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electrical_engineering_1:preparation_properties_proportions [2023/10/11 11:27] – [Bearbeiten - Panel] mexleadminelectrical_engineering_1:preparation_properties_proportions [2023/10/12 03:47] – [Bearbeiten - Panel] mexleadmin
Zeile 654: Zeile 654:
   * The point in the $U$-$I$ diagram in which a system rests is called the operating point. In the <imgref BildNr14> an operating point is marked with a circle in the left diagram.   * The point in the $U$-$I$ diagram in which a system rests is called the operating point. In the <imgref BildNr14> an operating point is marked with a circle in the left diagram.
   * For nonlinear resistors, the resistance value is $R={{U_R}\over{I_R(U_R)}}=f(U_R)$. This resistance value depends on the operating point.   * For nonlinear resistors, the resistance value is $R={{U_R}\over{I_R(U_R)}}=f(U_R)$. This resistance value depends on the operating point.
-  * Often small changes around the operating point are of interest (e.g. for small disturbances of load machines). For this purpose, the differential resistance $r$ (also dynamic resistance) is determined: \\ $\boxed{r={{dU_R}\over{dI_R}} \approx{{\Delta U_R}\over{\Delta I_R}} }$ with unit $[R]=1~\Omega$.+  * Often small changes around the operating point are of interest (e.g. for small disturbances of load machines). For this purpose, the differential resistance $r$ (also dynamic resistance) is determined: \\ $\boxed{r={{{\rm d}U_R}\over{{\rm d}I_R}} \approx{{\Delta U_R}\over{\Delta I_R}} }$ with unit $[R]=1~\Omega$.
   * As with the resistor $R$, the reciprocal of the differential resistance $r$ is the differential conductance $g$.   * As with the resistor $R$, the reciprocal of the differential resistance $r$ is the differential conductance $g$.
-  * In <imgref BildNr14> the differential conductance $g$ can be read from the slope of the straight line at each point $g={{dI_R}\over{dU_R}}$+  * In <imgref BildNr14> the differential conductance $g$ can be read from the slope of the straight line at each point $g={{{\rm d}I_R}\over{{\rm d}U_R}}$
 </callout> </callout>
  
Zeile 864: Zeile 864:
  
 The power supply line to a consumer has to be replaced. Due to the application, the conductor resistance must remain the same. The power supply line to a consumer has to be replaced. Due to the application, the conductor resistance must remain the same.
-  * The old aluminium supply cable had a specific conductivity $\kappa_{Al}=33\cdot 10^6 ~{\rm {S}\over{m}}$ and a cross-section $A_{Al}=115~{\rm mm}^2$. +  * The old aluminium supply cable had a specific conductivity $\kappa_{\rm Al}=33\cdot 10^6 ~{\rm {S}\over{m}}$ and a cross-section $A_{\rm Al}=115~{\rm mm}^2$. 
-  * The new copper supply cable has a specific conductivity $\kappa_{Cu}=56\cdot 10^6 ~{\rm {S}\over{m}}$+  * The new copper supply cable has a specific conductivity $\kappa_{\rm Cu}=56\cdot 10^6 ~{\rm {S}\over{m}}$
  
-Which wire cross-section $A_{Cu}$ must be selected?+Which wire cross-section $A_{\rm Cu}$ must be selected?
 </WRAP></WRAP></panel> </WRAP></WRAP></panel>