184_notes:resistors

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184_notes:resistors [2021/02/26 17:46] – bartonmo184_notes:resistors [2021/03/04 19:46] (current) – bartonmo
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 ===== Resistors in Circuits ===== ===== Resistors in Circuits =====
-To this point, we have talked about what happens inside a wire when connected to two ends of battery - both in the //steady state current// situation and in the initial transient when the circuit is first connected. We found a few important conclusions about the circuit in steady state:+To this point, we have talked about what happens inside a wire when connected to two ends of battery - both in the __//steady state current//__ situation and in the initial transient when the circuit is first connected. We found a few important conclusions about the circuit in //__steady state:__//
   * The electron current going into a location must be the same as the current leaving that location because [[184_notes:charge|charge is conserved]].   * The electron current going into a location must be the same as the current leaving that location because [[184_notes:charge|charge is conserved]].
   * The electron current moves through the wire because there is a constant electric field inside the wire. This electric field comes primarily from the [[184_notes:q_in_wires|surface charges along the wire]].   * The electron current moves through the wire because there is a constant electric field inside the wire. This electric field comes primarily from the [[184_notes:q_in_wires|surface charges along the wire]].
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 $$E_{thin}=\frac{A_{thick}}{A_{thin}}E_{thick}$$ $$E_{thin}=\frac{A_{thick}}{A_{thin}}E_{thick}$$
  
-[{{  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}}]
  
 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. 
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