144 lines
8.3 KiB
TeX
144 lines
8.3 KiB
TeX
\section{Gesamtwiderstand}
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Von der Schaltung (Bild 1) sind die Zeiger $\uline{U}_0$ und $\uline{I}_0$ gegeben (Bild 2).
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\renewcommand{\labelenumi}{\alph{enumi})}
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\begin{enumerate}
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\item Ist der Gesamtwiderstand $\uline{Z}$ induktiv, ohmsch oder kapazitiv? (Stichwortartige Begründung !)
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\item Vervollständigen Sie Bild 2 zu einem qualitativen Zeigerdiagramm \uline{aller} Ströme und Spannungen.\\
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(Rechte Winkel oder Parallelen sind zu kennzeichnen. Alle Ströme und Spannungen müssen im Schaltbild (Bild 1) und im Zeigerbild unmissverständlich benannt werden.)\\
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\end{enumerate}
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\begin{align*}
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\begin{tikzpicture}[very thick,scale=2]
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\begin{scope}[>=latex,very thick,xshift=0.5cm,yshift=0cm,rotate=90]%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) [right] {$R_C$};
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\end{scope}
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\begin{scope}[>=latex,very thick,xshift=-0.5cm,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] {$C$};
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\end{scope}
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\begin{scope}[>=latex,very thick,xshift=0cm,yshift=-1cm,rotate=90]%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) [right] {$R$};
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\end{scope}
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\begin{scope}[>=latex,very thick,xshift=0cm,yshift=-2cm,rotate=90]%Spule |
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\draw (0,0)--(.3,0) (.7,0)--(1,0)node at(.5,-.0667) [right] {$L$};
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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]%Knotenpunkte
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\draw (-.5,.2)--(-0.5,0)--(.5,0)--(.5,.2) (-1,1)--(.5,1)--(.5,.8) (-1,-2)--(0,-2)--(0,-1.8);
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\draw [->,blue] (-1,.9)--(-1,-1.9)node at(-1,-.5)[right]{$\underline{U}_{0}$};
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\draw node at(-1,-.5)[left]{$\underline{Z}\Rightarrow$};
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\fill (-1,1)circle(.025) (-1,-2)circle(.025);
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\draw [->,red] (-.9,1.1)--(-.6,1.1) node at (-.75,1.1)[above]{$\underline{I}_{0}$};
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\draw node at (0,-2.2)[below]{Bild 1};
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\end{scope}
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\begin{scope}[>=latex,very thick,xshift=2cm,yshift=0cm]
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\draw [->,blue] (0,0)--(3,0)node [right]{$\underline{U}_{0}$};
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\draw [->,red] (0,0)--(-33:1.5)node [right]{$\underline{I}_{0}$};
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\draw node at (1.5,-2.2)[below]{Bild 2};
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\end{scope}
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\end{tikzpicture}
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\end{align*}
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\ifthenelse{\equal{\toPrint}{Lösung}}{%
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\begin{align}
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\intertext{Merksätze:}
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&\text{Ohm'scher Widerstand: Strom und Spannung in Phase}\\
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&\text{Kondensator: Strom eilt $90\degree$ vor}\\
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&\text{Induktivität: Spannung eilt $90\degree$ vor}
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\end{align}
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Berechnung:\\[\baselineskip]
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a) Induktiv, da nacheilender Strom.\\
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\begin{align*}
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\intertext{b) Schaltbild mit Strom- und Spannungspfeilen ergänzen, Zeigerdiagramm erstellen.}
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\begin{tikzpicture}[very thick,scale=2]
