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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.

Added Tue, 16 Jun '15

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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

Added Tue, 16 Jun '15

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