A  and B are two points on a uniform ring of resistance 15Ω. The ∠AOB = 45. The equivalent resistance between A and B is
  • a)
    1.64Ω
  • b)
    2.84Ω
  • c)
    4.57Ω
  • d)
    2.64Ω
Correct answer is option 'A'. Can you explain this answer?

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Answers

Shiksha Academy
Feb 07, 2022
Resistance per unit length of ring,

Length of sections ADB and ACB are rθ and r(2π − θ)
∴ Resistance of section ADB,

and resistance of section ACB,
R2 = ρr(2π − θ)

Now, R and R2 are connected in parallel between A and B then


Putting θ = 45∘ = π/4 rad and R = 15Ω


= 1.64Ω

Resistance per unit length of ring,Length of sections ADB and ACB are rθ and r(2π − θ)∴ Resistance of section ADB,and resistance of section ACB,R2 = ρr(2π − θ)=Now, R and R2 are connected in parallel between A and B then=Putting θ = 45= π/4 rad and R = 15Ω== 1.64Ω
Resistance per unit length of ring,Length of sections ADB and ACB are rθ and r(2π − θ)∴ Resistance of section ADB,and resistance of section ACB,R2 = ρr(2π − θ)=Now, R and R2 are connected in parallel between A and B then=Putting θ = 45= π/4 rad and R = 15Ω== 1.64Ω