KVPY 2019 SB SX Exam Previous Papers

Question : 29 of 120

Marks: +1, -0

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.

Validate

Solution:

As I = constant
& V = iR & V in general

V = i(R_0 + ∆R)

R={ρl}/A

{∆R}/R=ρ({ ∆l}/l-{ ∆A}/A)

{ ∆A}/A=-{ ∆l}/l

ρ =

constant as there is no joule heating
So

∆R = R ({ρ2∆l}/l)=Rρ(2ε)

⇒

V =i(R + 2ρRε)

so graph will look like

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