A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is [2025]

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Solution

Q.
A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is [2025]

1 9/8

2 8/9

3 27/32

4 32/27

Ans.
(4)

For the wire bent into an equilateral triangle, each side has a resistance $\frac{R}{3}$

$R_{eq} = \frac{(\frac{2 R}{3}) (\frac{R}{3})}{\frac{2 R}{3} + \frac{R}{3}} = \frac{2 R}{9} = R_{1}$ (lets say)

.For the wire bent into a square, each side has a resistance $\frac{R}{4}$

. $R_{eq} = \frac{(\frac{3 R}{4}) (\frac{R}{4})}{\frac{3 R}{4} + \frac{R}{4}} = \frac{3 R}{16} = R_{3}$ (lets say)

$\Rightarrow \frac{R_{1}}{R_{3}} = \frac{\frac{2 R}{9}}{\frac{3 R}{16}} = \frac{32}{27}$

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