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ET2_Uebung_BEI
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ET2_Uebung_BEI/ET2_L_B14_A2.tex

ET2_L_B14_A2.tex 8.3KB
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  1. \section{Gesamtwiderstand}

  2. Von der Schaltung (Bild 1) sind die Zeiger $\uline{U}_0$ und $\uline{I}_0$ gegeben (Bild 2).

  3. \renewcommand{\labelenumi}{\alph{enumi})}

  4. \begin{enumerate}

  5. \item Ist der Gesamtwiderstand $\uline{Z}$ induktiv, ohmsch oder kapazitiv? (Stichwortartige Begründung !)

  6. \item Vervollständigen Sie Bild 2 zu einem qualitativen Zeigerdiagramm \uline{aller} Ströme und Spannungen.\\

  7. (Rechte Winkel oder Parallelen sind zu kennzeichnen. Alle Ströme und Spannungen müssen im Schaltbild (Bild 1) und im Zeigerbild unmissverständlich benannt werden.)\\

  8. \end{enumerate}

  9. \begin{align*}

  10. 	\begin{tikzpicture}[very thick,scale=2]

  11. 		\begin{scope}[>=latex,very thick,xshift=0.5cm,yshift=0cm,rotate=90]%Widerstand - nach EN 60617			

  12. 			\draw (0,0)--(.3,0) (.3,-0.0667)rectangle(.7,0.0667) (.7,0)--(1,0)node at (.5,-.0667) [right] {$R_C$};

  13. 		\end{scope}

  14. 		\begin{scope}[>=latex,very thick,xshift=-0.5cm,yshift=0cm,rotate=90]%Kondensator | 			

  15. 			\draw (0,0)--(.475,0) (.475,-.125)--(.475,.125) (.525,-.125)--(.525,.125) (.525,0)--(1,0)node at (.5,-.133) [right] {$C$};

  16. 		\end{scope}

  17. 		\begin{scope}[>=latex,very thick,xshift=0cm,yshift=-1cm,rotate=90]%Widerstand - nach EN 60617			

  18. 			\draw (0,0)--(.3,0) (.3,-0.0667)rectangle(.7,0.0667) (.7,0)--(1,0)node at (.5,-.0667) [right] {$R$};

  19. 		\end{scope}

  20. 		\begin{scope}[>=latex,very thick,xshift=0cm,yshift=-2cm,rotate=90]%Spule | 			

  21. 			\draw (0,0)--(.3,0) (.7,0)--(1,0)node at(.5,-.0667) [right] {$L$};

  22. 			\fill (.3,-0.0667)rectangle(.7,0.0667);

  23. 		\end{scope}							

  24. 		\begin{scope}[>=latex,very thick]%Knotenpunkte

  25. 			\draw (-.5,.2)--(-0.5,0)--(.5,0)--(.5,.2) (-1,1)--(.5,1)--(.5,.8) (-1,-2)--(0,-2)--(0,-1.8);

  26. 			\draw [->,blue] (-1,.9)--(-1,-1.9)node at(-1,-.5)[right]{$\underline{U}_{0}$};	

  27. 			\draw node at(-1,-.5)[left]{$\underline{Z}\Rightarrow$};					

  28. 			\fill (-1,1)circle(.025) (-1,-2)circle(.025);

  29. 			\draw [->,red] (-.9,1.1)--(-.6,1.1) node at (-.75,1.1)[above]{$\underline{I}_{0}$};			

  30. 			\draw node at (0,-2.2)[below]{Bild 1};									

  31. 		\end{scope}	

  32. 		\begin{scope}[>=latex,very thick,xshift=2cm,yshift=0cm]

  33. 			\draw [->,blue] (0,0)--(3,0)node [right]{$\underline{U}_{0}$};

  34. 			\draw [->,red] (0,0)--(-33:1.5)node [right]{$\underline{I}_{0}$};

  35. 			\draw node at (1.5,-2.2)[below]{Bild 2};		

  36. 		\end{scope}				

  37. 	\end{tikzpicture}

  38. \end{align*}

  39. \ifthenelse{\equal{\toPrint}{Lösung}}{%

  40. \begin{align}

  41. \intertext{Merksätze:}

  42. &\text{Ohm'scher Widerstand: Strom und Spannung in Phase}\\

  43. &\text{Kondensator: Strom eilt $90\degree$ vor}\\

  44. &\text{Induktivität: Spannung eilt $90\degree$ vor}

  45. \end{align}

  46. Berechnung:\\[\baselineskip]

  47. a) Induktiv, da nacheilender Strom.\\

  48. \begin{align*}

  49. \intertext{b) Schaltbild mit Strom- und Spannungspfeilen ergänzen, Zeigerdiagramm erstellen.}

  50. 	\begin{tikzpicture}[very thick,scale=2]

