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A tungsten wire has a radius of 0.066 mm and is heated from 20.0 to 1405 degrees C. The temperature coefficient of resistivity is = 4.5 * 10^-3 degree. When 240 V is applied across the ends of the hot wire, a current of 1.3 A is produced.
How long is the wire? Neglect any effects due to thermal expansion of the wire.
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The radius of the tungsten wire is
r = 0.066mm = (0.066mm)*(10^-3 m / 1 mm)
= 0.066 * 10^-3 m

The area of the wire is
A = Pi*r^2 = Pi*(0.066*1-^-3)^2
= 1.368 * 10^-8 m^2

The change in temperature
Delta T = 1405 degrees - 20 degrees
= 1385 degrees

The temperature coefficient of resistivity
alpha = 4.5*10^-3 degrees

The resistance of the wire is
R = V/I = 240V / 1.3 A
= 184.615 Ohms

When the temperature of the wire increases then the resistance of the wire is,
R = R_0[1+alpha*delta-T]
= rho(L/A)[1+alpha*delta-T]

Rearrange the equation for length L.
L = RA / (rho*[1 + alpha * delta-T])
= (184.615 ohm) * (1.368*10^-8 m^2) / ( 5.6 * 10^-8 Ohm * [ 1 + (4.5 * 10^-3)(1385)])
= 6.23 m
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