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\begin{scope}[>=latex,very thick,xshift=0.5cm,yshift=0cm,rotate=90]%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) [right] {$R_C$};
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\draw [<-,blue] (.3,.5)--(.7,.5)node at(.5,.5)[right]{\footnotesize$\uline{U}_{C}$};
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\end{scope}
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\begin{scope}[>=latex,very thick,xshift=-0.5cm,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] {$C$};
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% \draw [->,blue] (.3,-.2)--(.7,-.2) node at (.5,-.2)[below]{\footnotesize$\uline{U}_{C}$};
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\end{scope}
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\begin{scope}[>=latex,very thick,xshift=0cm,yshift=-1cm,rotate=90]%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) [right] {$R$};
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\draw [<-,blue] (.3,.2)--(.7,.2)node at(.5,.2)[left]{\footnotesize$\uline{U}_{R}$};
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\end{scope}
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\begin{scope}[>=latex,very thick,xshift=0cm,yshift=-2cm,rotate=90]%Spule |
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\draw (0,0)--(.3,0) (.7,0)--(1,0)node at(.5,-.0667) [right] {$L$};
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\fill (.3,-0.0667)rectangle(.7,0.0667);
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\draw [<-,blue] (.3,.2)--(.7,.2)node at(.5,.2)[left]{\footnotesize$\uline{U}_{L}$};
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\draw [<-,blue] (.5,-.5)--(1.5,-.5)node at(1,-.5)[right]{\footnotesize$\uline{U}_{RL}$};
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\end{scope}
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\begin{scope}[>=latex,very thick]%Knotenpunkte
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\draw (-.5,.2)--(-0.5,0)--(.5,0)--(.5,.2) (-1,1)--(.5,1)--(.5,.8) (-1,-2)--(0,-2)--(0,-1.8);
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\draw [->,blue] (-1,.9)--(-1,-1.9)node at(-1,-.5)[right]{$\underline{U}_{0}$};
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\draw node at(-1,-.5)[left]{$\underline{Z}\Rightarrow$};
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\fill (-1,1)circle(.025) (-1,-2)circle(.025);
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\draw [->,red] (-.9,1.1)--(-.6,1.1) node at (-.75,1.1)[above]{$\underline{I}_{0}$};
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\draw [<-,red] (-.7,.3)--(-.7,.7) node at (-.7,.5)[left]{$\underline{I}_{C}$};
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\draw [<-,red] (1.,.3)--(1.,.7) node at (1.,.5)[right]{$\underline{I}_{RC}$};
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% \draw node at (0,-2.2)[below]{Bild 1};
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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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%\uline{I}_0&=\uline{I}_{RC}+\uline{I}_C\\
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%\uline{I}_C\,& \bot \,\uline{I}_{RC}\\
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%\uline{I}_C &\text{ eilt vor } [\text{ für }\uline{I}_{RC}\text{ und }\uline{I}_{C}]
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%\end{align*}
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\begin{align*}
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\begin{tikzpicture}[very thick,scale=2.5]
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\begin{scope}[>=latex,very thick,xshift=0cm,yshift=0cm]
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\draw [->,blue] (0,0)--(3,0)node [above left]{$\underline{U}_{0}$};
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\draw [->,red] (0,0)--(-33:1.5)node at (-33:1)[above right]{$\underline{I}_{0}$};
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\fill [black!50!](-33:.75)circle(.02);
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\draw [very thin](-33:.0)arc(147:327:.75);
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\draw (-66:1.258)+(24:.15)arc(24:114:.15) ; %Rechter Winkel
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\fill (-66:1.258)+(69:.075)circle(.02) ; %Punkt Rechter Winkel
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\draw [->,red] (0,0)--(-66:1.258)node at(-68:.8)[above left]{$\underline{I}_{RC}$};
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\draw [->,red] (-66:1.258)--(-33:1.5)node at (-55:1.2)[above right]{$\underline{I}_{C}$};
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\draw (4,-.3)node [right] {$\uline{I}_0=\uline{I}_{RC}+\uline{I}_C$ und};
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\draw (4,-.6)node [right] {$\uline{I}_C\, \bot \,\uline{I}_{RC}$ (Thaleskreis) und};
