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

Question

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 .

TestHub · Accepted Answer

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

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