Question

A uniform metal wire of length $l$ has 10 Ω resistance. Now this wire is stretched to a length $2l$ and then bent to form a perfect circle. The equivalent resistance across any arbitrary diameter of that circle is :

• A. 10 Ω
• B. 5 Ω
• C. 40 Ω
• D. 20 Ω

Answer 1

Answer: (A)

10 Ω

Answer 2

Let R0 be initial resistance = 10 Ω. When stretched to length 2 l , the resistance becomes R1 = $\frac{2l}{l}$R0 = 20 Ω. When bent into a circle, the total resistance remains 20 Ω.

The resistance of the semi-circle along any diameter is given by 20/2 = 10 Ω.