Question

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

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

Answer 1

The correct option is A maximum when the battery is connected across$1cm\times \frac{1}{2}cm$ faces

Given, length of the metal rod, $l=10cm$

Area of rectangular cross-section,

$A=1cm\times \frac{1}{2}cm$

Resistance of the wire of resistivity $\rho$ is given by,
$R=\frac{\rho l}{A}$

Resistance of the wire will be maximum when length of the wire is maximum, and area is minimum.

Therefore, for maximum resistance battery should be connected across $1cm\times \frac{1}{2}cm$ faces.

Final answer: (a)