The resistance
R of a wire is given by the formula:
R=ρwhere:
ρ is the resistivity of the material,
L is the length of the wire, and
A is the cross-sectional area of the wire.
When the wire is stretched to double its original length (from
24cm to
48cm ), its volume
(V=A×L ) remains constant because the material is conserved. Thus, if the length
L is doubled, the cross-sectional area A must be halved to keep the volume constant.
The new resistance,
R′, can then be calculated using the new length
L′=48cm and the new area
A′=, keeping in mind that the resistivity
ρ does not change because it depends only on the material:
R′=ρ=ρ=4ρ=4RGiven that the original resistance is
8Ω :
R′=4×8Ω=32ΩTherefore, the correct answer is Option A:
32Ω.