Answered: Find the diameter in inches of 3000ft…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Find the diameter in inches of 3000ft of copper wire that has a resistance of 77.78Ω

Expert Solution

Step 1

Given:

Length of copper wire,

$\begin{array}{rcl} l & = & 3000 ft \\ = & 914.4 m \end{array}$

Resistance, $R = 77.78 Ω$

Step 2

The resistivity of copper is given as $ρ = 1.724 \times 10^{- 8} Ωm$

$\begin{array}{rcl} R & = & \frac{ρ l}{A} \\ R & = & \frac{ρ l}{π r^{2}} \\ 77.78 & = & \frac{1.724 \times 10^{- 8} \times 914.4}{π \times r^{2}} \\ r^{2} & = & \frac{1.724 \times 10^{- 8} \times 914.4}{π \times 77.78} \\ r & = & \sqrt{6.45143 \times 10^{- 8}} m \\ r & = & 2.54 \times 10^{- 4} m \end{array}$

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