In 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)
Text Solution
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Let p 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
$R_{BB} = \rho \cdot \frac{2x}{x \times 4x} = \frac{\rho}{2x} = \frac{4 \rho}{8x}$
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.
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