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\draw (4,-.9)node [right] {$\uline{I}_C$ eilt $\uline{I}_{RC}$ vor.};
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% \draw node at (1.5,-2.2)[below]{Bild 2};
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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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\begin{tikzpicture}[very thick,scale=2.5]
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\begin{scope}[>=latex,very thick,xshift=0cm,yshift=0cm]
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\draw [->,blue] (0,0)--(3,0)node at(2,0)[above left]{$\underline{U}_{0}$};
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\draw [->,red] (0,0)--(-33:1.5)node at (-33:1)[above right]{$\underline{I}_{0}$};
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\fill [black!50!](-33:.75)circle(.02);
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\draw [very thin](-33:.0)arc(147:327:.75);
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\draw [->,red] (0,0)--(-66:1.258)node at(-68:.8)[above left]{$\underline{I}_{RC}$};
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\draw [->,red] (-66:1.258)--(-33:1.5)node at (-55:1.2)[above right]{$\underline{I}_{C}$};
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% \draw node at (1.5,-2.2)[below]{Bild 2};
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\draw [->,blue] (0,0)--(-66:2)node at(-68:1.5)[above left]{$\underline{U}_{C}$};
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\draw [->,blue] (-66:2)--(3,0)node at (2.5,-.2)[below left]{$\underline{U}_{RL}$};
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% \draw [red,very thin,dashed](-66:.5)arc(114:-66:1.5) (0:3)+(114:1.5)arc(114:294:1.5);%Seitenhalbierende
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\draw [very thin,dashed](-66:2.0)+(70:1.5)arc(70:10:1.5) (0:3)+(190:1.5)arc(190:250:1.5);%Seitenhalbierende Teilkreise
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\fill [black!60!](-25.6:2.115)circle(.02); %Mittelpunkt Thaleskreis 2
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\draw [very thin](0:3)arc(40:-140:1.425); %Tahleskreis 2
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\draw [very thin](-14.3:1.5)--(-31.9:2.8); %Seitenhalbierende
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\draw (-66:1.258)+(24:.15)arc(24:114:.15) ; %Rechter Winkel
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\fill (-66:1.258)+(69:.075)circle(.02) ; %Punkt Rechter Winkel
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\draw [->,blue!50!red](-66:2)--+(-30:1)node at(1.2,-2.3)[below right]{$\underline{U}_{R}$};
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\draw [->,blue!50!red](-66:2)--+(-30:1)--(0:3)node at(2.6,-.7)[below right]{$\underline{U}_{L}$};
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\draw (-66:2)++(-30:1)++(60:0.15)arc(60:150:.15) ; %Rechter Winkel
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\fill (-66:2)++(-30:1)++(106:.075)circle(.02) ; %Punkt Rechter Winkel
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\draw (4,-.6)node [right] {$\uline{U}_C\, ||\, \uline{I}_{RC}$};
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\draw (4,-.9)node [right] {$\uline{U}_{0}=\uline{U}_C+\uline{U}_{RL}$};
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\draw (4,-1.5)node [right] {$\uline{U}_R\, ||\, \uline{I}_{0}$};
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\draw (4,-1.8)node [right] {$\uline{U}_{RL}=\uline{U}_{R}+\uline{U}_{L}$};
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\draw (4,-2.1)node [right] {$\uline{U}_L\, \bot \,\uline{U}_R$ (oder $\uline{U}_L\, \bot \,\uline{I}_0$)};
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\draw (4,-2.4)node [right] {$\uline{U}_L\,$ eilt $\uline{U}_R\,$ vor};
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\end{scope}
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\begin{scope}[>=latex,xshift=.86cm,yshift=-.552cm]%Parallelen
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\draw [double](0:-.1)--+(57:.1);
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\end{scope}
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\begin{scope}[>=latex,xshift=1.4cm,yshift=-2.167cm]%Parallelen
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\draw [double](0:-.1)--+(57:.1);
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\end{scope}
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\end{tikzpicture}
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\end{align*}
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\clearpage
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}{}%
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