Question

A current-carrying ohmic metal wire has a cross sectional area that gradually becomes smaller from one end of the wire to the other. The current has the same value for each section of the wire, so charge does not accumulate at any one point. How does the resistance per unit length vary along the wire as the area becomes smaller?.

Answer 1

The cross-sectional area decreases, so the resistance per unit length, increases

What is resistance ?

The limitation of current flow in an electrical circuit is measured in terms of resistance. The ohm, or the Greek letter omega, stands for the unit of measurement for resistance.

According to the given information

We know that

Resistance of the wire is directly proportional to length of the wire and inversely proportional to the area of the wire

So,

R ∝
`(L)/(A)`

Proportionality constant ρ = resistivity constant

R = ρ
`(L)/(A)`

So If the cross sectional area decreases , Resistance per unit length increases