   Chapter 17, Problem 43P

Chapter
Section
Textbook Problem

A copper cable is designed to carry a current of 300. A with a power loss of 2.00 W/m. What is the required radius of this cable?

To determine
The radius of copper cable.

Explanation

Given Info: The copper cable carry current 300A . The power loss is 2.00Wm-1 .

Explanation:

Formula to calculate the power loss is,

I2RL=PL

• P is the power loss,
• L is the length of copper cable,
• I is the current through the copper cable,
• R is the resistance of copper cable,

Substitute 2.00Wm-1 for PL and 300A for I in the above equation to find R in terms of L ,

R=(2.00Wm-1(300A)2)L=(2.22×103)LΩ (I)

The resistance of copper wire is (2.22×103)LΩ

Formula to calculate the resistance of copper cable is,

R=ρLπr2

• ρ is the resistivity of copper,
• r radius of circular cross section of copper cable,

Substitute the value of R from equation (I), 1

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