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electrical_engineering_and_electronics_1:block14 [2025/11/02 21:32] – mexleadminelectrical_engineering_and_electronics_1:block14 [2025/11/02 21:32] (aktuell) – [Conceptual overview] mexleadmin
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-  - **Analogy:** Replace *displacement flow* in dielectrics ($\vec{D}=\varepsilon\vec{E}$, charge storage) by **flow density** in conductors ($\vec{J}=\sigma\vec{E}$, charge transport). Driving cause is still the electric field $\vec{E}$; the material parameter changes from $\varepsilon$ to $\sigma=\dfrac{1}{\rho}$. +  - **Analogy:** Replace *displacement flow* in dielectrics ($\vec{D}=\varepsilon\vec{E}$, charge storage) by **flow density** in conductors ($\vec{J}=\sigma\vec{E}$, charge transport). \\ Driving cause is still the electric field $\vec{E}$; the material parameter changes from $\varepsilon$ to $\sigma=\dfrac{1}{\rho}$. 
-  - **Global relations:** Voltage is a line integral $U=\int \vec{E}\cdot{\rm d}\vec{s}$; current is a flux integral $I=\iint_A \vec{J}\cdot{\rm d}\vec{A}$. Their ratio defines $G=\dfrac{I}{U}$ and $R=\dfrac{U}{I}$ for a given geometry and material. +  - **Global relations:** Voltage is a line integral $U=\int \vec{E}\cdot{\rm d}\vec{s}$; current is a flux integral $I=\iint_A \vec{J}\cdot{\rm d}\vec{A}$. \\ Their ratio defines $G=\dfrac{I}{U}$ and $R=\dfrac{U}{I}$ for a given geometry and material. 
-  - **Geometry matters:** Uniform fields (parallel plates) give $E=\text{const}$ and simple $G=\dfrac{\sigma A}{l}$. Curved fields (coax) spread with radius → logarithmic dependence.+  - **Geometry matters:** Uniform fields (parallel plates) give $E=\text{const}$ and simple $G=\dfrac{\sigma A}{l}$. \\ Curved fields (coax) spread with radius → logarithmic dependence.
   - **Checks:** Units ($\sigma$ in $\rm S/m$, $G$ in $\rm S$, $R$ in $\Omega$). Limits: \\ $A\!\to\!\infty \Rightarrow R\!\to\!0$ \\ $l\!\to\!0 \Rightarrow R\!\to\!0$ \\ $r_a\!\downarrow r_i \Rightarrow R\!\to\!0$.   - **Checks:** Units ($\sigma$ in $\rm S/m$, $G$ in $\rm S$, $R$ in $\Omega$). Limits: \\ $A\!\to\!\infty \Rightarrow R\!\to\!0$ \\ $l\!\to\!0 \Rightarrow R\!\to\!0$ \\ $r_a\!\downarrow r_i \Rightarrow R\!\to\!0$.
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