Question

An aluminum power transmission line has a resistance of 0.0620 Ω/km. What is its mass per kilometer?

What is the mass per kilometer of a copper line having the same resistance?

Answer 1

Solution :

Since : Resistance of wire is given by :

Thus : Resistance per unit length will be :

Now, Volume (V) = A L = Mass / Density

Thus :

From equation (i) and (ii)

Therefore : Mass per unit length will be given by :

.

For Aluminium :

Resistivity (ρ) = 2.65 x 10^-8 Ωm

R/L = 0.0620 Ω/km = 6.2 x 10^-5 Ω/m

And, Density of Aluminium (d) = 2.7 x 10³ kg/m³

^.

Therefore : Mass per unit length will be given by :

.

Similarly,

For Copper :

Resistivity (ρ) = 1.72 x 10^-8 Ωm

R/L = 0.0620 Ω/km = 6.2 x 10^-5 Ω/m

And, Density of Aluminium (d) = 8.94 x 10³ kg/m³

^.

Therefore : Mass per unit length will be given by :