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Review When a metal rod is heated, its resistance changes both because of a change in resistivity and because of a change in the length of the rod. If a silver rod has a resistance of 2.00 Ω at 22.0°C, what is its resistance when it is heated to 200.0°C? The temperature coefficient for silver is α = 6.1 × 10−3 °C−1, and its coefficient of linear expansion is 18 × 10−6 C−1. Assume that the rod expands in all three dimensions.
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Resistance of the silver rod when it is heated to
Answer to Problem 75PQ
Resistance of the silver rod when it is heated to
Explanation of Solution
Given that the initial temperature of the rod is
Write the general expression for the resistance of a conductor.
Here,
Write the expression for the temperature dependence of resistivity.
Here,
Write the expression for the linear thermal expansion of material.
Here,
Write the expression for the cross sectional area of the conductor.
Here,
The linear thermal expansion affects the radius of the conductor in accordance with equation (III). Thus, the cross sectional area at a final temperature
Here,
Use equation (II), (III), and (V) in (I).
Write the expression for the resistance of the conductor, corresponding to an initial temperature
Use equation (VII) in (VI).
Conclusion:
Substitute
Therefore, resistance of the silver rod when it is heated to
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Chapter 28 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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