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electrical_engineering_and_electronics_1:block18 [2025/12/02 18:51] – mexleadminelectrical_engineering_and_electronics_1:block18 [2025/12/02 18:52] (aktuell) – mexleadmin
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 ===== Exercises ===== ===== Exercises =====
 +
 +{{page>electrical_engineering_and_electronics:task_rdz03rspbwusy7wk_with_calculation&nofooter}}
 +{{page>electrical_engineering_and_electronics:task_ludzwiuhjxitz85b_with_calculation&nofooter}}
 +
 +
 +<panel type="info" title="Exercise 4.1.4 Effects of induction I"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
 +
 +A change of magnetic flux is passing a coil with a single winding. The following pictures <imgref ImgNrEx01> show different flux-time-diagrams as examples.
 +
 +  * Create for each $\Phi(t)$-diagram the corresponding $u_{\rm ind}(t)$-diagram!
 +  * Write down each maximum value of $u_{\rm ind}(t)$
 +
 +<WRAP> <imgcaption ImgNrEx01| Flux-Time-Diagrams> </imgcaption> <WRAP> {{drawio>FluxTimeDia1.svg}} \\ </WRAP></WRAP>
 +
 +<button size="xs" type="link" collapse="Solution_4_1_4_1_Solution">{{icon>eye}} Solution for (a)</button><collapse id="Solution_4_1_4_1_Solution" collapsed="true">
 +
 +For partwise linear $u_{\rm ind}$ one can derive: 
 +\begin{align*} 
 +u_{\rm ind} &= -{{{\rm d}\Phi}\over{{\rm d}t}} \\ 
 +            &= -{{\Delta \Phi}\over{\Delta t}} 
 +\end{align*}
 +
 +For diagram (a):
 +
 +  * $t= 0.0 ... 0.6 ~\rm s$: $u_{\rm ind} = -{{0 ~\rm Vs}\over{0.6 ~\rm s}}= 0$
 +  * $t= 0.6 ... 1.5 ~\rm s$: $u_{\rm ind} = -{{-3.75\cdot 10^{-3} ~\rm Vs}\over{0.9 ~\rm s}}= +4.17 ~\rm mV$
 +  * $t= 1.5 ... 2.1 ~\rm s$: $u_{\rm ind} = -{{0 ~\rm Vs}\over{0.6 ~\rm s}}= 0$
 +
 +</collapse>
 +
 +<button size="xs" type="link" collapse="Solution_4_1_4_1_Finalresult">
 +{{icon>eye}} Final result for (a)</button><collapse id="Solution_4_1_4_1_Finalresult" collapsed="true"> 
 +<WRAP> <imgcaption ImgNrEx01| Flux-Time-Diagrams Solution> </imgcaption> <WRAP> {{drawio>FluxTimeDia1Solution.svg}} \\ 
 +</WRAP></WRAP> \\ 
 +</collapse>
 +
 +</WRAP></WRAP></panel>
 +
 +<panel type="info" title="Exercise 4.1.5 Effects of induction II"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
 +
 +A changing of magnetic flux is passing a coil with a single winding and induces the voltage $u_{\rm ind}(t)$. 
 +The following pictures <imgref ImgNrEx02> show different voltage-time diagrams as examples.
 +
 +  * Create for each $u_{\rm ind}(t)$-diagram the corresponding $\Phi(t)$-diagram!
 +  * Write down each maximum value of $\Phi(t)$
 +
 +Note the given start value $\Phi_0$ for each flux.
 +
 +<WRAP> <imgcaption ImgNrEx02| Voltage-Time-Diagrams> </imgcaption> <WRAP> {{drawio>FluxTimeDia2.svg}} \\ </WRAP></WRAP>
 +
 +#@HiddenBegin_HTML~415_1S,Solution for (a)~@#
 +
 +For partwise linear $u_{\rm ind}$ one can derive: 
 +\begin{align*} 
 +u_{\rm ind}        &= -{{{\rm d}\Phi}\over{{\rm d}t}} \\ 
 +\rightarrow  \Phi  &= -\int_0^t{ u_{\rm ind} \;{\rm d}t} \\
 +\Phi               &= \Phi_0 -\sum_k {u_{{\rm ind},~k} \; \Delta t} \\
 +\end{align*}
 +
 +For diagram (a):
 +
 +  * $t= 0.00 ... 0.04 ~\rm s\quad$: $\quad \Phi = \Phi_0 - {0 \cdot \; \Delta t} \quad\quad\quad\quad\quad\quad\quad= 0 ~\rm Wb$
 +  * $t= 0.04 ... 0.10 ~\rm s\quad$: $\quad \Phi =   0 {~\rm Wb} - {{30 ~\rm mV} \cdot \; (t - 0.04 ~\rm s)} = \quad {1.2 ~\rm mWb} - t \cdot 30 ~\rm mV$
 +  * $t= 0.10 ... 0.14 ~\rm s\quad$: $\quad \Phi =   {1.2 ~\rm mWb} - {0.10 ~\rm s} \cdot 30 ~\rm mV \quad = - {1.8 ~\rm mWb}$
 +
 +#@HiddenEnd_HTML~415_1S,Solution ~@#
 +
 +#@HiddenBegin_HTML~415_1R,Result for (a)~@#
 +{{drawio>FluxTimeDia2Res.svg}} 
 +#@HiddenEnd_HTML~415_1R,Result~@#
 +
 +
 +</WRAP></WRAP></panel>
 +
 +
  
