Question

(i) Consider a conductor of resistance ‘R’, length ‘L’, thickness‘d’ and resistivity ‘rho’. Now this conductor is cut into four equal parts. What will be the new resistivity of each of these parts? Why?

Answer 1

using formula, R = ρL/A

where A is cross sectional area of wire.

given, thickness of wire is d.

so, diameter of wire = d

then, radius of wire = d/2

so, cross sectional area of wire , A = πd²/4

so, R = ρL/(πd²/4)

it is clear that R ∝ L/d²

now wire is cut into four equal parts.

length of each part of wire, l = L/4

thickness of wire remains same.

so, d = constant.

then, R ∝ L

means, resistance of each part will be 1/4 th of R.

i.e., resistance of each part , r = R/4

Answer 2

$\huge\bold\purple{Answer:-}$

We know that resistivity is a material properties and does not depends on the physical dimensions.So even wire cuts in 4 equal but still resistivity will remain same. So the answer is, resistivity will be same. For given voltage parallel connection consume more power because it have low equivalent resistance.