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Question:

A power cable has length 2000m. The cable is made of twelve parallel strands of copper wire each of diameter is 0.51mm, what is the resistance of cable?

What is resistance of the cable (resistivity of copper is1.7x10^-8)Answer is 14 ohms. But please explain how do we get there in full detail.

Answer:

Resistance (R) of a wire is given by: R = ρ.L / A where (ρ) is the resistivity of the wire in Ω.m ; (A) is the cross sectional area of the cable in m? ; (L) is the length of the wire in metres. Radius (r) of one strand = (0.51 / 2) = 0.255 mm = 0.000255 m Cross sectional area of one strand = πr? = (π * 0.000255?) = 2.0428 x 10^-7 m? Total cross section of cable = (12 * 2.0428 x 10^-7 m?) = 2.45 x 10^-6 m? R = (1.7 x 10^-8 * 2000 / 2.45 x 10^-6) = 13.87 = 14 Ω to 2 significant figures.
Find total cross sectional area of copper in cable ie 12 * area of one. calculate the resistance of 1 m then multiply by 2000.

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