Question

let there be a wire of resistance R, length L and thickness D. If it is cut into two equal parts. What will the new resistivity of each part? Justify your answer

Answer 1

Answer:

Let Resistivity be p

Resistance=R

Length=L

Thickness=D

Radius= D/2

Area of cross section (A)= πr^2= πD^2/4

$R= \: \frac{p \times \: L \: }{A \: }$

R=(p×L)/(πD^2/4)

p= πRD^2/ 4L

Since resistivity of wire does not depend on length of the wire and depend only on material of the wire,

So even after cutting the wire into 2 equal parts,

Resistivity of each part is still p= πRD^2/ 4L

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