A copper cable needs to carry a current of 160 A with a power loss of only 2.0 W/m.What is the required radius of the copper cable? (The resistivity of copper is 1.7 × 10−⁸ Ω⋅m). A)0.43 cm B)0.83 cm C)1.7 cm D)2.6 cm E)0.33 cm

Question

Quizplus · Accepted Answer

The power loss in a cable is given by:
P = I^2 * R * L 
where I is the current, R is the resistance, and L is the length of the cable.

We can rearrange this equation to solve for the resistance:
R = P / (I^2 * L)

The resistance of a cylinder of length L and radius r is given by:
R = (ρ * L) / (π * r^2)
where ρ is the resistivity of the material.

Equating these two expressions for R, we get:
(ρ * L) / (π * r^2) = P / (I^2 * L)
Solving for r, we get:
r = sqrt((ρ * L * P) / (π * I^2))

Substituting the given values, we get:
r = sqrt((1.7e-8 Ω*m * 1 m * 2 W/m) / (π * (160 A)^2))
r = 0.00834 m = 0.83 cm

Therefore, the required radius of the copper cable is 0.83 cm, which is answer choice B.

A Copper Cable Needs to Carry a Current of 160