112 lines
2.9 KiB
TeX
112 lines
2.9 KiB
TeX
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\documentclass[12pt,a4paper,german]{article}
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\usepackage{url}
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%\usepackage{graphics}
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\usepackage{times}
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\usepackage[T1]{fontenc}
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\usepackage{ngerman}
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\usepackage{float}
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\usepackage{diagbox}
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\usepackage[latin1]{inputenc}
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\usepackage{geometry}
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\usepackage{amsfonts}
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\usepackage{amsmath}
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\usepackage{csquotes}
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\usepackage{graphicx}
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\usepackage{epsfig}
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\usepackage{paralist}
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\geometry{left=2.0cm,textwidth=17cm,top=3.5cm,textheight=23cm}
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%%%%%%%%%% Fill out the the definitions %%%%%%%%%
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\def \name {Valentin Brandl} %
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\def \matrikel {108018274494} %
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% \def \pname {Vorname2 Nachname2} %
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% \def \pmatrikel {Matrikelnummer2} %
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\def \gruppe {Gruppenkuerzel} %
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\def \uebung {1} %
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% DO NOT MODIFY THIS HEADER
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\newcommand{\hwsol}{
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\vspace*{-2cm}
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\noindent \matrikel \quad \name \hfill Gruppe:\gruppe \\
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% \noindent \pmatrikel \quad \pname \\
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\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
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}
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\begin{document}
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%Import header
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\hwsol
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\section*{Aufgabe (a)}
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\begin{itemize}
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\item $\frac{\text{m}}{\text{s}}$
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\item $N = \frac{\text{kg}\cdot \text{m}}{\text{s}^2}$
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\item $J = \frac{\text{kg}\cdot \text{m}^2}{\text{s}^2}$
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\item $C = \text{As}$
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\end{itemize}
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\section*{Aufgabe (b)}
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\begin{enumerate}[1.]
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\item
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\begin{itemize}
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\item $32 mm = 0.032m$
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\item $765kV = 765000 V = 765000 \frac{W}{A} = 765000 \frac{kg \cdot m^2}{s^3 \cdot A}$
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\item $15 \mu m = 15 * 10^{-6} m$
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\item $0,7 ms = 0,0007s$
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\item $12 M\Omega = 12000000 \Omega = 12000000 \frac{kg \cdot m^2}{A^2 \cdot s^3}$
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\item $462 \mu g = 0.000000462 kg$
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\item $3580 kHz = 3580000 \frac{1}{s}$
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\item $65 nF = 0.000000065 \frac{A^2 \cdot s^4}{kg \cdot m^2}$
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\item $84 daN = 840 N$
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\item $43 GV = 43000000000 \frac{kg \cdot m^2}{s^3 \cdot A}$
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\item $50 \mu s = 0.00005 s$
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\end{itemize}
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\item
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\begin{itemize}
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\item $22853000 \Omega = 22.853000 M\Omega$
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\item $7180 N = 718 daN$
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\item $13950 g = 13.950 kg$
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\item $0.00028 mm = 0.28 \mu m$
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\item $415 \mu A = 0.000415 A$
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\item $0.00005 s = 50 \mu s$
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\item $0.000189 F = 189000 nF$
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\item $17800 kV = 0.0178 GV$
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\item $0.00025 A = 0.25 mA$
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\item $27000 Hz = 27 kHz$
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\item $0.75 s = 750 ms$
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\end{itemize}
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\item
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\begin{itemize}
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\item $3.6 \frac{km}{h} = 1 \frac{m}{s}$
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\item $100 \frac{N}{cm} = 1 \frac{kg}{s^2}$
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\item $0.58 \frac{g}{cm^3} = 0.00058 \frac{kg}{m^3}$
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\item $6001 mm = 6.001 m$
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\end{itemize}
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\end{enumerate}
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\section*{Aufgabe (c)}
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\[
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W (kJ) = \frac{5}{18} \cdot P (W) \cdot t(h) = \frac{10^{-10}}{3600} \cdot U (kV) \cdot I (\mu A) \cdot t(h)
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\]
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\section*{Aufgabe (d)}
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\begin{itemize}
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\item $\frac{kg \cdot m^2}{s^3} = \frac{Nm}{s} = W \Rightarrow P$
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\item $\frac{N}{m} = J \Rightarrow W$
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\item $\frac{kp}{cm^2} \approx 0.1 \frac{N}{m} = 0.1 J \Rightarrow W$
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\item $VA = W \Rightarrow P$
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\end{itemize}
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\end{document}
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