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Question

A conductor with rectangular cross-section has dimensions (a×2a×4a) as shown in figure. Resistance across AB is R1, across CD is R2 and across EF is R3. Then which of the following is true?


A
R1=R2=R3
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B
R1 > R2 > R3
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C
R2 > R3 > R1
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D
R1 > R3 > R2
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Solution

The correct option is B R1 > R2 > R3

Resistance R=ρlA
From the figure the dimensions are a, 2a and 4a, i.e.
Distance between faces A and B = 4a
Distance between faces C and D= 2a
Distance between faces E and F= a

As Rl, AB having the highest length will have the most resistance followed by CD and EF being of the lowest length will have the least resistance. So, the order is R1>R2>R3.

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