Final answer:
When the length of a cylindrical wire is increased by 100%, the resistance of the wire will also increase by 100%. The decrease in diameter will not have any effect on the resistance of the wire. The correct answer is A. 100%.
Step-by-step explanation:
When the length of a cylindrical wire is increased by 100%, it is doubled in length. The resistance (R) of the wire is directly proportional to its length (L) and inversely proportional to its cross-sectional area (A), given by the formula R = ρ (L/A), where ρ is the resistivity of the material.
Since the volume remains constant when stretching the wire without any material being added, the cross-sectional area decreases when the length increases.
When the length of a cylindrical wire is increased by 100%, the resistance of the wire will also increase by 100%. This is because resistance is directly proportional to length.
However, the decrease in diameter will not have any effect on the resistance of the wire, as resistance is not affected by diameter. So, the change in resistance will be 100%.