\documentclass[12pt,a4paper,german]{article}
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%%%%%%%%%% Fill out the the definitions %%%%%%%%%
\def \name {Valentin Brandl}					%
\def \matrikel {108018274494}				%
% \def \pname {Vorname2 Nachname2}				%
% \def \pmatrikel {Matrikelnummer2}				%
\def \gruppe {Gruppenkuerzel}					%
\def \uebung {1}								%
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\newcommand{\hwsol}{
\vspace*{-2cm}
\noindent \matrikel \quad \name \hfill Gruppe:\gruppe \\
% \noindent \pmatrikel \quad \pname \\
\begin{center}{\Large \bf L\"osung f\"ur \"Ubung \# \uebung}\end{center}
}

\begin{document}
%Import header
\hwsol


\section*{Aufgabe (a)}

\begin{itemize}
	\item $\frac{\text{m}}{\text{s}}$
	\item $N = \frac{\text{kg}\cdot \text{m}}{\text{s}^2}$
	\item $J = \frac{\text{kg}\cdot \text{m}^2}{\text{s}^2}$
	\item $C = \text{As}$
\end{itemize}


\section*{Aufgabe (b)}

\begin{enumerate}[1.]
	\item
		\begin{itemize}
			\item $32 mm = 0.032m$
			\item $765kV = 765000 V = 765000 \frac{W}{A} = 765000 \frac{kg \cdot m^2}{s^3 \cdot A}$
			\item $15 \mu m = 15 * 10^{-6} m$
			\item $0,7 ms = 0,0007s$
			\item $12 M\Omega = 12000000 \Omega = 12000000 \frac{kg \cdot m^2}{A^2 \cdot s^3}$
			\item $462 \mu g = 0.000000462 kg$
			\item $3580 kHz = 3580000 \frac{1}{s}$
			\item $65 nF = 0.000000065 \frac{A^2 \cdot s^4}{kg \cdot m^2}$
			\item $84 daN = 840 N$
			\item $43 GV = 43000000000 \frac{kg \cdot m^2}{s^3 \cdot A}$
			\item $50 \mu s = 0.00005 s$
		\end{itemize}

	\item
		\begin{itemize}
			\item $22853000 \Omega = 22.853000  M\Omega$
			\item $7180 N = 718 daN$
			\item $13950 g = 13.950 kg$
			\item $0.00028 mm = 0.28 \mu m$
			\item $415 \mu A = 0.000415 A$
			\item $0.00005 s = 50 \mu s$
			\item $0.000189 F = 189000 nF$
			\item $17800 kV = 0.0178 GV$
			\item $0.00025 A = 0.25 mA$
			\item $27000 Hz = 27 kHz$
			\item $0.75 s = 750 ms$
		\end{itemize}

	\item
		\begin{itemize}
			\item $3.6 \frac{km}{h} = 1 \frac{m}{s}$
			\item $100 \frac{N}{cm} = 1 \frac{kg}{s^2}$
			\item $0.58 \frac{g}{cm^3} = 0.00058 \frac{kg}{m^3}$
			\item $6001 mm = 6.001 m$
		\end{itemize}

\end{enumerate}

\section*{Aufgabe (c)}

\[
W (kJ) = \frac{5}{18} \cdot P (W) \cdot t(h) = \frac{10^{-10}}{3600} \cdot U (kV) \cdot I (\mu A) \cdot t(h)
\]

\section*{Aufgabe (d)}

\begin{itemize}
	\item $\frac{kg \cdot m^2}{s^3} = \frac{Nm}{s} = W \Rightarrow P$
	\item $\frac{N}{m} = J \Rightarrow W$
	\item $\frac{kp}{cm^2} \approx 0.1 \frac{N}{m} = 0.1 J \Rightarrow W$
	\item $VA = W \Rightarrow P$
\end{itemize}


\end{document}

