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Q.

A wire of resistance 20 Ω is bent in the form of a square. What is the resistance between the ends of the diagonal?
 

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a

10 Ω

b

5 Ω

c

20 Ω

d

15 Ω

answer is B.

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Detailed Solution

Since the sides of the square are equal and the wire is bent into a square, each side will have the same resistance, which is 20/4 or 5 Ω.
 

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 Now if we make a diagonal, there will be two faces on each side of the diagonal and these two faces will have a resistance of 10 Ω.

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 The resistance between the ends of a diagonal is in parallel combination.

RD= R1R2R1+ R2

RD= 10 X1010 + 10

RD = 5 Ω

Therefore, the resistance between the ends of a diagonal of the square will be 5 Ω.

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