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| Beide Seiten der vorigen Revision Vorhergehende Überarbeitung Nächste Überarbeitung | Vorhergehende Überarbeitung | ||
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electrical_engineering_1:preparation_properties_proportions [2023/10/11 11:27] mexleadmin [Bearbeiten - Panel] |
electrical_engineering_1:preparation_properties_proportions [2023/10/12 03:48] (aktuell) mexleadmin [Bearbeiten - Panel] |
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| 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> | * The point in the $U$-$I$ diagram in which a system rests is called the operating point. In the <imgref BildNr14> | ||
| * 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> | + | * In <imgref BildNr14> |
| </ | </ | ||
| Zeile 856: | Zeile 856: | ||
| <panel type=" | <panel type=" | ||
| - | Let a cylindrical coil in the form of a multi-layer winding be given - this could for example occur in windings of a motor. The cylindrical coil has an inner diameter of $d_i=70~{\rm mm}$ and an outer diameter of $d_a = 120~{\rm mm}$. The number of turns is $n_W=1350$ turns, the wire diameter is $d=2.0~{\rm mm}$ and the specific conductivity of the wire is $\kappa_{Cu}=56 \cdot 10^6 ~{{{\rm S}}\over{{\rm m}}}$. | + | Let a cylindrical coil in the form of a multi-layer winding be given - this could for example occur in windings of a motor. |
| + | The cylindrical coil has an inner diameter of $d_{\rm i}=70~{\rm mm}$ and an outer diameter of $d_{\rm a} = 120~{\rm mm}$. | ||
| + | The number of turns is $n_{\rm W}=1350$ turns, the wire diameter is $d=2.0~{\rm mm}$ and the specific conductivity of the wire is $\kappa_{\rm Cu}=56 \cdot 10^6 ~{{{\rm S}}\over{{\rm m}}}$. | ||
| First, calculate the wound wire length and then the ohmic resistance of the entire coil. | First, calculate the wound wire length and then the ohmic resistance of the entire coil. | ||
| Zeile 864: | Zeile 866: | ||
| The power supply line to a consumer has to be replaced. Due to the application, | The power supply line to a consumer has to be replaced. Due to the application, | ||
| - | * 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? |
| </ | </ | ||