Q. A ring is made of a wire having a resistance R₀ = 12 Ω. Points A and B on the ring divide it into two arcs of lengths l₁ and l₂. At which points A and B should a current carrying conductor be connected so that the resistance R of the sub circuit between these points is equal to 8/3 Ω?
A) l₁/l₂ = 1/2
B) l₁/l₂ = 5/8
C) l₁/l₂ = 1/3
D) l₁/l₂ = 3/8
Explanation
[Solution from source] The two arcs have resistances R₁ and R₂ with R₁ + R₂ = 12 Ω, and they are in parallel between A and B: R₁R₂/12 = 8/3, so R₁R₂ = 32. Then R₁ = 4 Ω and R₂ = 8 Ω, and since resistance is proportional to length, l₁/l₂ = 1/2. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.