High School The resistance of an ohmic conductor

[Viona]

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?

 

[Vanadium 50]

Think of increasing the area as having many conductors in parallel. Decreasing is the opposite.

 

[Delta2]

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.)

 

[Vanadium 50]

If you like an intuitive model, adding length to a resistive wire is the same as adding resistors in series.

 

[Viona]

Thank you, that was helpful and nice.