Q. Given figure shows a rectangular block with dimensions $x,\ 2x$ and $4x.$ Electrical contacts can be made to the block between opposite pairs of faces (for example, between the faces labelled $A - A$, $B - B$ and $C - C$). Between which two faces would the maximum electrical resistance be obtained ($A - A$ : Top and bottom faces, $B - B$ : Left and right faces, $C - C$ : Front and rear faces)
A) $A - A$
B) $B - B$
C) $C - C$
D) Same for all three pairs
Explanation
(c) Let $\rho$ is the resistivity of the material
Resistance for contact $A - A$
$R_{AA} = \rho\frac{x}{2x \times 4x} = \frac{\rho}{8x}$
Similar for contacts $B - B$ and $C - C$ are respectively
$R_{BB} = \rho.\frac{2x}{x \times 4x} = \frac{\rho}{2x} = \frac{4\rho}{8x}$
and $R_{CC} = \rho\frac{4x}{x \times 2x} = \frac{2\rho}{x} = \frac{16\rho}{8x}$
It is clear maximum resistance will be for contact $C - C$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.