  51. 		\begin{scope}[>=latex,very thick,xshift=0.5cm,yshift=0cm,rotate=90]%Widerstand - nach EN 60617			

  52. 			\draw (0,0)--(.3,0) (.3,-0.0667)rectangle(.7,0.0667) (.7,0)--(1,0)node at (.5,-.0667) [right] {$R_C$};

  53. 			\draw [<-,blue] (.3,.5)--(.7,.5)node at(.5,.5)[right]{\footnotesize$\uline{U}_{C}$}; 

  54. 		\end{scope}

  55. 		\begin{scope}[>=latex,very thick,xshift=-0.5cm,yshift=0cm,rotate=90]%Kondensator | 			

  56. 			\draw (0,0)--(.475,0) (.475,-.125)--(.475,.125) (.525,-.125)--(.525,.125) (.525,0)--(1,0)node at (.5,-.133) [right] {$C$};

  57. %			\draw [->,blue] (.3,-.2)--(.7,-.2) node at (.5,-.2)[below]{\footnotesize$\uline{U}_{C}$};

  58. 		\end{scope}

  59. 		\begin{scope}[>=latex,very thick,xshift=0cm,yshift=-1cm,rotate=90]%Widerstand - nach EN 60617			

  60. 			\draw (0,0)--(.3,0) (.3,-0.0667)rectangle(.7,0.0667) (.7,0)--(1,0)node at (.5,-.0667) [right] {$R$};

  61. 			\draw [<-,blue] (.3,.2)--(.7,.2)node at(.5,.2)[left]{\footnotesize$\uline{U}_{R}$}; 

  62. 		\end{scope}

  63. 		\begin{scope}[>=latex,very thick,xshift=0cm,yshift=-2cm,rotate=90]%Spule | 			

  64. 			\draw (0,0)--(.3,0) (.7,0)--(1,0)node at(.5,-.0667) [right] {$L$};

  65. 			\fill (.3,-0.0667)rectangle(.7,0.0667);

  66. 			\draw [<-,blue] (.3,.2)--(.7,.2)node at(.5,.2)[left]{\footnotesize$\uline{U}_{L}$};

  67. 			\draw [<-,blue] (.5,-.5)--(1.5,-.5)node at(1,-.5)[right]{\footnotesize$\uline{U}_{RL}$};			

  68. 		\end{scope}							

  69. 		\begin{scope}[>=latex,very thick]%Knotenpunkte

  70. 			\draw (-.5,.2)--(-0.5,0)--(.5,0)--(.5,.2) (-1,1)--(.5,1)--(.5,.8) (-1,-2)--(0,-2)--(0,-1.8);

  71. 			\draw [->,blue] (-1,.9)--(-1,-1.9)node at(-1,-.5)[right]{$\underline{U}_{0}$};	

  72. 			\draw node at(-1,-.5)[left]{$\underline{Z}\Rightarrow$};					

  73. 			\fill (-1,1)circle(.025) (-1,-2)circle(.025); 

  74. 			\draw [->,red] (-.9,1.1)--(-.6,1.1) node at (-.75,1.1)[above]{$\underline{I}_{0}$};

  75. 			\draw [<-,red] (-.7,.3)--(-.7,.7) node at (-.7,.5)[left]{$\underline{I}_{C}$};

  76. 			\draw [<-,red] (1.,.3)--(1.,.7) node at (1.,.5)[right]{$\underline{I}_{RC}$};						

  77. %			\draw node at (0,-2.2)[below]{Bild 1};									

  78. 		\end{scope}	

  79. 		\end{tikzpicture}

  80. \end{align*}

  81. %\begin{align*}

  82. %\uline{I}_0&=\uline{I}_{RC}+\uline{I}_C\\

  83. %\uline{I}_C\,& \bot \,\uline{I}_{RC}\\

  84. %\uline{I}_C &\text{ eilt vor } [\text{ für }\uline{I}_{RC}\text{ und }\uline{I}_{C}]

  85. %\end{align*}

  86. \begin{align*}		

  87. 	\begin{tikzpicture}[very thick,scale=2.5]

  88. 		\begin{scope}[>=latex,very thick,xshift=0cm,yshift=0cm]

  89. 			\draw [->,blue] (0,0)--(3,0)node [above left]{$\underline{U}_{0}$};

  90. 			\draw [->,red] (0,0)--(-33:1.5)node at (-33:1)[above right]{$\underline{I}_{0}$};

  91. 			\fill [black!50!](-33:.75)circle(.02);			

  92. 			\draw [very thin](-33:.0)arc(147:327:.75);

  93. 			\draw (-66:1.258)+(24:.15)arc(24:114:.15) ;	%Rechter Winkel	

  94. 			\fill (-66:1.258)+(69:.075)circle(.02) ;	%Punkt Rechter Winkel				

  95. 			\draw [->,red] (0,0)--(-66:1.258)node at(-68:.8)[above left]{$\underline{I}_{RC}$};	

