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184_notes:resistivity [2018/10/09 13:39] – dmcpadden | 184_notes:resistivity [2021/02/27 04:07] (current) – [Making sense of $R$] bartonmo | ||
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Section 19.2 in Matter and Interactions (4th edition) | Section 19.2 in Matter and Interactions (4th edition) | ||
- | [[184_notes: | + | /*[[184_notes: |
- | [[184_notes: | + | [[184_notes: |
===== Resistors and Conductivity ===== | ===== Resistors and Conductivity ===== | ||
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[{{ 184_notes: | [{{ 184_notes: | ||
- | === 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 $\sigma$). | ||
- | Resistance has units of volts per amp, which is also called an ohm. An ohm is represented by a capital omega ($\Omega$). Sometimes you may see resistance rewritten in terms of **resistivity**($\rho$), | + | **Resistance has units of volts per amp, which is also called an ohm.** An ohm is represented by a capital omega ($\Omega$). Sometimes you may see resistance rewritten in terms of **resistivity**($\rho$), |
- | === Ohm's Model === | + | ==== Ohm's Model ==== |
Perhaps equally as important, we can now relate the change in electric potential over a resistor to the resistance and current passing through the resistor. This model of resistance works well for low voltage and currents. This model is also often called " | Perhaps equally as important, we can now relate the change in electric potential over a resistor to the resistance and current passing through the resistor. This model of resistance works well for low voltage and currents. This model is also often called " |