Part A Nichrome wire, often used for heating elements, has resistivity of 1.0 x

Question

Part A Nichrome wire, often used for heating elements, has resistivity of 1.0 x 106 %u03A9 %u2219 m at room temperature. What length of No. 30 wire (diameter 0.250 mm) is needed to wind a resistor that has 50 ohms at room temperature?

6.54m
.61m
3.66m
22.4m
2.45m
Part A Nichrome wire, often used for heating elements, has resistivity of 1.0 x 106 %u03A9 %u2219 m at room temperature. What length of No. 30 wire (diameter 0.250 mm) is needed to wind a resistor that has 50 ohms at room temperature?

6.54m
.61m
3.66m
22.4m
2.45m

Explanation / Answer

Given Resistivity of Nichrome wire, %u03C1 = 1.0 * 10^-6 %u03A9-m Diameter of wire , d = 0.250 mm Radius of wire, r = 0.125 mm = 0.125 *10^-3 m Resistance , R = 50 %u03A9 From the relation,          R = %u03C1 l / A 50 %u03A9 = (1.0 * 10^-6 %u03A9-m) * l / %u03C0 ( 0.125 *10^-3 m)^2           l = 2.45 m Thus, the length of the wire is 2.45 m Given Resistivity of Nichrome wire, %u03C1 = 1.0 * 10^-6 %u03A9-m Diameter of wire , d = 0.250 mm Radius of wire, r = 0.125 mm = 0.125 *10^-3 m Resistance , R = 50 %u03A9 From the relation,          R = %u03C1 l / A 50 %u03A9 = (1.0 * 10^-6 %u03A9-m) * l / %u03C0 ( 0.125 *10^-3 m)^2           l = 2.45 m Thus, the length of the wire is 2.45 m

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