   Chapter 17, Problem 53AP

Chapter
Section
Textbook Problem

Consider an aluminum wire of diameter 0.600 mm and length 15.0 m. The resistivity of aluminum at 20.0°C is 2.82 × 1028 Ω · m. (a) Find the resistance of this wire at 20.0°C. (b) If a 9.00-V battery is connected across the ends of the wire, find the current in the wire.

(a)

To determine
The resistance of wire at 20.0°C

Explanation

Given Info: The length of aluminum wire is 15.0m . The diameter of wire is 0.600mm . The resistivity of aluminum is 2.82×1028Ωm .

Explanation:

Formula to calculate the resistance is,

R=ρLA

• R is the resistance of aluminum wire,
• ρ is the resistivity of aluminum,
• L is the length of the wire,
• A is the area of circular cross section of the wire,

Equation to find the area of cross section is

A=πd24

Substitute the relation for area in the previous equation and rewrite R

R=4ρLπd2

Substitute 2.82×108Ωm for ρ , 15

(b)

To determine
The current in the aluminum wire

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