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Example 27.3 The Resistance of Nichrome Wire A Calculate the resistance per unit length of a thin 22-gauge Nichrome wire which has a radius of 0.361 mm. B If a potential difference of 18 V is maintained across a 1.0 m length of the Nichrome wire, what is the current in the wire? Strategy Use the information obtained in Table 27.1. Solution A The cross-sectional area of the wire is calculated below. A = ?r² = ?(3.61 × 10?? m)² = ? m² The resistivity of Nichrome is 1.50 × 10?? ?·m (see Table 27.1). We use Equation 27.11 to find the resistance per unit length. R/l = ?/A = (1.50 × 10?? ?·m) / A = ? ?/m B Because a 1.0 m length of this wire has a resistance of R, we have the following. I = ?V/R = 18 V / R = ? A Note from Table 27.1 that the resistivity of Nichrome wire is two orders of magnitude larger than that of copper. A copper wire of the same radius would have a resistance per unit length of only 0.042 ?/m. A 1.0 m length of copper wire of the same radius would carry the same current with an applied voltage of only 0.11 V. Because of its high resistivity and resistance to oxidation, Nichrome is often used for heating elements in toasters, irons, and electric heaters. You can explore the resistance of different materials with this Interactive Example. Exercise 27.3 Hints: Getting Started | I'm Stuck For the wire in the example, calculate the following assuming that the wire carries a current of 3.6 A. (a) the current density J = ? A/m² (b) the electric field in the wire E = ? N/C

Example 27.3 The Resistance of Nichrome Wire
A Calculate the resistance per unit length of a thin 22-gauge Nichrome wire which has a radius of 0.361 mm.
B If a potential difference of 18 V is maintained across a 1.0 m length of the Nichrome wire, what is the current in the wire?
Strategy Use the information obtained in Table 27.1.
Solution
A The cross-sectional area of the wire is calculated below.
A = ?r² = ?(3.61 × 10?? m)² = ? m²
The resistivity of Nichrome is 1.50 × 10?? ?·m (see Table 27.1). We use Equation 27.11 to find the resistance per unit length.
R/l = ?/A = (1.50 × 10?? ?·m) / A = ? ?/m
B Because a 1.0 m length of this wire has a resistance of R, we have the following.
I = ?V/R = 18 V / R = ? A
Note from Table 27.1 that the resistivity of Nichrome wire is two orders of magnitude larger than that of copper. A copper wire of the same radius would have a resistance per unit length of only 0.042 ?/m. A 1.0 m length of copper wire of the same radius would carry the same current with an applied voltage of only 0.11 V.
Because of its high resistivity and resistance to oxidation, Nichrome is often used for heating elements in toasters, irons, and electric heaters.
You can explore the resistance of different materials with this Interactive Example.
Exercise 27.3
Hints: Getting Started | I'm Stuck
For the wire in the example, calculate the following assuming that the wire carries a current of 3.6 A.
(a) the current density
J = ? A/m²
(b) the electric field in the wire
E = ? N/C

Added by Javier A.

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