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  • A uniform wire of length 25m having resistance of 1 ohm/m is bent in the form of a circle as shown in the figure. If the equivalent resistance between X and Y is 4 ohm, then the length of the longe

A uniform wire of length 25m having resistance of 1 ohm/m is bent in the form of a circle as shown in the figure. If the equivalent resistance between X and Y is 4 ohm, then the length of the longer section is

Option: 1

20 m


Option: 2

5 m


Option: 3

18 m


Option: 4

15 m


Answers (1)

best_answer

Let x be resistance of smaller section then 25-x is the
resistance of the larger section.

\therefore \quad \frac{1}{x}+\frac{1}{25-x}=\frac{1}{4}

x=\frac{25 \pm \sqrt{625-400}}{2}=\frac{25 \pm 15}{2}=20.5

Thus, the resistance of smaller section is 5 \Omega that of bigger section is 20 \Omega, hence its length is 20 \mathrm{~m}.

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vinayak

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