A tungsten wire has a radius of 0.061 mm and is heated from 20.0 to 1335 °C. The temperature coefficient of resistivity is α = 4.5 10-3 (C°)−1. When 240 V is applied across the ends of the hot wire, a current of 1.2 A is produced. How long is the wire? Neglect any effects due to thermal expansion of the wire.
here,
resistivity of tungesten at 20 degree C , p0 = 5.6 * 10^-8 ohm.m
dT = 1335 - 20 Degree = 1315 degree
the new resistivity , p = p0 * ( 1 + alpha * dT)
p = 5.6 * 10^-8 * ( 1 + 0.0045 * 1315)
p = 3.87 * 10^-7 ohm.m
radius of wire , r = 0.061 mm = 6.1 * 10^-5 m
let the length of wire be l
resistance , R = p * l /area = V/I
3.87 * 10^-7 * l /(pi * ( 6.1 * 10^-5)^2) = 240 /1.2
solving for l
l = 6.04 m
the length of wire is 6.04 m
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