The resistance of an ohmic conductor

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Discussion Overview

The discussion revolves around the factors affecting the resistance of an ohmic conductor, specifically focusing on how the length and cross-sectional area influence resistance. Participants explore both intuitive models and formal definitions related to resistance.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant states that the resistance of an ohmic conductor increases with length due to more collisions experienced by electrons in a longer conductor.
  • Another participant suggests that increasing the cross-sectional area can be thought of as having multiple conductors in parallel, while decreasing the area is the opposite.
  • A different viewpoint questions the intuitive model linking resistance to collisions, proposing that resistance is formally defined as ##R=\frac{V}{I}##, and that decreasing the cross-sectional area leads to a decrease in current (I), which in turn increases resistance.
  • One participant compares adding length to a resistive wire to adding resistors in series, reinforcing the idea of resistance accumulation.
  • A participant expresses appreciation for the clarification provided in the discussion.

Areas of Agreement / Disagreement

Participants present multiple competing views on the relationship between resistance, length, and cross-sectional area, indicating that the discussion remains unresolved with no consensus reached.

Contextual Notes

Some assumptions regarding the intuitive models and formal definitions of resistance are not fully explored, and the discussion does not resolve the implications of these models on the understanding of resistance.

Viona
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I know that the resistance of an ohmic conductor increases with length because the electrons going through the conductor must undergo more collisions in a longer conductor. But why decreasing the cross-sectional area of the conductor also increases the resistance of a conductor?
 
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Think of increasing the area as having many conductors in parallel. Decreasing is the opposite.
 
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Likes   Reactions: Viona, vanhees71, DaveE and 1 other person
I am not sure that your intuitive model, according to which you conclude more resistance means more collisions is entirely correct.
Formally resistance is defined as ##R=\frac{V}{I}##. Decreasing the cross sectional area decreases I and that's why R is increasing. (it is ##I=nSve## where ##S## the cross sectional area, ##n## the density of free electrons, ##v## the average drift velocity and ##e## the charge of electron.)
 
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If you like an intuitive model, adding length to a resistive wire is the same as adding resistors in series.
 
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Thank you, that was helpful and nice.
 
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