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184_notes:resistivity [2018/06/19 14:44] – [Resistance] curdemma | 184_notes:resistivity [2018/10/09 13:38] – dmcpadden | ||
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====Resistance==== | ====Resistance==== | ||
- | Before when we talked about resistors, we said that a resistor was a section or part of the circuit where the passage of electrons requires more energy (conventionally, | + | [[184_notes: |
+ | |||
+ | [{{ 184_notes: | ||
- | [{{ 184_notes: | ||
== 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, | ||
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^ Micro ^ Macro ^ | ^ Micro ^ Macro ^ | ||
| $v_{avg}=uE$ | | $v_{avg}=uE$ | ||
- | | $i=nAv_{avg}=nAUE$ | | + | | $i=nAv_{avg}=nAuE$ | |
==== Examples ==== | ==== Examples ==== |