Q. 164.2( 16 Votes )

# Two wires of equa

Resistivity of aluminium, p1 = 2.63 × 10−8 Ω m

Relative density of aluminium, d1 = 2.7

Let l1 be the length of aluminium wire and m1 be its mass.

Resistance of the aluminium wire = R1

Area of cross-section of the aluminium wire = A1

Resistivity of copper, p2 = 1.72 × 10−8 Ω metre

Relative density of copper, d2 = 8.9

Let l2 be the length of copper wire and m2 be its mass.

Resistance of the copper wire = R2

Area of cross-section of the copper wire = A2

We can write,

R1 = (p1 × l1)/A1

R2 = (p2 × l2)/A2

Since R1 = R2

(p1 × l1)/A1 = (p2 × l2)/A2

And l1 = l2

Therefore p1/A1 = p2/A2

A1/A2 = (2.63 × 10-8)/(1.72 × 10–8)

A1/A2 = 2.63/1.72

Mass of the aluminium wire,

m1 = Volume × Density

= A1 × l1 × d1 = A1 l1 d1 .....1

Mass of the copper wire, m2 = Volume × Density

= A2 × l2 × d2 = A2 l2 d2 .......2

Dividing equation (1) by equation (2), we obtain

m1/m2 = (A1 l1 d1)/(A2 l2 d2)

Since l1 = l2

m1/m2 = A1 d1/A2 d2

Since A1/A2 = 2.63/1.72 calculated above

m1/m2 = (2.63 × 2.7)/(1.72 × 8.9)

m1/m2 = 0.46

Since m1 is smaller than m2 Hence, aluminium is lighter than copper.

Since aluminium is lighter, it is preferred for overhead power cables over copper.

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