Question

A cylindrical cable with 1.85 x 10-8 m resistivity carries a current of 1100 A. There is a potential difference of 1.5 x 10-3 V between two points on the cable that are 0.23 m apart. What is the radius of the cable?

Answer 1

The radius is 0.03 meters

Step-by-step explanation:

Assuming cable as ohmic material, it satisfies Ohm's law:

`R=(V)/(I)`

With R the resistance, V the voltage and I the current. So, the resistance between the points indicated in the problem is:

`R=(1.5*10^(-3))/(1100)=1.36*10^(-6) \Ohm`Ω

Now with this value we can use the fact that resistance is:

`R=\rho(L)/(A)`

with ρ the resistivity, L the length and A the cross area of the cylinder, so:

`R=(1.85*10^(-8))(0.23)/(\pi*r^2)=1.36*10^(-6)`

Solving for r:

`r=\sqrt{(1.85*10^(-8))(0.23)/(\pi*(1.36*10^(-6)))}=0.03 m`