Question

(a) Give one example to show how the resistance depends on the nature of material of the conductor.
(b) Calculate the resistance of an aluminium cable of length 10 km and diameter 2.0 mm if the resistivity of aluminium is 27 × 10−8 Ωm.

Answer 1

Answer:

(a)

If we take two similar wires of same length and same diameter, one of copper metal and other of nichrome alloy, we will find that the resistance of nichrome wire is about 60 times more than that of the copper wire. This shows that the resistance depends on the nature of material of the conductor.

(b)

Let ρ be the resistivity of the aluminum cable, A the cross sectional area of the cable and l the cable's length. The resistance R of the aluminum cable is now given by:

R = ρ·l / A = 2.7·10^-8·(10·10^3) / (π·r²) = 2.7·10^-8·(10·10^3) / (π·(1·10^-3)²)

= 85.9 Ω..

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