Example 21.2 The Resistance of Nichrome Wire The radius of 22-gauge Nichrome wire is 0.299 mm. (A) Calculate the resistance per unit length of this wire. (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? SOLVE IT (A) Calculate the resistance per unit length of this wire. Conceptualize Nichrome has a resistivity two orders of magnitude larger than the best conductors. Therefore, we expect it to have some special practical applications that the best conductors may not have. Categorize We model the wire as a cylinder so that a simple geometric analysis can be applied to find the resistance. Analyze Use the equation and the 1.50 x 10 5 0 .m resistivity of Nichrome to find the " (2.99 x 10 4 m) 2 resistance per unit length: = 5.34 (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? Analyze Find the current: AV AV 10 V 1 = R (R/e)e (5.34 0/m) (1.0 m) = 1.87 A Finalize A copper wire of the same radius would have a resistance per unit length of only 0.061 0/m. A 1.0-m length of copper wire of the same radius would carry the same current with an applied potential difference of only 0.114 V. Because of its high resistivity and resistance to oxidation, Nichrome is often used for heating elements in toasters, irons, and electric heaters. MASTER IT HINTS: GETTING STARTED | I'M STUCK! For the wire in the example, calculate the following assuming that the wire carries a current of 4.8 A. (a) the current density J = x A/m2 Make sure you are taking into account the units used for the radius of the wire. (b) the electric field in the wire E = N/C