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  • A cylindrical conductor has uniform cross section. Resistivity of its material Increases linearly from left end to right end. if left end of the conductor is maintained at zero potential and right

A cylindrical conductor has uniform cross section. Resistivity of its material Increases linearly from left end to right end. if left end of the conductor is maintained at zero potential and right end at +\mathrm{v}_0 . If at a distance x from left end, potential is equal to v,
which of the following graphs is correct.

Option: 1


Option: 2


Option: 3


Option: 4


Answers (1)

best_answer

\text { As } E=\frac{i \rho}{A}=\frac{i\left(\rho_0+\alpha x\right)}{A}=-\frac{d v}{d x} \quad \text { (potential gradient) }

\text { Therefore, } d V=|E| d x=\frac{i\left(\rho_0+\alpha x\right)}{A} d x

\Rightarrow \quad v=\frac{i}{A} \int_0^x\left(\rho_0+\alpha x\right) d x=\frac{i}{A}\left(\rho_0 x+\frac{1}{2} \alpha x^2\right)

This is a graph of a parabola passing through origin and having increasing slope.

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