Explanation Given info: The temperature coefficient of resistivity is α . The resistance of a straight wire is R = R 0 [ 1 + α ( T − T 0 ) ] . Write the expression for the resistance of wire. R = R 0 [ 1 + α ( T − T 0 ) ] Here, R is the resistance of the wire. R 0 is the resistance of initial temperature. α is the temperature coefficient of resistivity. T is the increased temperature T 0 is the initial temperature. The resistance of wire is increased with the increase of temperature. Write the expression for final length if wire., l = l 0 ( 1 + α ′ ( T − T 0 ) ) Here, l is the length of the wire at temperature T . l 0 is the length of wire at temperature T 0 . α ′ is the coefficient of linear expansion. Write the expression for the area of the cross section of the wire at temperature T . A = A 0 ( 1 + 2 α ′ ( T − T 0 ) ) Here, A is the area of the cross section of wire at temperature T . A 0 is the area of the cross section of wire at temperature T 0 . Write the expression for the resistivity of wire with change in temperature. ρ = ρ 0 ( 1 + α ( T − T 0 ) ) Here, ρ is the resistivity of wire at temperature T . ρ 0 is the resistivity of wire at temperature T 0 . Write the expression for resistance at temperature T 0 . R 0 = ρ 0 l 0 A 0 Write the expression for resistance at temperature T R = ρ l A Substitute ρ 0 ( 1 + α ( T − T 0 ) ) for ρ , l 0 ( 1 + α ′ ( T − T 0 ) ) for l and A 0 ( 1 + α ′ ( T − T 0 ) ) for A in above equation

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Author: SERWAY

Publisher: CENGAGE LEARNING (CUSTOM)

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Resistivity

Resistivity is a characteristic property of the conductor’s material that measures the extent to which the material opposes the flow of current. It is denoted by the Greek letter “rho”. Electrical resistivity, also known as specific resistance, depends o…

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Chapter 27, Problem 27.76AP

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The more precise expression for the resistance in terms of R0 , T , T0 , the temperature coefficient of resistivity α and the coefficient of linear expansion α′ .

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Chapter 27, Problem 27.75AP

Chapter 27, Problem 27.77AP

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The more precise expression for the resistance in terms of R 0 , T , T 0 , the temperature coefficient of resistivity α and the coefficient of linear expansion α ′ .

Solution Summary: The author explains the expression for the resistance of a straight wire: R=R_0left, alpha , and the coefficient of linear expansion.

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The more precise expression for the resistance in terms of R0 , T , T0 , the temperature coefficient of resistivity α and the coefficient of linear expansion α′ .

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Chapter 27 Solutions