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Question
A particular resistance wire has a resistance of 3·0 ohm per metre. Find the resistance of 5 m length of a wire of the same material, but with twice the area of cross section.
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Solution
R = `ρ l/a` ...(i)
∵ the wire's substance is the same, ρ will stay the same
l1 = 5l and l = 1m, a1 = 2a
∴ R1 = ρ `l_1/a_1`
or R1 = ρ `(5l)/(2a)` ...(ii)
(ii) ÷ (i)
`"R"_1/"R" = (ρ(5l)/(2a))/(ρ(l)/(a)`
= `5/2`
R1 = `5/2 "R"`
= `5/2 xx (3.0)`
= 7.5 Ω
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