A copper cable needs to carry a current of 200 A with a power loss of only 3.0 W/m.What is the required radius of the copper cable? (The resistivity of copper is 1.7 x 10^-8 W*m). A)0.21 cm B)0.85 cm C)3.2 cm D)4.0 cm

Question

Quizplus · Accepted Answer

The power loss in a wire is given by P=I^2*R, where P is the power loss, I is the current, and R is the resistance of the wire. The resistance of the wire can be given by R=rho*L/A, where rho is the resistivity of copper, L is the length of the wire, and A is the cross-sectional area of the wire. Since we want a power loss of 3.0 W/m, we can set P/L=3.0 to get:

3.0 = I^2*R/L
R/L = 3.0/I^2

Plugging in the given values, we get:

R/L = 3.0/(200^2*(1.7 x 10^-8))

Solving for the radius, we get:

A = pi*R^2
R = sqrt(A/pi) = sqrt((I^2*rho)/(pi*P/L)) = 0.0085 m or 0.85 cm (to 2 significant figures)

Therefore, the best choice is B.

A Copper Cable Needs to Carry a Current of 200