Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

The diameter of 0-gauge copper wire is 8.252 m m. Find the resistance of a 1.00 km length of such wire used for power transmission.

The resistance of the copper wire is obtained as: $R = 321 mΩ .$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Define Resistance

In an electrical circuit, resistance is a measure of the resistance to current flow. The Greek letter omega $(Ω)$ is used to represent resistance in ohms.

Step 2: Concepts and Principles

The electrical resistance of the value R of a resistive circuit element depends on its geometric structure (its length symbolized as L and cross-sectional area symbolized as A) and on the resistivity p of the material of which it is made:

$R = P = \frac{L}{A}$

Step 3: The given data

$• The length of the wire is : L = 1.00 [1 km \times \frac{1000 m}{1 km}] = 1000 m . • The diameter of the wire is : D = (8.252) . [1 mm \times \frac{1 m}{1000 mm}] = 8.252 \times 10^{- 3} m . • The radius of the wire is : r = D / 2 = 4.126 \times 10^{- 3} m . • The resistivity of the copper is : p = 1.72 \times 10^{- 8} Ω . m$

Step 4: Evaluation of resistance of the copper wire

The resistance of the copper wire is found from the above equation as:

$R = p \frac{L}{A} The value of A = {πr}^{2} which is the cross - sectional area of the wire : R = p \frac{L}{π r^{2}} Entering the values, we obtain : R = 1.72 \times 10^{- 8} Ω . m \times \frac{1000 m}{π \times {(4.126 \times 10^{- 3} m)}^{2}} = 0.321 Ω = (0.321) . (1 Ω \times \frac{1000 mΩ}{1 Ω}) = 321 mΩ Therefore, the resistance of the copper wire is : R = 321 mΩ$

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College Physics (Urone)

Answers without the blur.

Short Answer

The diameter of 0-gauge copper wire is 8.252 m m. Find the resistance of a 1.00 km length of such wire used for power transmission.

Step by Step Solution

Step 1: Define Resistance

Step 2: Concepts and Principles

Step 3: The given data

Step 4: Evaluation of resistance of the copper wire

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College Physics (Urone)

Answers without the blur.

Short Answer

The diameter of 0-gauge copper wire is 8.252 m m. Find the resistance of a 1.00 km length of such wire used for power transmission.

Step by Step Solution

Step 1: Define Resistance

Step 2: Concepts and Principles

Step 3: The given data

Step 4: Evaluation of resistance of the copper wire

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