The resistance of an ohmic conductor

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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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  • #2
Vanadium 50
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Think of increasing the area as having many conductors in parallel. Decreasing is the opposite.
 
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  • #3
Delta2
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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 thats 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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Vanadium 50
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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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  • #5
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Thank you, that was helpful and nice.
 

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