Physics
Physics
3rd Edition
ISBN: 9780073512150
Author: Alan Giambattista, Betty Richardson, Robert C. Richardson Dr.
Publisher: McGraw-Hill Education
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Chapter 18, Problem 143P

(a)

To determine

Find the resistance of aluminum wire.

(a)

Expert Solution
Check Mark

Answer to Problem 143P

The resistance of aluminum wire is 29 Ω.

Explanation of Solution

Given, LAl=3LCu and rAl=2rCu

Write the equation for resistance.

R=ρLA (I)

Here, ρ is the resistivity, R is the resistance, L is the length and A is the area.

Rewrite the above equation for aluminum and copper wire and divide them.

RAlRCu=ρAlLAlAAlρCuLCuACu (II)

Rewrite the above equation and substitute the area values to get resistance of aluminum.

RAl=ρAlLAlACuρCuLCuAAlRCu=ρAlLAlπrCu2ρCuLCuπrAl2RCu (III)

Conclusion:

Substitute 24 Ω for RCu, 2.65×108 Ωm for ρAl, 1.67×108 Ωm for ρCu, LAl=3LCu and rAl=2rCu in equation III.

RAl=(2.65×108 Ωm)(3LCu)πrCu2(1.67×108 Ωm)LCuπ(2rCu)2(24 Ω)=29 Ω

Therefore, the resistance of aluminum wire is 29 Ω.

(b)

To determine

Find the resistance of the wire when operating steadily.

(b)

Expert Solution
Check Mark

Answer to Problem 143P

The resistance of the wire when operating steadily is 30 Ω

Explanation of Solution

Write the equation for resistance.

R=VI (IV)

Here, R is the resistance, I is the current and V is potential difference.

Conclusion:

Substitute 300 V for V and 10 A for I in equation IV.

R=300 V10 A=30 Ω

Therefore, the resistance of the wire when operating steadily is 30 Ω.

(c)

To determine

Find the temperature of the copper wire.

(c)

Expert Solution
Check Mark

Answer to Problem 143P

The temperature of the copper wire is 82°C

Explanation of Solution

Write the equation for resistance.

R=R0(1+αΔT)

Here, R is the resistance, R0 is the initial resistance, α is the temperature coefficient of resistivity and ΔT is change in temperature.

Substitute ΔT=TT0 in above equation and rewrite to get final temperature T.

T=1α(RR01)+T0 (V)

Conclusion:

Substitute 20°C for T0, 4.05×103 °C1 for α, 30 Ω for R and 24 Ω for R0 in equation V.

T=14.05×103 °C1(30 Ω24 Ω1)+20°C=82°C

Therefore, the temperature of the copper wire is 82°C.

(d)

To determine

Does the thermal expansion of wire changes the answer in part c.

(d)

Expert Solution
Check Mark

Answer to Problem 143P

The thermal expansion of wire will not changes the answer in part c, since the expansion in wire is less than 0.1%.

Explanation of Solution

The thermal expansion in the wire for the temperature of 62°C is less than 0.1%. This change in the wire dimensions will not affect the answer in part c.

Conclusion:

Therefore, the thermal expansion of wire will not changes the answer in part c, since the expansion in wire is less than 0.1%.

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Chapter 18 Solutions

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