A cylindrical copper cable carries a current of 1170 A. There is a potential difference of 1.60 10-2 V between two points on the cable that are 0.21 m apart. What is the radius of the cable?
Resistancebetweenpoints=V/I solve that.
Resistance= resitivity*length/(PI*r^2)
solve for lenght. look up resistitivty of Cu.
To find the radius of the copper cable, we can use the formula for the resistance of a cylindrical conductor:
R = (ρ * L) / A
where R is the resistance, ρ is the resistivity of copper, L is the length of the cable, and A is the cross-sectional area of the cable.
First, let's find the resistivity of copper. The standard resistivity of copper is approximately 1.7 x 10^-8 Ω*m.
Next, we can calculate the resistance using Ohm's law:
R = V / I
where V is the potential difference and I is the current.
Now, substituting the given values into the formula:
R = (1.60 x 10^-2) / 1170
Simplifying, we find:
R = 1.37 x 10^-5 Ω
Next, we can rearrange the formula for resistance to solve for the cross-sectional area:
A = (ρ * L) / R
Substituting the known values:
A = (1.7 x 10^-8 * 0.21) / (1.37 x 10^-5)
Simplifying, we find:
A = 2.633 x 10^-6 m^2
Finally, we can use the formula for the area of a cylinder to find the radius:
A = π * r^2
2.633 x 10^-6 = π * r^2
Solving for r, we find:
r = sqrt(2.633 x 10^-6 / π)
Calculating this value, we get:
r ≈ 9.11 x 10^-4 m
Therefore, the radius of the copper cable is approximately 9.11 x 10^-4 meters.