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electrical_engineering_1:introduction_in_alternating_current_technology [2023/12/20 09:55] – mexleadminelectrical_engineering_1:introduction_in_alternating_current_technology [2024/12/04 14:43] (aktuell) – [Bearbeiten - Panel] mexleadmin
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 Generally, from now on not only the voltage will be considered as a phasor, but also the current $\underline{I}$ and derived quantities like the impedance $\underline{X}$. \\ Generally, from now on not only the voltage will be considered as a phasor, but also the current $\underline{I}$ and derived quantities like the impedance $\underline{X}$. \\
 Therefore, the known properties of complex numbers from Mathematics 101 can be applied: Therefore, the known properties of complex numbers from Mathematics 101 can be applied:
-  * A multiplication with $j\omega$ equals a phase shift of $+90°$ +  * A multiplication with $j$ equals a phase shift of $+90°$ 
-  * A multiplication with ${{1}\over{j\omega}}$ equals a phase shift of $-90°$+  * A multiplication with ${{1}\over{j}}$ equals a phase shift of $-90°$
  
 ===== 6.5 Complex Impedance ===== ===== 6.5 Complex Impedance =====
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   * $X = Z \sin \varphi$   * $X = Z \sin \varphi$
  
-value - and therefore a phasor - can simply ==== 6.5.2 Application on pure Loads ====+y ==== 6.5.2 Application on pure Loads ====
  
 With the complex impedance in mind, the <tabref tab01> can be expanded to:  With the complex impedance in mind, the <tabref tab01> can be expanded to: 
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 <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%> <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 reactance of $80\Omega$ at a frequency of $500 ~\rm Hz$. At which frequencies the impedance will have the following values?+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?
   - $85  ~\Omega$   - $85  ~\Omega$
   - $120 ~\Omega$   - $120 ~\Omega$
Zeile 650: Zeile 650:
  
 <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%> <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 currencies can be measured?+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?
   - $0.5 ~\rm A$   - $0.5 ~\rm A$
   - $0.8 ~\rm A$   - $0.8 ~\rm A$