Question

Let us consider a copper wire having radius r and length l. Let its resistance be R. If the radius of another copper wire is 2r and the length is l/2, then the resistance of this wire will be

(a) R

(b) 2R

(c) R/4

(d) R/8

Answer 1

Correct option is (d) R/8

Given, length of copper wire = l 

and radius of copper wire = r

∴ Resistance, R = ρ l/A = ρ. l/πr²

∵ A = πr² ....(i)

For second wire, length l₁ = l/2 and radius, r₁ = 2r

Resistance of wire,