As shown in the schematic below, a rod of uniform cross-sectional area A and length l is carrying a constant current i through it and voltage across the rod is measured using an ideal voltmeter. The rod is stretched by the application of a force F . Which of the following graphs would show the variation in the voltage across the rod as function of the strain ε when the strain is small. Neglect Joule heating.

Step-by-step solution

When rod is stretched, its length increases. Potential drop across the rod also increases due to increase in resistance of rod. Resistance of rod, R = ρ l A = ρ l 2 X ( ∵ volume of rod, X = A l ) Change in resistance of rod, Δ R = ρ . 2 l Δ l X Change in potential drop across rod, Δ V = i Δ R = i . ρ . 2 l Δ l X = 2 i ρ l 2 X . Δ l l = 2 i ρ l 2 X . ε or Δ V ∝ ε As change in potential drop is directly proportional to strain, voltage as a function of strain is as shown below;