A ring is made of a wire having a resistance R0 = 12 Ω.

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A ring is made of a wire having a resistance R₀ = 12 Ω. Find the points A and B as shown in the figure, at which a current carrying conductor should be connected so that the resistance R of the sub-circuit between these points is equal to 8/3 Ω .

1. l₁ - 5
  l₂ 8
2. l₁ - 1
  l₂ 3
3. l₁ - 3
  l₂ 8
4. l₁ - 1
  l₂ 2

Correct Option: D

Let x is the resistance per unit length then

8y² + 8 + 16y = 36y
⇒8y² – 20y + 8 = 0
⇒2y² – 5y + 2 = 0
⇒2y² – 4y – y + 2 = 0
⇒2y (y – 2) – 1(y – 2) = 0
⇒(2y – 1) (y – 2) = 0

⇒ y =	l₁	=	1	or 2
	l₂		2