Question

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

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

Hint:

Halving the length reduces resistance by half, while doubling the area reduces it further by half.

Answer 1

The Correct Option is C

When the wire is bent at the middle and twisted, its length becomes half and the effective cross-sectional area becomes double. Since R=ρ (L)/(A), the new resistance R' is R'=ρ (L/2)/(2A)=(R)/(4).