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Question
What length of copper wire of resistivity 1.7 × 10-8 Ω m and radius 1 mm is required so that its resistance is 2Ω?
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Solution
Resistance (R) = 2 ohm
Resistivity (ρ) = 1.7 × 10-8 ohm metre
Radius (r) = 1 mm = 10-3 m
Length (l) = ?
`R=ρ l/A`
`ρ=l/(pir^2)`
Substituting the values in the formula above we get,
`2 = 1.7xx10^-8l/(pi(10^-3)^2)`
`2 = 1.7xx10^-8l/(3.14xx(10^-3)^2)`
`2=(1.7xx10^-2xxl)/3.14`
`2 =(1.7xxl)/314`
⇒ l = `(314xx2)/1.7`
⇒ l = 369.4 m
Hence, the length of the copper wire = 369.4 m.
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