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184_notes:resistivity [2018/10/02 17:03] – [Summary] tallpaul | 184_notes:resistivity [2018/10/09 13:38] – dmcpadden | ||
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[[184_notes: | [[184_notes: | ||
- | [{{ 184_notes:resistorshape.jpg?350|A piece of a resistor with a potential difference of $\Delta$ V from one end to the other, a length L, and a cross-sectional area of A.}}] | + | [{{ 184_notes:resistor_shape.png?350|A piece of a resistor with a potential difference of $\Delta$ V from one end to the other, a length L, and a cross-sectional area of A.}}] |
== Derivation of $R$ == | == Derivation of $R$ == | ||
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$$\Delta V =- \int_i^f \vec{E} \cdot \vec{dl}$$ | $$\Delta V =- \int_i^f \vec{E} \cdot \vec{dl}$$ | ||
- | [{{ 184_notes:resistorefielddl.jpg? | + | [{{ 184_notes:resistor_efield_dl.png? |
Because $\vec{E}$ would point along the length of the wire, we would want to integrate along the length of the wire, which would mean that $\vec{E}$ and $\vec{dl}$ would be parallel. This simplifies the dot product to just a multiplication, | Because $\vec{E}$ would point along the length of the wire, we would want to integrate along the length of the wire, which would mean that $\vec{E}$ and $\vec{dl}$ would be parallel. This simplifies the dot product to just a multiplication, |