Question

A copper wire has a resistance of 0.5W.Another copper wire is of the same mass as the first one but double in length find the resistance of the second wire

Answer 1

The resistance of a wire will be proportional to its length and inversely proportional to its area.

So

R = k l / A

where l = length, A = cross section area and k is a constant. If we double the length we must halve the cross-section area. Hence we have a wire with length 2 l and area 0.5 A. The resistance of this wire will be

R = k (2 l) / (0.5 A) = 4 k l / A

four times the original.

Answer 2

Both the wires have same mass and also they are of the same material. So, their density is same and hence their volume will also be same.

Let ρ be the resistivity of the material of the wire.

First wire:

Length = L

Area of cross-section = A

Resistance, R = ρL/A

Second wire:

Length = 2L

Area of cross-section = A/

Since, volume of the wires are same.

Volume = AL = A/(2L)

=> A/ = A/2

So, the resistance of the second wire is,

R/ = ρ(2L)/(A/2) = 4R = 4 × 0.5 =1. 0 Ω