EBK WEBASSIGN FOR KATZ'S PHYSICS FOR SC
EBK WEBASSIGN FOR KATZ'S PHYSICS FOR SC
1st Edition
ISBN: 9781337684651
Author: Katz
Publisher: VST
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Chapter 28, Problem 42PQ
To determine

The length and the radius of the conductor.

Expert Solution & Answer
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Answer to Problem 42PQ

The length and the radius of the conductor are 108m and 8.35×105m.

Explanation of Solution

Write the resistance of the conductor.

   R=ρlA                                                                                                         (I)

Here, R is resistance of the conductor, l is length of the conductor, and A is area of the conductor, and ρ is resistivity.

Rearrange equation (I) for l/A.

   lA=Rρ                                                                                                         (II)

Write the relation for the volume of the given silver cylindrical conductor.

   V=mρ                                                                                                         (III)

Here, V is volume of the given cylindrical conductor, m is mass of the cylinder, and ρ is density of silver conductor.

Alternatively the volume of the cylindrical conductor is,

   V=lA                                                                                                         (IV)

Write the relation for the area of the conductor.

   A=πr2r=Aπ                                                                                                       (V)

Conclusion:

Substitute 78.5Ω for R, 1.586×108Ωm for ρ to find l/A in equation (II).

  lA=78.5Ω1.586×108Ωm=4.95×109m1

Substitute 0.0250kg for m and 10490kg/m3 for ρ to find V in equation (III).

   V=0.0250kg10490kg/m3=2.38×106m3

Combine equation (II) and (IV).

   lAA2=(4.95×109m1)lA=(4.95×109m1)A22.38×106m3=(4.95×109m1)A2A=2.38×106m3(4.95×109m1)=2.19×108m2

Length of the wire is given by

   l=(4.95×109m1)A

Substitute 2.19×108m2 for A to find l in above expression.

   l=(4.95×109m1)(2.19×108m2)=108m

Substitute 2.19×108m2 for A in equation (V) to find r.

   r=2.19×108m2π=8.35×105m

Therefore, the length and the radius of the conductor are 108m and 8.35×105m.

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Chapter 28 Solutions

EBK WEBASSIGN FOR KATZ'S PHYSICS FOR SC

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