Eight copper wire of length l and diameter d are joined in parallel to form a single composite conductor of resistance R . If a single copper wire of length 2 l have the same resistance R then its diameter will be _____ d .

Step-by-step solution

Each wire has resistance, r = ρ 4 l π d 2 Eight wire in parallel, then equivalent resistance is R = r 8 = ρ l 2 π d 2 Single copper wire of length 2 l has resistance R = ρ 2 l × 4 π d 1 2 . Comparing both equations, we get, ρ 8 l π d 1 2 = ρ l 2 π d 2 ⇒ d 1 = 4 d