Question

The resistance of a wire is R. It is bent at the middle by 180^∘ and both ends are twisted together to make a short of the new wire. The resistance of the new wire is

• A. \(2R\)
• B. \( \dfrac{R}{2} \)
• C. \( \dfrac{R}{4} \)
• D. (R)/(8)

Hint:

Bending and twisting often create parallel paths for current.

Answer 1

The Correct Option is C

Step 1: Original resistance: R = ρ (L)/(A)
Step 2: After bending, wire forms two equal halves in parallel, each of length L/2. Resistance of each half: R' = (R)/(2)
Step 3: Parallel combination: 1/Rₑq = (1)/(R') + (1)/(R') = (2)/(R') ⟹ Rₑq = (R')/(2) = (R)/(4)