Concept explainers
Review. When a straight wire is warmed, its resistance is given by R = R0,[1 + a(T – T0)] according to Equation 27.20, where a is the temperature coefficient of resistivity. This expression needs to be modified if we include the change in dimensions of the wire due to thermal expansion. For a copper wire of radius 0.100 0 mm and length 2.000 m, find its resistance at 100.0°C, including the effects of both thermal expansion and temperature variation of resistivity. Assume the coefficients are known to four significant figures.
The resistance of wire at
Answer to Problem 27.75AP
The resistance of wire at
Explanation of Solution
Given info: The radius of copper wire is
Write the expression of the resistance of the wire.
Here,
The resistance of wire is increased with the increase of temperature because increase in temperature causes to collision between free electrons in metal with crystal lattice ions.
The length of wire is changed with the increase of temperature. So the final length of the wire is,
Here,
The area of the cross section of the wire at temperature
Here,
Resistivity of wire with change in temperature is,
Here,
The resistivity of copper is
Write the expression for the resistance of wire at
The area of wire is,
Here,
Substitute
Thus, the area of the wire is
Substitute
The relation between resistance of wire, the length of wire and the cross sectional area at final temperature is,
Substitute
Substitute
The coefficient of linear expansion is
Substitute
Conclusion:
Therefore, the resistance of wire at
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Chapter 27 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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