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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Shiksha Academy
Feb 07, 2022 |
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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
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
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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
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