alculate the resistance of 2 km long copper wire of radius 2 mm. (Resistivity of copper = 1.72 x 1 0-8)
Question
alculate the resistance of 2 km long copper wire of radius 2 mm. (Resistivity of copper = 1.72 x 1 0-8)
Solution
To calculate the resistance of a copper wire, we can use the formula:
R = (ρ * L) / A
Where: R is the resistance, ρ is the resistivity of copper, L is the length of the wire, and A is the cross-sectional area of the wire.
Given: Length of the wire (L) = 2 km = 2000 m Radius of the wire (r) = 2 mm = 0.002 m Resistivity of copper (ρ) = 1.72 x 10^-8 Ω·m
First, we need to calculate the cross-sectional area (A) of the wire using the formula:
A = π * r^2
Substituting the values: A = π * (0.002)^2 A = 3.14 * 0.000004 A = 0.00001256 m^2
Now, we can substitute the values of ρ, L, and A into the resistance formula:
R = (1.72 x 10^-8 * 2000) / 0.00001256 R = 0.0000344 / 0.00001256 R = 2.74 Ω
Therefore, the resistance of the 2 km long copper wire with a radius of 2 mm is 2.74 Ω.
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