ET2_Uebung_BEI/ET2_L_B17_A4.tex

\section{Stromortskurve}
Konstruieren Sie die Stromortskurve $\uline{I}=f(p)$ zu der abgebildeten Schaltung\\
für $0\leq p\leq 1$ !\\
Es ist $Z_{RL}=p(R_0+jX_{L_0})$. Die Parameterwerte $p=0$; $0{,}25$; $0{,}5$; $0{,}75$ und $1$  sind zu markieren.\\
Für welches $p$ wird $I=I_{max}$? Geben Sie diesen Stromwert an.\\
Gegeben sind: $\uline{U}=U=10\,\volt$; $X_C=-3\,\kilo\ohm$; $R_0=6\,\kilo\ohm$; $X_{L_0}=8\,\kilo\ohm$.\\
Maßstäbe: $1\,\kilo\ohm\,\widehat{=}\,1\,\centi\metre $; $50\,\micro\second\,\widehat{=}\, 1\,\centi\metre$\\
\begin{align*}
	\begin{tikzpicture}[very thick,scale=2]
		\begin{scope}[>=latex,very thick,xshift=0cm,yshift=1cm]%Kondensator -		
			\draw (0,0)--(.475,0) (.475,-.125)--(.475,.125) (.525,-.125)--(.525,.125) (.525,0)--(1,0)node at (.5,.10) [above] {$C$};
		\end{scope}	
		\begin{scope}[>=latex,very thick,xshift=1cm,yshift=1cm]%Widerstand - nach EN 60617
			\draw (0,0)--(.3,0) (.3,-0.0667)rectangle(.7,0.0667) (.7,0)--(1,0)node at (.5,.0667) [above] {$R_{\phantom{L}}$};
		\end{scope}	
		\begin{scope}[>=latex,very thick,xshift=2cm,yshift=1cm]%Spule -			
			\draw (0,0)--(.3,0) (.7,0)--(1,0)node at (.45,.0667) [above] {$X_{L}$};
			\fill (.3,-0.0667)rectangle(.7,0.0667);
		\end{scope}		
		\begin{scope}[>=latex,very thick,xshift=0cm]%Knotenpunkte
			\draw (0,0)--(3,0)--(3,1)--(2.9,1);
			\draw [->,blue] (0,.9)--(0,.1)node at(0,.5)[right]{$\underline{U}$};				 \fill (0,0)circle(.025) (0,1)circle(.025);
			\draw [->,red] (0,1.1)--(.4,1.1) node at (.25,1.1)[above]{$\underline{I}$};
		\end{scope}
		\begin{scope}[>=latex,very thick]%Variablen Pfeile
            \draw[->] (1.3,.75)--(1.7,1.25);
            \draw[->] (2.3,.75)--(2.7,1.25);
            \draw[dashed] (1.3,.75)--(2.3,.75);
        \end{scope}
	\end{tikzpicture}
\end{align*}
\ifthenelse{\equal{\toPrint}{Lösung}}{%
%\begin{align}
%\intertext{Formeln:}
%\end{align}
Berechnung: (Platzbedarf in x: $11\,\centi\metre$; in y: $12\,\centi\metre$)\\[0.5\baselineskip]
\begin{align*}
\uline{I}(p)&=\uline{Y}(p)\cdot \uline{U}\\
\intertext{$\uline{Z}(p)$ durch Vektoraddition der Widerstände zeichnen,}
Z(p)&=\sqrt{R_O^2+X^2_{LO}}=\sqrt{6^2+8^2}\,\kilo\ohm=10\,\kilo\ohm\qquad \text{für }p=1
\intertext{$\uline{Z}^*(p)$ durch Spiegelung an der reellen Achse zeichnen und Parameter $p$ einzeichnen.}
X_C&=-3\,\kilo\ohm\,\widehat{=}\,-3\,\centi\metre\\
R_0&=6\,\kilo\ohm\,\widehat{=}\,6\,\centi\metre\\
X_{L_0}&=8\,\kilo\ohm\,\widehat{=}\,8\,\centi\metre\\
\intertext{Senkrechte zu $\uline{Z}^*(p)$ durch den Ursprung zeichnen}
\overline{0N}&=1{,}8\,\centi\metre\,\widehat{=}\,1{,}8\,\kilo\ohm\\
\intertext{Invertieren ergibt Durchmesser des Kreises} \overline{0D}&=\frac{1}{\overline{0N}}=\frac{1}{1{,}8\,\kilo\ohm}=555{,}5\,\micro\siemens
\,\widehat{=}\,11{,}1\,\centi\metre\\
\intertext{Mittelpunkt bestimmen} \overline{0M}&=\frac{1}{2}\,\,\overline{0D}\,\widehat{=}\,5{,}55\,\centi\metre\\
\text{$\uline{Y}(p)$ Kreis zeichnen. Max. Strom bei größtem Leitwert im Punkt D\newline (Durchmesser des Kreises = max. Abstand vom Ursprung)}
\intertext{Ablesen von $p=0{,}24$ (Abstand zwischen $N(OD\,\cap\,\uline{Z}^*(p))$ und $\uline{Z}^*(p)|_{p=0}$)}
%\uline{Z}^*(p)\text{ gibt }\Delta p=0{,}1\,\kilo\ohm\,\widehat{=}1\,\centi\metre,\text{ auf }
%I_{max}\text{ für }p&=0{,}24\\
I_{max}&=\uline{Y}(p)\cdot \uline{U}=555{,}5\,\micro\siemens\cdot 10\,\volt=\uuline{5{,}55\,\milli\ampere}
\end{align*}
