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| 184_notes:resistors [2021/02/26 19:17] – [Resistors in Circuits] bartonmo | 184_notes:resistors [2021/03/04 19:46] (current) – bartonmo |
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| $$E_{thin}=\frac{A_{thick}}{A_{thin}}E_{thick}$$ | $$E_{thin}=\frac{A_{thick}}{A_{thin}}E_{thick}$$ |
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| [{{ 184_notes:5notes_surfacecharge.png?300|Electric field and surface charges around a circuit in steady state with a thin wire}}] | [{{ :184_notes:thinresistorefield_new_.png?300|Electric field and surface charges around a circuit in steady state with a thin wire}}] |
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| Since $A_{thick}>A_{thin}$, this means that the electric field will be bigger in the thin section of wire compared to the thick wires. Because $v_{avg}=uE$, this also means that the average speed of the electrons in the thin wire must also be bigger than the average speed in the thick wires. Ultimately, this means that in the steady state situation, the largest surface charge gradient occurs over the resistor, with only small gradients in the thick wires. | Since $A_{thick}>A_{thin}$, this means that the electric field will be bigger in the thin section of wire compared to the thick wires. Because $v_{avg}=uE$, this also means that the average speed of the electrons in the thin wire must also be bigger than the average speed in the thick wires. Ultimately, this means that in the steady state situation, the largest surface charge gradient occurs over the resistor, with only small gradients in the thick wires. |