Question

How do you verify that resistance of a conductor is proportional to the length of the conductor
for constant cross section area and temperature? (ASI)​

Answer 1

Answer:

Resistance:

Electric resistance is the opposition of the flow of current through it.

higher is the resistance, lower is the current flowing.

Back to your question,

Consider two copper wires so that they are having different lengths, of course they do have same resistivity and same cross-sectional areas(A)

The same copper wires will have same resistivity only if they are at same

temperature, where ions can move in same manner in both wires.

Suppose the first wire has a length l and the other has length l'  

The formula for resistance for first wire,

 R = ρ l / A

R = k l   ....(1)  (since ρ,A are constants)

You can prove by here itself,

 Since R is a constant multiplied by l

  So R changes as the same manner as l

  So, length is directly proportional to the resistance.

The equation for resistance for second wire,

 R' = ρ l' / A

R' = k l'    ......(2)  

divide (1) over (2)

R / R'  = l / l'

You can check out experimentally by taking few copper wires of different lengths make them in circuits and finding the resistance variance over the different lengths.

There are more ways to explain this proof.