Question

A wire of resistance RΩ is bent to form a circle as shown in diagram.
What is the equivalent resistance between points A and B?

Answer 1

Answer:

3R/16

Explanation:

Please refer the attached picture for the step-by-step solution of the given question.

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Answer 2

Given info : A wire of resistance R ohm is bent to form a circle as shown in diagram.

To find : the equivalent resistance between points A and B is ....

solution : let the length of wire is L and radius is r.

we know, R = ρl/A

so, R ∝ l

⇒R₁/R₂ = l₁/l₂

but l = rθ

l₁ = r × π/2 and l₂ = r × (2π - π/2) = r × 3π/2

so, l₁/l₂ = 1/3

Therefore R₁/R₂ = l₁/l₂ = 1/3

resistance of smaller resistor , R₁ = R/4

and resistance of bigger resistor , R₂ = 3R/4

both are joined in parallel combination

so, equivalent resistance between points A and B is Req = R₁R₂/(R₁ + R₂)

= (R/4)(3R/4)/(R/4 + 3R/4)

= 3R/16

Therefore the equivalent resistance between points A and B is 3R/16.

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