Q138 / 180 · KCET 2020 · Physics

A metal rod of length $10 \mathrm{~cm}$ and a rectangular cross-section of $1 \mathrm{~cm} \times \frac{1}{2} \mathrm{~cm}$ is connected to a battery across opposite faces. The resistance will be

  • Correct answer
    A
    maximum when the battery is connected across $1 \mathrm{~cm} \times \frac{1}{2} \mathrm{~cm}$ faces
  • B
    maximum when the battery is connected across $10 \mathrm{~cm} \times \frac{1}{2} \mathrm{~cm}$ faces
  • C
    maximum when the battery is connected across $10 \mathrm{~cm} \times 1 \mathrm{~cm}$ faces
  • D
    same irrespective of the three faces

Solution

Given, length, $l=10 \mathrm{~cm}$ Resistance of metal rod. $R=\rho \cdot \frac{l}{A}$ i.e., $\quad R \propto \frac{1}{A}$ Since, among given faces in the options, area is minimum corresponding to face $1 \mathrm{~cm} \times \frac{1}{2} \mathrm{~cm}$. Hence, resistance will be maximum when the battery is connected across the face of dimension $1 \mathrm{~cm} \times \frac{1}{2} \mathrm{~cm}$.

Hence, the correct answer is option: 'A'.

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