Final answer:
The new resistance of a wire stretched to n times its original length, without mass change, is n² times its original resistance, as the wire's length is directly proportional to its resistance while its area is inversely proportional.
option d is the correct
Step-by-step explanation:
When the length of a wire is changed to n times its original length while keeping its mass the same, the resistance of the wire also changes. The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. As the mass remains constant and the wire is stretched to n times its original length, its cross-sectional area decreases.
Using the formula for resistance, R = resistivity x (length/area), when the length is increased by a factor of n, the area will decrease by a factor of n (since the volume of the wire remains constant).
Substituting these factors into the formula gives us a new resistance of new R = resistivity x (n x original length)/(original area/n), which simplifies to new R = n2 x original resistance (r). Thus, the new resistance is n2 times the original resistance.