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Question
What length of copper wire of specific resistance 1.7 × 10-8 Ω m and radius 1 mm is required so that its resistance is 2 Ω?
Solution
r = 1 mm = `1/1000`m
R = 1Ω
ρ = 1.7 × 10-8 Ω
l = ?
R = `"ρ"l/a`
`l = "Ra"/"ρ"`
= `("R"pir^2)/"ρ"`
= `(2 xx 3.142 xx 1/1000 xx 1/1000)/(1.7 xx 10^-8)`
= `((2 xx 3142 xx 10)/(17 xx 1000)) xx 10^8/10^6`
= `6284/17 xx 10^(8+1-6-3)`
= 369.4 × 100
= 369.4 × 1
l = 369.4 m
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