A cylindrical copper cable carries a current of 1260 A. There is a potential difference of 1.6 10-2 V between two points on the cable that are 0.32 m apart. What is the radius of the cable?
The current and potential difference together tell you the resistance R = V/I = 1.27*10^-5 Ohms
1.27*10^-5 = (rho)*L/A
where rho = the resisitivity of copper, in ohm-m, and A = the cross-sectional area (m^2), which is pi R^2
Solve for R. You will have to look up rho of copper.
To find the radius of the copper cable, we can use the formula for resistance, which is given by:
R = (ρ * L) / A
where R is the resistance, ρ is the resistivity of the material (copper in this case), L is the length of the cable, and A is the cross-sectional area of the cable.
We can rearrange this formula to solve for the cross-sectional area:
A = (ρ * L) / R
The resistivity of copper (ρ) is a known constant, which is 1.68 x 10^-8 ohm-meters.
We also know the length of the cable (L), which is given as 0.32 m.
Now, we need to determine the resistance (R) of the cable.
We can use Ohm's Law to find the resistance:
R = V / I
where V is the potential difference between the two points on the cable and I is the current flowing through the cable.
Plugging in the values for V and I, we get:
R = (1.6 x 10^-2) / 1260
Now that we have the resistance, we can substitute the values into the equation A = (ρ * L) / R to find the cross-sectional area (A) of the cable.
Finally, we can use the formula for the area of a circle to find the radius (r) of the cable:
A = π * r^2
By substituting the value of A, we can solve for the radius (r).
Once we have the radius, we will have the answer to the question.