Question

Prove resistance of a conductor is inversely proportional to (i) the square
of the radius of conductor and (ii) the square of the diameter of the
conductor?

Answer 1

Answer:

Why is the square of the diameter of a wire inversely proportional to its resistance?

Where can you find data about materials online?

The answer is simple.

Consider a wire with diameter D

So the cross-section area of the wire is A=πD²/4

We know that R(Resistance)=p.l/A

Where p is specific resistance of the wire.

l is the length of the wire.

A is Area of cross section of wire.

So,by this formula you can see that as area A increases the resistance decreases.

Let's go to your question.

Square of the diameter of a wire =D²

So now the new area A¹=π(D²)²/4

A¹=πD⁴/4

So the area will increase and resistance will decrease.

As the area of contact increases there will be more electrons flow so the resistance is low.

Correct me if I am wrong.