Two Wires of Equal Length, One of Aluminium and the Other of Copper Have the Same Resistance. Which of the Two Wires is Lighter? - Physics

Two wires of equal length, one of aluminium and the other of copper have the same resistance. Which of the two wires is lighter? Hence explain why aluminium wires are preferred for overhead power cables. (ρAl = 2.63 × 10−8 Ω m, ρCu = 1.72 × 10−8 Ω m, Relative density of Al = 2.7, of Cu = 8.9.)

Solution

Resistivity of aluminium, ρAl = 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, ρCu = 1.72 × 10−8 Ω m

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

The two relations can be written as

R_1=rho_1l_1/A_1     ...(1)

R_2=rho_2l_2/A_2     ...(2)it is given that

R_1=R_2

therefore rho_1l_1/A_1=rho_2l_2/A_2

And

l_1=l_2

therefore rho_1/A_1=rho_2/A_2

A_1/A_2=rho_1/rho_2

=(2.63xx10^-8)/(1.72xx10^-8)=2.63/1.72

Mass of the aluminium wire,

m1 = Volume × Density

A1l1 × dA1 l1d1 … (3)

Mass of the copper wire,

m2 = Volume × Density

A2l2 × dA2 l2d2 … (4)

Dividing equation (3) by equation (4), we obtain

m_1/m_2=(A_1l_1d_1)/(A_2l_2d_2)

for l_1=l_2

m_1/m_2=(A_1d_1)/(A_2d_2)

For A_1/A_2=2.63/1.72

m_1/m_2=2.63/1.72xx2.7/8.9=0.46

It can be inferred from this ratio that m1 is less than m2. Hence, aluminium is lighter than copper.

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

Concept: Resistivity of Various Materials
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APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 3 Current Electricity
Q 16 | Page 129