\begin{align*}
    \begin{tikzpicture}[very thick,scale=1]
		\begin{scope}[>=latex,very thick,xshift=0cm,yshift=0cm]
            \draw[ultra thin,black!50!](0,-5)grid(10,10);
            \draw[thin,->](0,0)--(10.5,0)node[right]{$\Re$};
            \draw[thin,->](0,-5.5)--(0,10.5)node[above]{$\Im$};
            \foreach \y in {10,9,...,-5}
            \draw(0,\y)--(-.1,\y)node[left]{$\y$};
            \draw[red,->](0,0)--(0,-3)node at(.5,-1.5){$-jX_C$};
            \draw[red,->](0,-3)--(6,-3)node at(3,-2.75){$R$};
            \draw[red,->](6,-3)--(6,5)node at(6.5,1){$jX_{LO}$};
            \draw[red,->](0,-3)--(6,5)node at(4,1.25){$\uline{Z}(p)$};
            \draw[red,->](0,3)--(6,-5)node at(6,-4){$\uline{Z}^*(p)$};
            \draw[black!35!,thin](0,1.5)circle(1.5cm);
            \draw[blue,thin](0,0)--(36.87:11.1cm)node at(9.1,6.75){D};
            \draw[blue]node at(9,7.5){$\uline{Y}(p)$};
            \filldraw[blue](36.87:5.55)circle(0.05cm)node[left]{M};
            \filldraw[blue](0,0)--(8,6)node at(1,1.1){N};
            \draw[blue](36.87:5.55)circle(5.55cm);
            \filldraw[red!50!blue](0,3)circle(0.05cm)node [right]{\footnotesize{$p=0$}};
            \filldraw[red!50!blue](0,3)++(-53.13:2.5cm)circle(0.05cm)node [right]{\footnotesize{$p=0{,}25$}};
            \filldraw[red!50!blue](0,3)++(-53.13:5cm)circle(0.05cm)node [right]{\footnotesize{$p=0{,}5$}};
            \filldraw[red!50!blue](0,3)++(-53.13:7.5cm)circle(0.05cm)node [above right]{\footnotesize{$p=0{,}75$}};
            \filldraw[red!50!blue](0,3)++(-53.13:10cm)circle(0.05cm)node [right]{\footnotesize{$p=1$}};
            \filldraw[green!50!black](0,-3)circle(0.05cm)node [below right]{\footnotesize{$p=0$}};
            \filldraw[green!50!black](0,-3)++(53.13:2.5cm)circle(0.05cm)node [right]{\footnotesize{$p=0{,}25$}};
            \filldraw[green!50!black](0,-3)++(53.13:5cm)circle(0.05cm)node [below right]{\footnotesize{$p=0{,}5$}};
            \filldraw[green!50!black](0,-3)++(53.13:7.5cm)circle(0.05cm)node [right]{\footnotesize{$p=0{,}75$}};
            \filldraw[green!50!black](0,-3)++(53.13:10cm)circle(0.05cm)node [left]{\footnotesize{$p=1$}};
            \draw[red!50!blue,very thin](0,0)--(6,-5);
            \draw[red!50!blue,very thin](0,0)--(4.5,-3);
            \draw[red!50!blue,very thin](0,0)--(6,-2);
            \draw[red!50!blue,very thin](0,0)--(12,8);
            \draw[red!50!blue,very thin](0,0)--(0,6.7);
            \filldraw[red!50!blue,very thin](-40.5:2.45cm)circle(0.05cm)node [right]{\footnotesize{$p=1$}};
            \filldraw[red!50!blue,very thin](-34.4:3.6cm)circle(0.05cm)node [right]{\footnotesize{$p=0{,}75$}};
            \filldraw[red!50!blue,very thin](6,-2)circle(0.05cm)node [right]{\footnotesize{$p=0{,}5$}};
            \filldraw[red!50!blue,very thin](33.69:11.1cm)circle(0.05cm)node [right]{\footnotesize{$p=0{,}25$}};
            \filldraw[red!50!blue,very thin](90:6.666cm)circle(0.05cm)node [right]{\footnotesize{$p=0$}};
            \foreach \x in {0,1,...,10}
            \filldraw(\x,.1)--(\x,-.1)node at (\x,-.33){$\x$};
		\end{scope}	
	\end{tikzpicture}
\end{align*}
Reihenfolge: $j\underline{X}_C; R; j\underline{X}_L; \underline{Z}(p)$; p-Werte; $\bot \underline{Z^*}(p) 
\Rightarrow \overline{ON}; \\
\overline{OD}$ Durchmesser; Kreis um $\overline{OM} \Rightarrow \underline{Y(p)}$ 
\clearpage
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