# The resistance of an ohmic conductor

• B
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?

Delta2

Staff Emeritus
2021 Award
Think of increasing the area as having many conductors in parallel. Decreasing is the opposite.

Viona, vanhees71, DaveE and 1 other person
Homework Helper
Gold Member
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.)

Viona
Staff Emeritus