Answer:
(a) 20 kA (B) [tex]diameter=5.0035\times 10^{-2}m[/tex] (c) length = 29.94 m
Explanation:
We have given power P = 100 KW
Voltage V = 5 V
Current density [tex]10A/m^2=10\times 10^{6}A/m^2[/tex]
(A) We have to calculate current
We know that power P = voltage × current
So [tex]100\times 1000=5\times i[/tex]
[tex]i=20kA[/tex]
(b) We know that current density is given by
Current density [tex]=\frac{current}{area}[/tex]
So [tex]10\times 10^{6}A/m^2=\frac{20\times 10^3}{area}[/tex]
[tex]area=2\times 10^{-3}m^2[/tex]
We know that [tex]a=\pi r^2[/tex]
[tex]2\times 10^{-3}=3.14\times r^2[/tex]
[tex]r^2=6.34\times 10^{-4}[/tex]
[tex]r=2.517\times 10^{-2}m[/tex]
[tex]d=2 r=2\times 2.517\times 10^{-2}=5.035\times 10^{-2}m[/tex]
(c) We have to find the length of the cable
We know that resistance [tex]R=\frac{V}{I}=\frac{5}{20\times 10^3}=0.25mohm[/tex]
Resistance is given by [tex]R=\rho \frac{l}{A}[/tex]
So [tex]0.25\times 10^{-3}=1.67\times 10^{-8}\frac{l}{2\times 10^{-3}}[/tex]
l = 29.94 m
