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electrical_engineering_1:task_x357drkaqv84jnsc_with_calculation [2023/04/02 00:31] – mexleadminelectrical_engineering_1:task_x357drkaqv84jnsc_with_calculation [Unbekanntes Datum] (aktuell) – gelöscht - Externe Bearbeitung (Unbekanntes Datum) 127.0.0.1
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-{{tag>  exam_ee1_WS2022}} 
-{{include_n>3000}} 
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-#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~  Pure Resistor Network Simplification  \\ <fs medium>(written test, approx. 13 % of a 60-minute written test, WS2022)</fs> #@TaskText_HTML@#     
  
-The following circuit with $R_1=200 ~\Omega$, $R_2=R_3=100 ~\Omega$ and the switch $S$ is given. \\ 
-{{drawio>electrical_engineering_1:70jjg4yzwctqarsqCircuit.svg}} 
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-1. The switch shall now be open. Calculate the equivalent resistance $R_{\rm eq}$ between $\rm A$ and $\rm B$. 
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-#@PathBegin_HTML~1~@# 
-{{drawio>electrical_engineering_1:70jjg4yzwctqarsqCircuitSolution1.svg}} 
-The equivalent resistor is given by a parallel configuration of resistors in series: 
-\begin{align*} 
-R_{\rm eq} &= (R_2 + R_1 + R_1)||(R_2 + R_2)\\ 
-R_{\rm eq} &= (100 ~\Omega + 200 ~\Omega + 200 ~\Omega )&&||(100 ~\Omega + 100 ~\Omega ) &&\\ 
-R_{\rm eq} &= (500 ~\Omega )&&||(200 ~\Omega )&&\\ 
-R_{\rm eq} &= {{500 ~\Omega \cdot 200 ~\Omega }\over{500 ~\Omega + 200 ~\Omega}}&&\\ 
-\end{align*} 
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-#@PathEnd_HTML~1~@# 
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-#@ResultBegin_HTML~1~@# 
-\begin{align*} 
-R_{\rm eq} &= 142.8 ~\Omega \\ 
-\end{align*} 
- \\ 
-#@ResultEnd_HTML~1~@# 
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-2. The switch shall now be closed. Calculate the equivalent resistance $R_{\rm eq}$ between $A$ and $B$. 
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-#@PathBegin_HTML~2~@# 
-Now a wye-delta transformation is necessary. 
-{{drawio>electrical_engineering_1:70jjg4yzwctqarsqCircuitSolution2.svg}} 
-Since $R_2=R_3$ and based on the equations for the transformation, the transformed $R_Y$ is given as: 
-\begin{align*} 
-R_{Y} &= {{R_2 \cdot R_2}\over{R_2 + R_2 + R_2}} \\ 
-      &= {{(100 ~\Omega)^2}\over{3 \cdot 100 ~\Omega}} \\ 
-      &= {{1}\over{3}} \cdot 100 ~\Omega = 33.33 ~\Omega 
-\end{align*} 
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-The equivalent resistor is given by a parallel configuration of resistors in series: 
-\begin{align*} 
-R_{\rm eq} &= R_Y + (R_Y + R_1 + R_1)||(R_Y + R_2)\\ 
-R_{\rm eq} &= 33.33 ~\Omega + (33.33 ~\Omega + 400 ~\Omega)||(33.33 ~\Omega + 100 ~\Omega)\\ 
-\end{align*} 
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-#@PathEnd_HTML~2~@# 
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-#@ResultBegin_HTML~2~@# 
-\begin{align*} 
-R_{\rm eq} &= 135.3 ~\Omega \\ 
-\end{align*} 
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-#@ResultEnd_HTML~2~@# 
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-#@TaskEnd_HTML@#