{split}
}
}
\DeclarePairedDelimiter\ceil{\lceil}{\rceil}
\DeclarePairedDelimiter\floor{\lfloor}{\rfloor}
\DeclarePairedDelimiter\paren{\lparen}{\rparen}
\DeclarePairedDelimiter\abs{\lvert}{\rvert}
\begin{document}
\section{Introduktion}
\subsection{Formelzeichen und Einheiten}
\begin{align*}
\text{el. Ladung: }& Q\\
[Q] &= 1 \text{ Coulomb} = 1 C = 1 As \\
\text{Stromstärke: }& I\\
[I] &= 1 \text{ Ampere} = 1 A \\
\text{Stromstärke: }& I\\
[I] &= 1 \text{ Ampere} = 1 A \\
\text{Widerstand: }& R\\
[R] &= 1 \text{ Ohm} = 1 \Omega = 1 \frac{V}{A} = 1 \frac{kg \cdot m^2}{s^3 \cdot A^2}\\
\text{Spannung: }& U\\
[U] &= 1 \text{ Volt} = 1 V \\
\text{Kapazität: }& C\\
[C] &= 1 \text{ Volt} = 1 V \\
\text{Leistung: }& P\\
[P] &= 1 \text{ Watt} = 1 W = 1 VA\\
\text{el. Arbeit: }& W\\
[W] &= 1 \text{ Joule} = 1 J = 1 Ws \\
\text{el. Feldstärke: }& E\\
[E] &= 1 \text{ Volt durch Meter} = 1 \frac{N}{As} = 1 \frac{kg \cdot m}{As^3} = 1 \frac{V}{m} \\
\end{align*}
\subsection{Konstanten}
\begin{align*}
\text{Elementarladung: }& e\\
e &= 1,602176\cdot10^{-19}C \\
\text{el. Feldkonstante: }& \varepsilon_0\\
\varepsilon_0 &= 8,854188\cdot10^{-12} \frac{As}{Vm} \\
\text{Permittivität im Vakuum: }& \varepsilon_r\\
\varepsilon_r &= 1 \text{ im Vakuum}\\
\varepsilon_r &> 1 \text{ im nicht Vakuum} \\
\end{align*}
\pagebreak
\section{Gleichstromrechnung}
\subsection{Elektrische Ladung $Q$}
Allgemein:
\begin{equation*}
\qquad
\mathmakebox[0.3\textwidth][l]{
\begin{split}
Q &= I \cdot t \\
Q &= \pm N \cdot e,\; N \in \mathbb{N}
\end{split}
}
\mathmakebox[0.1\textwidth][l]{}
\mathmakebox[0.45\textwidth][l]{
\begin{split}
I &: \text{ Stromstärke} \\
t &: \text{ Zeit} \\
N &: \text{ Anzahl der elemenatar Ladungen}\\
e &: \text{ Elementarladung}
\end{split}
}
\end{equation*}
Coulombsches Gesetz:
\begin{equation*}
\qquad
\mathmakebox[0.3\textwidth][l]{
\begin{split}
\vec{F} &= \frac{1}{4 \pi \varepsilon_0 \varepsilon_r }\frac{Q_1 \cdot Q_2}{r^2}\vec{e}_r
\end{split}
}
\mathmakebox[0.1\textwidth][l]{}
\mathmakebox[0.45\textwidth][l]{
\begin{split}
r &: \text{ Abstand} \\
\vec{e}_r &: \text{ Einheitsvektor zwischen Ladungen} \\
\varepsilon_0 &: \text{ el. Feldkonstante} \\
\varepsilon_r &: \text{ Permittivität}
\end{split}
}
\end{equation*}
\subsection{Stromstärke $I$}
Allgemein:
\begin{equation*}
\qquad
\mathmakebox[0.3\textwidth][l]{
\begin{split}
I &= \frac{Q}{t} \\
I &= \frac{U}{R} \\
\end{split}
}
\mathmakebox[0.1\textwidth][l]{}
\mathmakebox[0.45\textwidth][l]{
\begin{split}
Q &: \text{ Ladung} \\
t &: \text{ Zeit} \\
U &: \text{ Spannung}\\
R &: \text{ Widerstand}
\end{split}
}
\end{equation*}
\subsection{Spannung $U$}
Allgemein:
\begin{equation*}
\qquad
\mathmakebox[0.3\textwidth][l]{
\begin{split}
U &= R \cdot I \\
\end{split}
}
\mathmakebox[0.1\textwidth][l]{}
\mathmakebox[0.45\textwidth][l]{
\begin{split}
R &: \text{ Widerstand}\\
I &: \text{ Stromstärke}
\end{split}
}
\end{equation*}
\subsection{Widerstand $R$}
Allgemein:
\begin{equation*}
\qquad
\mathmakebox[0.3\textwidth][l]{
\begin{split}
R &= \frac{U}{I} \\
\end{split}
}
\mathmakebox[0.1\textwidth][l]{}
\mathmakebox[0.45\textwidth][l]{
\begin{split}
U &: \text{ Spannung}\\
I &: \text{ Stromstärke}
\end{split}
}
\end{equation*}
\end{document}
# GdS Formelsammlung
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