A wire of Nichrome (a nickel-chromium-iron alloy commonly used in heating elemen

Question

A wire of Nichrome (a nickel-chromium-iron alloy commonly used in heating elements) is 50 cm long and has a 1.0 mm^2 cross-sectional area. It carries a current of 8.0 A when a 2.0 V potential difference is applied between its ends. Calculate the resistance of this piece of wire. Calculate the resistivity of Nichrome. What would the resistance of the wire be if it were made of copper instead of Nichrome? What would happen to the resistance of the Nichrome wire if it were stretched until its length was 1.0 m?

Explanation / Answer

a) Use Ohm's law

V = IR so R = V/I = 2/8 = 0.25 ohm

Resistance of piece of wire is 0.25 ohm

b) Resistivity = RA/L

= (0.25*1*10-6)/(0.50) all values are converted in SI units

= 5*10-7 ohm.metre

c) Resistivity of copper is 1.68*10-8 ohm.metre, which is less than the value of resistivity of Nichrome

Therefore, R = (Resistivity of Copper* Length)/ Area = (1.68*10-8 * 0.50) / (1*10-6) = 8*10-3 = 0.008 ohm

d) Now resistance and length are directly proportional to each other so if length double resistivity of nichrome will also double i.e new resistivity of Nichrome = 2* 5*10-7 ohm.metre = 10*10-7 ohm.metre = 10-6 ohm.metre

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