Question

Copper and aluminum are being considered for a high-voltage transmission line that must carry a current of 51.5 A. The resistance per unit length is to be 0.144 Ω/km. The densities of copper and aluminum are 8960 and 2600 kg/m3, respectively. Compute (a) the magnitude J of the current density and (b) the mass per unit length λ for a copper cable and (c) J and (d) λ for an aluminum cable.

Answer 1

Answer:

a).Jcu= 436.44$x10^{3} \frac{A}{m^{2}}$

b).λcu=1.05728 $\frac{kg}{m}$

c).Jal= 274.66 $x10^{3} \frac{A}{m^{2}}$

d).λcu=0.487 $\frac{kg}{m}$

Explanation:

a).

ζcu=1.7$x10^{-8}$Ωm

ζal=2.76$x10^{-8}$Ωm

$A=\frac{w}{R}$

wcu=ζcu*l

$Acu=\frac{1.7x10^{-8}*1000}{0.144} =1.18x10^{-4} m^{2}$

$J=\frac{I}{Acu}=\frac{51.5A}{1.18x10^{-4}m^{2}} \\J=436.44x10^{3} \frac{A}{m^{2}}$

b).

mass per unit Copper

λcu=Dcu*Acu

λcu=8960 $\frac{kg}{m^{3}}$*1.18$x10^{-4} m^{2}$

λcu=1.05728 $\frac{kg}{m}$

c).

wal=ζal*l

$Aal=\frac{2.7x10^{-8}*1000}{0.144} =0.187x10^{-3} m^{2}$

$J=\frac{I}{Aal}=\frac{51.5A}{0.187x10^{-3}m^{2}} \\J=274.66x10^{3} \frac{A}{m^{2}}$

d).

mass per unit Aluminum

λal=Dal*Aal

λal=2600 $\frac{kg}{m^{3}}$*0.1875$x10^{-3} m^{2}$

λcu=0.487 $\frac{kg}{m}$