A metal wire of length l and diameter d has a resistance R. What would be the resistance of another wire of the same metal and of same length but having double the diameter ?
R
R/4
R/2
2R
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CDS-2 – 2022
If the diameter is doubled (2d), the new area becomes A’ = π(2d)^2/4 = π(4d^2)/4 = πd^2. This means the area becomes four times the original area (A’ = 4A).
Since R ∝ 1/A, the new resistance R’ will be R’ = R / (A’/A) = R / 4.
– Cross-sectional area is proportional to the square of the diameter.