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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.

Respuesta :

davidlcastiblanco

Answer:

a).Jcu= 436.44[tex]x10^{3} \frac{A}{m^{2}}[/tex]

b).λcu=1.05728 [tex]\frac{kg}{m}[/tex]

c).Jal= 274.66 [tex]x10^{3} \frac{A}{m^{2}}[/tex]

d).λcu=0.487 [tex]\frac{kg}{m}[/tex]

Explanation:

a).

ζcu=1.7[tex]x10^{-8}[/tex]Ωm

ζal=2.76[tex]x10^{-8}[/tex]Ωm

[tex]A=\frac{w}{R}[/tex]

wcu=ζcu*l

[tex]Acu=\frac{1.7x10^{-8}*1000}{0.144} =1.18x10^{-4} m^{2}[/tex]

[tex]J=\frac{I}{Acu}=\frac{51.5A}{1.18x10^{-4}m^{2}} \\J=436.44x10^{3} \frac{A}{m^{2}}[/tex]

b).

mass per unit Copper

λcu=Dcu*Acu

λcu=8960 [tex]\frac{kg}{m^{3}}[/tex]*1.18[tex]x10^{-4} m^{2}[/tex]

λcu=1.05728 [tex]\frac{kg}{m}[/tex]

c).

wal=ζal*l

[tex]Aal=\frac{2.7x10^{-8}*1000}{0.144} =0.187x10^{-3} m^{2}[/tex]

[tex]J=\frac{I}{Aal}=\frac{51.5A}{0.187x10^{-3}m^{2}} \\J=274.66x10^{3} \frac{A}{m^{2}}[/tex]

d).

mass per unit Aluminum

λal=Dal*Aal

λal=2600 [tex]\frac{kg}{m^{3}}[/tex]*0.1875[tex]x10^{-3} m^{2}[/tex]

λcu=0.487 [tex]\frac{kg}{m}[/tex]