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Question
Calculate the resistance of a copper wire 1.0 km long and 0.50 mm diameter if the resistivity of copper is 1.7 × 10−8 Ω m.
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Solution
Length of the cable wire, l = 1 km = 1000 m
Diameter of the cable wire, d = 0.5 mm
Area of cross-section,
A `= "A"pi^2`
`= 3.14xx(2.5xx10^-4)^2`
`= 0.96xx10^(-8)m^2`
To find the resistance of the copper cable,
We know that `"R"="l"/"A"`
R `= (1.7xx10^-8xx1000)/(19.6xx10^-8)`
So, R = 86.73 Ω
Thus, the resistance of the copper wire, R = 86.73 Ω
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