COMEDK 2023 Shift 1 Paper

The resistance R of a wire is given by the formula:
R=ρ‌

L

A

where:
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′=‌

A

2

, keeping in mind that the resistivity ρ does not change because it depends only on the material:
R′=ρ‌

L′

A′

=ρ‌

2L

A 2

=4ρ‌

L

A

=4R
Given that the original resistance is 8Ω :
R′=4×8Ω=32Ω
Therefore, the correct answer is Option A: 32Ω.