A wire of length L is uniformly stretched to triple its original length.By what factor does its resistance change?
A) 1,i.e. ,no change
B) 3
C) 9

Question

A wire of length L is uniformly stretched to triple its original length.By what factor does its resistance change?
A) 1,i.e. ,no change 
B) 3 
C) 9

Quizplus · Accepted Answer

The resistivity of a material depends on the dimensions of the material and the material itself. For a wire of length L and cross-sectional area A, the resistance R can be expressed as:

R = (ρL)/A

where ρ is the resistivity of the material.

When the wire is stretched to triple its original length, its new length will be 3L. The cross-sectional area will remain the same. Therefore, the new resistance of the wire can be expressed as:

R' = (ρ(3L))/A

Dividing the new resistance by the original resistance gives:

R'/R = [(ρ(3L))/A]/[(ρL)/A] = 3

Therefore, the resistance of the wire will increase by a factor of 3. The answer is C).

A Wire of Length L Is Uniformly Stretched to Triple