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Q.

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)

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a

B-B

b

C-C

c

A-A

d

Same for all three pairs

answer is C.

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Detailed Solution

Let ρ  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 maximum for contact C-C

 

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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)