The Resistance of Nichrome Wire The radius of a piece of Nichrome wire is 0.306 mm. (Assume the wire's temperature is 20°C.) (a) Calculate the resistance per unit length of this wire. SOLUTION Conceptualize This table shows that Nichrome has a resistivity two orders of magnitude larger than the best conductors in the table. Therefore, we expect it to have some special practical applications that the best conductors may not have. Categorize We model the wire as a ---Select--- e so that a simple geometric analysis can be applied to find the resistance. Analyze Use this equation and the resistivity of Nichrome to find the resistance per unit length (in 0/m): R. 0/m (b) If a potential difference of 10 V is maintained across a 1.0 m length of the Nichrome wire, what is the current in the wire? SOLUTION Analyze Use this equation to find the current (in A): AV R Finalize Because of its high resistivity and resistance to oxidation, Nichrome is often used for heating elements in toasters, irons, and electric heaters. EXERCISE A Nichrome wire of length 1.5 m is connected to a 6.00 V voltage source, and the current through the wire is measured to be 1.35 A. What is the cross-sectional area of the wire? (Give your answer in mm?.) Hint mm
The Resistance of Nichrome Wire The radius of a piece of Nichrome wire is 0.306 mm. (Assume the wire's temperature is 20°C.) (a) Calculate the resistance per unit length of this wire. SOLUTION Conceptualize This table shows that Nichrome has a resistivity two orders of magnitude larger than the best conductors in the table. Therefore, we expect it to have some special practical applications that the best conductors may not have. Categorize We model the wire as a ---Select--- e so that a simple geometric analysis can be applied to find the resistance. Analyze Use this equation and the resistivity of Nichrome to find the resistance per unit length (in 0/m): R. 0/m (b) If a potential difference of 10 V is maintained across a 1.0 m length of the Nichrome wire, what is the current in the wire? SOLUTION Analyze Use this equation to find the current (in A): AV R Finalize Because of its high resistivity and resistance to oxidation, Nichrome is often used for heating elements in toasters, irons, and electric heaters. EXERCISE A Nichrome wire of length 1.5 m is connected to a 6.00 V voltage source, and the current through the wire is measured to be 1.35 A. What is the cross-sectional area of the wire? (Give your answer in mm?.) Hint mm
Chapter9: Current And Resistance
Section: Chapter Questions
Problem 81CP: A 10-gauge copper wire has a cross-sectional area A=5.26mm2 and carries a current of I=5.00A . The...
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Transcribed Image Text:The Resistance of Nichrome Wire
The radius of a piece of Nichrome wire is 0.306 mm. (Assume the wire's temperature is 20°C.)
(a) Calculate the résistance per unit length of this wire.
SOLUTION
Conceptualize This table shows that Nichrome has a resistivity two orders of magnitude larger than the best conductors in the table. Therefore, we expect it to have some special practical
applications that the best conductors may not have.
Categorize We model the wire as a
---Select---
so that a simple geometric analysis can be applied to find the resistance.
Analyze Use this equation and the resistivity of Nichrome to find the resistance per unit length (in 0/m):
R
0/m
%3D
%3D
%3D
A
(b) If a potential difference of 10 V is maintained across a 1.0 m length of the Nichrome wire, what is the current in the wire?
SOLUTION
Analyze Use this equation to find the current (in A):
AV
I =
%3D
A
R
Finalize Because of its high resistivity and resistance to oxidation, Nichrome is often used for heating elements in toasters, irons, and electric heaters.
EXERCISE
A Nichrome wire of length 1.5 m is connected to a 6.00 V voltage source, and the current through the wire is measúred to be 1.35 A. What is the cross-sectional area of the wire? (Give your answer
in mm?.)
Hint
mm2
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