Answer:
The radius of the cable is 0.0083 m or 8.3 mm.
Explanation:
The resistance of copper cable of 1 meter length will be given by
[tex]R_{cable} = \frac{\rho \times l}{a}[/tex] .... (i)
where the resistivity of copper is [tex]\rho = 1.7 \times 10^{-8} \Omega.m[/tex] , and l is the length of the wire which is considered to be 1m, and a is the cross sectional area of the wire in [tex]m^{2}[/tex].
From the formula of power we know that, [tex]P = I^2 R[/tex] .... (ii)
Therefore 2 W/m = [tex](160)^2 \times R[/tex] .... (iii)
where the resistance,R, actually means the resistance of the cable per meter.
Therefore R ( resistance of cable per meter)
= [tex]\frac{2}{160^2} = 7.812 \times 10^{-5}[/tex] ohms / meter. .... (iv)
Therefore from (i)
[tex]7.812 \times 10^{-5}[/tex] = [tex]\frac{1.7 \times 10^{-8} \times 1}{a} = \frac{1.7 \times 10^{-8} \times 1}{\pi r^{2} }[/tex] ..... (v)
where cross sectional area of the cable, a = [tex]\pi r^2[/tex],
where r is the radius of the cable, and length of cable,l = 1m.
Therefore r = [tex]\sqrt{\frac{ 1.7 \times 10^{-8}}{\pi \times 7.812 \times 10^{-5} } } = 0.0083m = 8.3 mm[/tex]
