43 lines
1.9 KiB
TeX
43 lines
1.9 KiB
TeX
\section{Leitwert}
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Der Widerstand des abgebildeten Netzwerkes soll $\uline{Z}=1\,\kilo\ohm\cdot e^{j60\,\degree}$ sein.\\[\baselineskip]
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Wie groß müssen $R$ und $B_C$ sein, wenn $B_L=-3{,}33\,\milli\siemens$ ist?
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\ifthenelse{\equal{\toPrint}{Lösung}}{%
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%\begin{align}
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%\intertext{Formeln:}
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%\text{...noch einfügen...}
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%\end{align}
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\begin{align*}
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\begin{tikzpicture}[scale=3]
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\begin{scope}[>=latex,very thick,xshift=0cm,yshift=1cm]%Widerstand - nach EN 60617
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\draw (0,0)--(.3,0) (.3,-0.0667)rectangle(.7,0.0667) (.7,0)--(1,0)node at (.5,.0667) [above] {$R$};
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\end{scope}
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\begin{scope}[>=latex,very thick,xshift=1cm,yshift=0cm,rotate=90]%Kondensator |
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\draw (0,0)--(.475,0) (.475,-.125)--(.475,.125) (.525,-.125)--(.525,.125) (.525,0)--(1,0)node at (.5,-.133) [right] {$B_C$};
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\end{scope}
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\begin{scope}[>=latex,very thick,xshift=2cm,yshift=0cm,rotate=90]%Spule |
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\draw (0,0)--(.3,0) (.7,0)--(1,0)node at(.5,-.0667) [right] {$B_L$};
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\fill (.3,-0.0667)rectangle(.7,0.0667);
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\end{scope}
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\begin{scope}[>=latex,very thick,xshift=0cm,yshift=0cm]%Fehlstellen Eckverbindungen.
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\draw (.8,1)--(2,1)--(2,.9) (0,0)--(2,0)--(2,.2);
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\end{scope}
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\begin{scope}[>=latex,very thick,xshift=0cm,yshift=0cm]%End Knoten
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\fill (0,0)circle(.02);
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\fill (0,1)circle(.02);
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\draw node at (0,.5)[left] {$\uline{Z}\Rightarrow$};
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\end{scope}
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\end{tikzpicture}
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\end{align*}
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\begin{align*}
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\intertext{Berechnung:}
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\uline{Z}&\stackrel{!}{=}\power{10}{3}\,\ohm\cdot e^{j60\,\degree}\quad\,=(500+j866{,}25)\,\ohm\\
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\uline{Z}&=R+\frac{1}{j(B_C+B_L)}=\,\,\, R\,\,\, -j\frac{1}{(B_C+B_L)}\\[\baselineskip]
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\intertext{$\Re$}
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R&=\uuline{500\,\ohm}\\
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\intertext{$\Im$}
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B_C+B_L&=\frac{-1}{866{,}25}\,\siemens=-1{,}1547\,\milli\siemens\\
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B_C&=-1{,}1547\,\milli\siemens -B_L=-1{,}1547\,\milli\siemens +3{,}33\,\milli\siemens =\uuline{2{,}175\,\milli\siemens}\\
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\end{align*}
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\clearpage
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}{}%
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