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| 184_notes:resistivity [2018/10/09 13:38] – dmcpadden | 184_notes:resistivity [2018/10/09 13:39] – dmcpadden | ||
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| - | == Derivation of $R$ == | + | === Derivation of $R$ === |
| For example, suppose we have a resistor that has a cross sectional area of $A$, a length $L$, and a potential difference of $\Delta V$ from one end to the other. If we //__assume a steady state current__//, | For example, suppose we have a resistor that has a cross sectional area of $A$, a length $L$, and a potential difference of $\Delta V$ from one end to the other. If we //__assume a steady state current__//, | ||
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| $$R =\frac{L}{\sigma A}$$ | $$R =\frac{L}{\sigma A}$$ | ||
| - | == Making sense of $R$ == | + | === Making sense of $R$ === |
| Why does the bottom fraction make sense? A longer, thinner wire should be more resistive, so the geometric properties make sense (directly proportionally to $L$ and inversely proportional to $A$). A wire with higher conductivity should be less resistive, which also make sense (inversely proprtional to $\sigma$). | Why does the bottom fraction make sense? A longer, thinner wire should be more resistive, so the geometric properties make sense (directly proportionally to $L$ and inversely proportional to $A$). A wire with higher conductivity should be less resistive, which also make sense (inversely proprtional to $\sigma$). | ||