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electrical_engineering_1:dummy_with_calculation [2023/03/29 12:15] – mexleadminelectrical_engineering_1:dummy_with_calculation [2023/03/29 16:55] (aktuell) – mexleadmin
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-#@TaskTitle_HTML@#~~#@ee1_taskctr.#~~  Power loss and efficiency II    +#@TaskTitle_HTML@#@numbering@  Power loss and efficiency II    
 \\ <fs medium>(written test, approx. 14 % of a 60-minute written test, WS2022)</fs> \\ <fs medium>(written test, approx. 14 % of a 60-minute written test, WS2022)</fs>
 #@TaskText_HTML@#     #@TaskText_HTML@#    
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 Use equivalent sources in order to simplify the circuit! Use equivalent sources in order to simplify the circuit!
  
-#@SolutionBegin_HTML@#+#@PathBegin_HTML~1~@#
  
 The best thing is to re-think the wiring like rubber bands and adjust them: The best thing is to re-think the wiring like rubber bands and adjust them:
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 Therefore the voltage between $A$ and $B$ is given as: Therefore the voltage between $A$ and $B$ is given as:
 \begin{align*} \begin{align*}
-U_{AB} &= U_{24} \cdot {{R_7}\over{R_6 + R_7 + R_1||R_3||R_5}} \\ +U_{\rm AB} &= U_{24} \cdot {{R_7}\over{R_6 + R_7 + R_1||R_3||R_5}} \\ 
-       &= ({{U_2}\over{R_1}} - I_4) \cdot {{R_7 \cdot R_1||R_3||R_5}\over{R_6 + R_7 + R_1||R_3||R_5}} \\+           &= ({{U_2}\over{R_1}} - I_4) \cdot {{R_7 \cdot R_1||R_3||R_5}\over{R_6 + R_7 + R_1||R_3||R_5}} \\
 \end{align*} \end{align*}
  
 For the internal resistance $R_i$ the ideal voltage source is substituted by its resistance ($=0\Omega$, so a short-circuit): For the internal resistance $R_i$ the ideal voltage source is substituted by its resistance ($=0\Omega$, so a short-circuit):
 \begin{align*} \begin{align*}
-R_{AB} &= R_7 || ( R_6 + R_1||R_3||R_5) \\+R_{\rm AB} &= R_7 || ( R_6 + R_1||R_3||R_5) \\
 \end{align*} \end{align*}
  
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 \begin{align*} \begin{align*}
-U_{AB} &= ({{6.0 ~\rm{V}}\over{5.0 ~\Omega}} - 4.2 ~\Omega) \cdot {{15 ~\Omega \cdot 2.5 ~\Omega}\over{7.5 ~\Omega + 15 ~\Omega + 2.5 ~\Omega}} \\ +U_{\rm AB} &= ({{6.0 ~\rm{V}}\over{5.0 ~\Omega}} - 4.2 ~\Omega) \cdot {{15 ~\Omega \cdot 2.5 ~\Omega}\over{7.5 ~\Omega + 15 ~\Omega + 2.5 ~\Omega}} \\ 
-R_{AB} &= 15 ~\Omega|| ( 7.5 ~\Omega + 2.5 ~\Omega) \\+R_{\rm AB} &= 15 ~\Omega|| ( 7.5 ~\Omega + 2.5 ~\Omega) \\
 \end{align*} \end{align*}
  
-#@SolutionEnd_HTML@#+#@PathEnd_HTML@#
  
-<button size="xs" type="link" collapse="6tqttque1e2nf2c7_1_solution">{{icon>eye}} Final result</button><collapse id="6tqttque1e2nf2c7_1_solution" collapsed="true"> +#@ResultBegin_HTML~1~@# 
-<callout type="tip" icon="true">\begin{align*}+\begin{align*}
 U_{AB} &= 4.5 ~\rm{V}\\ U_{AB} &= 4.5 ~\rm{V}\\
 R_{AB} &= 6 ~\Omega  R_{AB} &= 6 ~\Omega 
 \end{align*} \end{align*}
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