 <panel type="info" title="Exercise 4.1.1 Magnetic Field Strength around a horizontal straight Conductor"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> <panel type="info" title="Exercise 4.1.1 Magnetic Field Strength around a horizontal straight Conductor"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
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 </collapse> </WRAP></WRAP></panel> </collapse> </WRAP></WRAP></panel>
  
-{{page>electrical_engineering_and_electronics:task_rdz03rspbwusy7wk_with_calculation&nofooter}} 
-{{page>electrical_engineering_and_electronics:task_ludzwiuhjxitz85b_with_calculation&nofooter}} 
  
- 
-<panel type="info" title="Exercise 4.1.4 Effects of induction I"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> 
- 
-A change of magnetic flux is passing a coil with a single winding. The following pictures <imgref ImgNrEx01> show different flux-time-diagrams as examples. 
- 
-  * Create for each $\Phi(t)$-diagram the corresponding $u_{\rm ind}(t)$-diagram! 
-  * Write down each maximum value of $u_{\rm ind}(t)$ 
- 
-<WRAP> <imgcaption ImgNrEx01| Flux-Time-Diagrams> </imgcaption> <WRAP> {{drawio>FluxTimeDia1.svg}} \\ </WRAP></WRAP> 
- 
-<button size="xs" type="link" collapse="Solution_4_1_4_1_Solution">{{icon>eye}} Solution for (a)</button><collapse id="Solution_4_1_4_1_Solution" collapsed="true"> 
- 
-For partwise linear $u_{\rm ind}$ one can derive:  
-\begin{align*}  
-u_{\rm ind} &= -{{{\rm d}\Phi}\over{{\rm d}t}} \\  
-            &= -{{\Delta \Phi}\over{\Delta t}}  
-\end{align*} 
- 
-For diagram (a): 
- 
-  * $t= 0.0 ... 0.6 ~\rm s$: $u_{\rm ind} = -{{0 ~\rm Vs}\over{0.6 ~\rm s}}= 0$ 
-  * $t= 0.6 ... 1.5 ~\rm s$: $u_{\rm ind} = -{{-3.75\cdot 10^{-3} ~\rm Vs}\over{0.9 ~\rm s}}= +4.17 ~\rm mV$ 
-  * $t= 1.5 ... 2.1 ~\rm s$: $u_{\rm ind} = -{{0 ~\rm Vs}\over{0.6 ~\rm s}}= 0$ 
- 
-</collapse> 
- 
-<button size="xs" type="link" collapse="Solution_4_1_4_1_Finalresult"> 
-{{icon>eye}} Final result for (a)</button><collapse id="Solution_4_1_4_1_Finalresult" collapsed="true">  
-<WRAP> <imgcaption ImgNrEx01| Flux-Time-Diagrams Solution> </imgcaption> <WRAP> {{drawio>FluxTimeDia1Solution.svg}} \\  
-</WRAP></WRAP> \\  
-</collapse> 
- 
-</WRAP></WRAP></panel> 
- 
-<panel type="info" title="Exercise 4.1.5 Effects of induction II"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> 
- 
-A changing of magnetic flux is passing a coil with a single winding and induces the voltage $u_{\rm ind}(t)$.  
-The following pictures <imgref ImgNrEx02> show different voltage-time diagrams as examples. 
- 
-  * Create for each $u_{\rm ind}(t)$-diagram the corresponding $\Phi(t)$-diagram! 
-  * Write down each maximum value of $\Phi(t)$ 
- 
-Note the given start value $\Phi_0$ for each flux. 
- 
-<WRAP> <imgcaption ImgNrEx02| Voltage-Time-Diagrams> </imgcaption> <WRAP> {{drawio>FluxTimeDia2.svg}} \\ </WRAP></WRAP> 
- 
-#@HiddenBegin_HTML~415_1S,Solution for (a)~@# 
- 
-For partwise linear $u_{\rm ind}$ one can derive:  
-\begin{align*}  
-u_{\rm ind}        &= -{{{\rm d}\Phi}\over{{\rm d}t}} \\  
-\rightarrow  \Phi  &= -\int_0^t{ u_{\rm ind} \;{\rm d}t} \\ 
-\Phi               &= \Phi_0 -\sum_k {u_{{\rm ind},~k} \; \Delta t} \\ 
-\end{align*} 
- 
-For diagram (a): 
- 
-  * $t= 0.00 ... 0.04 ~\rm s\quad$: $\quad \Phi = \Phi_0 - {0 \cdot \; \Delta t} \quad\quad\quad\quad\quad\quad\quad= 0 ~\rm Wb$ 
-  * $t= 0.04 ... 0.10 ~\rm s\quad$: $\quad \Phi =   0 {~\rm Wb} - {{30 ~\rm mV} \cdot \; (t - 0.04 ~\rm s)} = \quad {1.2 ~\rm mWb} - t \cdot 30 ~\rm mV$ 
-  * $t= 0.10 ... 0.14 ~\rm s\quad$: $\quad \Phi =   {1.2 ~\rm mWb} - {0.10 ~\rm s} \cdot 30 ~\rm mV \quad = - {1.8 ~\rm mWb}$ 
- 
-#@HiddenEnd_HTML~415_1S,Solution ~@# 
- 
-#@HiddenBegin_HTML~415_1R,Result for (a)~@# 
-{{drawio>FluxTimeDia2Res.svg}}  
-#@HiddenEnd_HTML~415_1R,Result~@# 
- 
- 
-</WRAP></WRAP></panel> 
  
 <panel type="info" title="Exercise 4.1.6 Coil in magnetic Field I"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> <panel type="info" title="Exercise 4.1.6 Coil in magnetic Field I"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>