  96. 			\draw [->,red] (-66:1.258)--(-33:1.5)node at (-55:1.2)[above right]{$\underline{I}_{C}$};

  97. 			\draw (4,-.3)node [right] {$\uline{I}_0=\uline{I}_{RC}+\uline{I}_C$ und};

  98. 			\draw (4,-.6)node [right] {$\uline{I}_C\, \bot \,\uline{I}_{RC}$ (Thaleskreis) und};	

  99. 			\draw (4,-.9)node [right] {$\uline{I}_C$ eilt $\uline{I}_{RC}$ vor.};

  100. %			\draw node at (1.5,-2.2)[below]{Bild 2};		

  101. 		\end{scope}				

  102. 	\end{tikzpicture}

  103. \end{align*}

  104. \begin{align*}		

  105. 	\begin{tikzpicture}[very thick,scale=2.5]

  106. 		\begin{scope}[>=latex,very thick,xshift=0cm,yshift=0cm]

  107. 			\draw [->,blue] (0,0)--(3,0)node at(2,0)[above left]{$\underline{U}_{0}$};

  108. 			\draw [->,red] (0,0)--(-33:1.5)node at (-33:1)[above right]{$\underline{I}_{0}$};

  109. 			\fill [black!50!](-33:.75)circle(.02);			

  110. 			\draw [very thin](-33:.0)arc(147:327:.75);

  111. 			\draw [->,red] (0,0)--(-66:1.258)node  at(-68:.8)[above left]{$\underline{I}_{RC}$};	

  112. 			\draw [->,red] (-66:1.258)--(-33:1.5)node  at (-55:1.2)[above right]{$\underline{I}_{C}$};					

  113. %			\draw node at (1.5,-2.2)[below]{Bild 2};

  114. 			\draw [->,blue] (0,0)--(-66:2)node at(-68:1.5)[above left]{$\underline{U}_{C}$};	

  115. 			\draw [->,blue] (-66:2)--(3,0)node at (2.5,-.2)[below left]{$\underline{U}_{RL}$};

  116. %			\draw [red,very thin,dashed](-66:.5)arc(114:-66:1.5) (0:3)+(114:1.5)arc(114:294:1.5);%Seitenhalbierende	

  117. 			\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

  118. 			\fill [black!60!](-25.6:2.115)circle(.02); %Mittelpunkt Thaleskreis	2		

  119. 			\draw [very thin](0:3)arc(40:-140:1.425); %Tahleskreis 2

  120. 			\draw [very thin](-14.3:1.5)--(-31.9:2.8);	%Seitenhalbierende				

  121. 			\draw (-66:1.258)+(24:.15)arc(24:114:.15) ;	%Rechter Winkel	

  122. 			\fill (-66:1.258)+(69:.075)circle(.02) ;	%Punkt Rechter Winkel	

  123. 			\draw [->,blue!50!red](-66:2)--+(-30:1)node at(1.2,-2.3)[below right]{$\underline{U}_{R}$};	

  124. 			\draw [->,blue!50!red](-66:2)--+(-30:1)--(0:3)node at(2.6,-.7)[below right]{$\underline{U}_{L}$};	

  125. 			\draw (-66:2)++(-30:1)++(60:0.15)arc(60:150:.15) ;	%Rechter Winkel	

  126. 			\fill (-66:2)++(-30:1)++(106:.075)circle(.02) ;	%Punkt Rechter Winkel	

  127. 			\draw (4,-.6)node [right] {$\uline{U}_C\, ||\, \uline{I}_{RC}$};

  128. 			\draw (4,-.9)node [right] {$\uline{U}_{0}=\uline{U}_C+\uline{U}_{RL}$};	

  129. 			\draw (4,-1.5)node [right] {$\uline{U}_R\, ||\, \uline{I}_{0}$};

  130. 			\draw (4,-1.8)node [right] {$\uline{U}_{RL}=\uline{U}_{R}+\uline{U}_{L}$};

  131. 			\draw (4,-2.1)node [right] {$\uline{U}_L\, \bot \,\uline{U}_R$ (oder $\uline{U}_L\, \bot \,\uline{I}_0$)}; 

  132.                         \draw (4,-2.4)node [right] {$\uline{U}_L\,$ eilt $\uline{U}_R\,$ vor};												

  133. 		\end{scope}	

  134. 		\begin{scope}[>=latex,xshift=.86cm,yshift=-.552cm]%Parallelen

  135. 			\draw [double](0:-.1)--+(57:.1);		

  136. 		\end{scope}		

  137. 		\begin{scope}[>=latex,xshift=1.4cm,yshift=-2.167cm]%Parallelen

  138. 			\draw [double](0:-.1)--+(57:.1);

  139. 		\end{scope}							

  140. 	\end{tikzpicture}

  141. \end{align*}

  142. \clearpage

  143. }{}%