Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

Link zu dieser Vergleichsansicht

electrical_engineering_and_electronics_2:block02 [2026/03/05 02:40] – angelegt mexleadminelectrical_engineering_and_electronics_2:block02 [2026/03/05 03:09] (aktuell) – mexleadmin
Zeile 167: Zeile 167:
 \end{align*} \end{align*}
 </callout> </callout>
- 
-<panel type="info" title="Exercise 6.2.1 The Rectified Value of rectangular and triangular signals"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> 
- 
-Calculate the rectified value of rectangular and triangular signals! Use similar symmetry simplifications as shown for AC signals. Compare it to the values shown in <imgref imageNo5>. 
- 
-</WRAP></WRAP></panel> 
  
 == The RMS Value == == The RMS Value ==
Zeile 227: Zeile 221:
  
 </callout> </callout>
- 
-<panel type="info" title="Exercise 6.3.2 The RMS Value of rectangular and triangular signals"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> 
- 
-Calculate the RMS value of rectangular and triangular signals! Use similar symmetry simplifications as shown for AC signals.  
-Compare it to the values shown in <imgref imageNo5>. 
- 
-</WRAP></WRAP></panel> 
  
 == Comparison of the different Averages == == Comparison of the different Averages ==
Zeile 403: Zeile 390:
  
 ===== Exercises ===== ===== Exercises =====
 +
 +<panel type="info" title="Exercise 6.2.1 The Rectified Value of rectangular and triangular signals"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
 +
 +Calculate the rectified value of rectangular and triangular signals! Use similar symmetry simplifications as shown for AC signals. Compare it to the values shown in <imgref imageNo5>.
 +
 +</WRAP></WRAP></panel>
 +
 +<panel type="info" title="Exercise 6.3.2 The RMS Value of rectangular and triangular signals"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
 +
 +Calculate the RMS value of rectangular and triangular signals! Use similar symmetry simplifications as shown for AC signals. 
 +Compare it to the values shown in <imgref imageNo5>.
 +
 +</WRAP></WRAP></panel>
 +
 +
 +<panel type="info" title="Exercise 6.3.1 Impedance of single Components I"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
 +A coil has a impedance of $80~\Omega$ at a frequency of $500 ~\rm Hz$. At which frequencies the impedance will have the following values?
 +  - $85  ~\Omega$
 +  - $120 ~\Omega$
 +  - $44  ~\Omega$
 +
 +<button size="xs" type="link" collapse="Loesung_6_3_1_1_Endergebnis">{{icon>eye}} Solution</button><collapse id="Loesung_6_3_1_1_Endergebnis" collapsed="true">
 +When the frequency changes the reactance changes but the inductance is constant. Therefore, the inductance is needed. \\
 +It can be calculated by the given reactance for $f_0 = 500 ~\rm Hz$.
 +\begin{align*}
 +X_{L0}&=2\pi f_0L\\
 +L     &=\frac{X_{L0}}{2\pi f_0}
 +\end{align*}
 +
 +On the other hand, one can also use the rule of proportion here, and circumvent the calculation of inductance.\\
 +It is possible to calculate the reactance at other frequencies with the given reactance.
 +\begin{align*}
 +X_L&=2\pi fL\\
 +f  &=\frac{X_L}{2\pi L}\\
 +   &=\frac{X_L}{X_{L0}}f_0
 +\end{align*}
 +
 +With the values given:
 +\begin{equation*}
 +f_1 = \frac{85 ~\Omega}{80~\Omega}\cdot500~{\rm Hz}\qquad 
 +f_2 = \frac{120~\Omega}{80~\Omega}\cdot500~{\rm Hz}\qquad 
 +f_3 = \frac{44 ~\Omega}{80~\Omega}\cdot500~{\rm Hz}
 +\end{equation*}
 +
 +</collapse><button size="xs" type="link" collapse="Loesung_6_3_1_2_Endergebnis">{{icon>eye}} Final value</button><collapse id="Loesung_6_3_1_2_Endergebnis" collapsed="true">
 +\begin{equation*}
 +f_1=531.25~{\rm Hz}\qquad f_2=750~{\rm Hz}\qquad f_3=275~{\rm Hz}
 +\end{equation*}
 +</collapse>
 +</WRAP></WRAP></panel>
 +
 +<panel type="info" title="Exercise 6.3.2 Impedance of single Components II"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
 +A capacitor with $5 ~{\rm µF}$ is connected to a voltage source which generates $U_\sim = 200 ~{\rm V}$. At which frequencies the following currents can be measured?
 +  - $0.5 ~\rm A$
 +  - $0.8 ~\rm A$
 +  - $1.3 ~\rm A$
 +</WRAP></WRAP></panel>
 +
 +<panel type="info" title="Exercise 6.3.3 Impedance of single Components III"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
 +A capacitor shall have a capacity of $4.7 ~{\rm µF} \pm 10~\%$. This capacitor shall be used with an AC voltage of $400~\rm V$ and $50~\rm Hz$.
 +What is the possible current range which could be found on this component?
 +</WRAP></WRAP></panel>
 +
 +
 +
 ==== Worked examples ==== ==== Worked examples ====