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College Physics (Urone)
Found in: Page 733

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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 .

See the step by step solution

Step by Step Solution

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:


Step 3: The given data

The length of the wire is: L =1.001km ×1000m1 km=1000m. The diameter of the wire is: D=(8.252).1 mm×1 m1000 mm=8.252×10-3 m. The radius of the wire is: r=D/2=4.126×10-3m. The resistivity of the copper is: p=1.72×10-8Ω.m

Step 4: Evaluation of resistance of the copper wire

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

R=pLAThe value of A=πr2 which is the cross-sectional area of the wire:R=pLπr2Entering the values, we obtain:R=1.72×10-8Ω.m×1000mπ×(4.126×10-3m)2 =0.321Ω =(0.321).(1Ω×10001Ω) =321Therefore, the resistance of the copper wire is: R=321

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