Wheatstone bridge principle is used to measure the specific resistance (S₁) of given wire, having length L, radius r. If X is the resistance of wire, then specific resistance is ; S₁=X((π r²)/L). If the length of the wire gets doubled then the value of specific resistance will be :

Solution

Physics sir · 3 steps

Resistivity belongs to the material, not the shape: double the length and X doubles too, so S stays put.

1. What S depends on. Specific resistance (resistivity) is a property of the material and its temperature. Cutting or stretching the sample does not change it.
2. Length doubles. Take a wire of the same material and radius but length 2L. Since X = (S₁ L)/(π r²), the new resistance is X' = 2X.

   S' = X'(π r²)/2L = 2X(π r²)/2L = X(π r²)/L = S₁

3. So. The factor of 2 in X' cancels the factor of 2 in the length, and the specific resistance stays S₁. The answer is (d).

The idea to keep. Resistance R changes with length and area, but resistivity ρ does not. Only a change of material or temperature can change ρ.

Answer from the NTA final answer key. Solution by PrepWiser.