General Physics, 2nd Edition
General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
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Chapter 17, Problem 63E

(a)

To determine

The room temperature resistance of the aluminum wire.

(a)

Expert Solution
Check Mark

Answer to Problem 63E

The room temperature resistance of the aluminum wire is 2.09×103ohm_.

Explanation of Solution

Given that the length of the wire is 1m, the radius is 0.002m. The resistivity of aluminum is 2.63×108ohmm.

Write the expression for the resistance in terms of dimensions of the conductor.

  R=ρlA        (I)

Here, R is the resistance, ρ is the resistivity, l is the length, and A is the cross sectional area.

Write the expression for the cross sectional area of the wire.

  A=πr2        (II)

Here, r is the radius.

Use equation (II) in (I).

  R=ρlπr2        (III)

Conclusion:

Substitute 2.63×108ohmm for ρ, 1m for l, and 0.002m for r in equation (III) to find R.

  R=(2.63×108ohmm)(1m)π(0.002m)2=2.09×103ohm

Therefore, the room temperature resistance of the aluminum wire is 2.09×103ohm_.

(b)

To determine

The radius of the copper wire with same resistance as of aluminum.

(b)

Expert Solution
Check Mark

Answer to Problem 63E

The radius of the copper wire with same resistance as of aluminum is 0.00162m_.

Explanation of Solution

Solve equation (III) for r.

  r=ρlπR        (IV)

It is obtained that the resistance is 2.09×103ohm, the length is 1m, and the resistivity of copper is 1.72×108ohmm.

Conclusion:

Substitute 1.72×108ohmm for ρ, 1m for l, and 2.09×103ohm for R in equation (IV) to find r.

  r=(1.72×108ohmm)(1m)π(2.09×103ohm)=0.00162m

Therefore, the radius of the copper wire with same resistance as of aluminum is 0.00162m_.

(c)

To determine

To compare the weight of aluminum wire and copper wire.

(c)

Expert Solution
Check Mark

Answer to Problem 63E

The weight of aluminum is 0.462times_ of that of copper.

Explanation of Solution

Given that the length of both wires is 1m, the density of copper is 8900kgm3, the density of aluminum is 2700kgm3. The radius of copper wire is 0.00162m, the radius of aluminum wire is 0.002m.

Write the expression for the mass in terms of the density.

  m=DV        (V)

Here, m is the mass, D is the density, and V is the volume.

Write the expression for the volume of the wire.

  V=πr2l        (VI)

The ratio of weights will be equal to the ratio of masses of the two wires.

  wAlwCu=DAlVAlDCuVCu        (VII)

Here, wAl is the weight of aluminum, and wCu is the weight of copper.

Use the expression for the volume in equation (VII) (consider the equal lengths of the wire).

  wAlwCu=DAl(πrAl2l)DCu(πrCu2l)=DAlrAl2DCurCu2        (VIII)

Conclusion:

Substitute 8900kgm3 for DCu, 2700kgm3 for DAl, 0.00162m for rCu, and 0.002m for rAl in equation (VIII) to find wAl/wCu.

  wAlwCu=(2700kgm3)(0.002m)2(8900kgm3)(0.00162m)2=0.462wAl=0.462wCu

Therefore, the weight of aluminum is 0.462times_ of that of copper.

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Chapter 17 Solutions

General Physics, 2nd Edition

Ch. 17 - Prob. 11RQCh. 17 - Prob. 12RQCh. 17 - Prob. 1ECh. 17 - Prob. 2ECh. 17 - Prob. 3ECh. 17 - Prob. 4ECh. 17 - Prob. 5ECh. 17 - Prob. 6ECh. 17 - Prob. 7ECh. 17 - Prob. 8ECh. 17 - Prob. 9ECh. 17 - Prob. 10ECh. 17 - Prob. 11ECh. 17 - Prob. 12ECh. 17 - Prob. 13ECh. 17 - Prob. 14ECh. 17 - Prob. 15ECh. 17 - Prob. 16ECh. 17 - Prob. 17ECh. 17 - Prob. 18ECh. 17 - Prob. 19ECh. 17 - Prob. 20ECh. 17 - Prob. 21ECh. 17 - Prob. 22ECh. 17 - Prob. 23ECh. 17 - Prob. 24ECh. 17 - Prob. 25ECh. 17 - Prob. 26ECh. 17 - Prob. 27ECh. 17 - Prob. 28ECh. 17 - Prob. 29ECh. 17 - Prob. 30ECh. 17 - Prob. 31ECh. 17 - Prob. 32ECh. 17 - Prob. 33ECh. 17 - Prob. 34ECh. 17 - Prob. 35ECh. 17 - Prob. 36ECh. 17 - Prob. 37ECh. 17 - Prob. 38ECh. 17 - Prob. 39ECh. 17 - Prob. 40ECh. 17 - Prob. 41ECh. 17 - Prob. 42ECh. 17 - Prob. 43ECh. 17 - Prob. 44ECh. 17 - Prob. 45ECh. 17 - Prob. 46ECh. 17 - Prob. 47ECh. 17 - Prob. 48ECh. 17 - Prob. 49ECh. 17 - Prob. 50ECh. 17 - Prob. 51ECh. 17 - Prob. 52ECh. 17 - Prob. 53ECh. 17 - Prob. 54ECh. 17 - Prob. 55ECh. 17 - Prob. 56ECh. 17 - Prob. 57ECh. 17 - Prob. 58ECh. 17 - Prob. 59ECh. 17 - Prob. 60ECh. 17 - Prob. 61ECh. 17 - Prob. 62ECh. 17 - Prob. 63ECh. 17 - Prob. 64ECh. 17 - Prob. 65ECh. 17 - Prob. 66ECh. 17 - Prob. 67ECh. 17 - Prob. 68ECh. 17 - Prob. 69ECh. 17 - Prob. 70ECh. 17 - Prob. 71ECh. 17 - Prob. 72ECh. 17 - Prob. 73ECh. 17 - Prob. 74ECh. 17 - Prob. 75ECh. 17 - Prob. 76ECh. 17 - Prob. 77ECh. 17 - Prob. 78ECh. 17 - Prob. 79ECh. 17 - Prob. 80ECh. 17 - Prob. 81ECh. 17 - Prob. 82ECh. 17 - Prob. 83ECh. 17 - Prob. 84ECh. 17 - Prob. 85ECh. 17 - Prob. 86ECh. 17 - Prob. 87ECh. 17 - Prob. 88ECh. 17 - Prob. 89ECh. 17 - Prob. 90ECh. 17 - Prob. 91ECh. 17 - Prob. 92E
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