Physics HW- Electricity problem?

Question

The filament in an incandescent light bulb is made from tungsten. The light bulb is plugged into a 120-V outlet and draws a current of 1.24 A. If the radius of the tungsten wire is 0.0030 mm, how long must the wire be?

Answer 1

The filament in an incandescent light bulb is made from tungsten. The light bulb is plugged into a 120-V outlet and draws a current of 1.24 A. If the radius of the tungsten wire is 0.0030 mm, how long must the wire be?

This could be a straightforward calculation of resistance, but the resistance varies a lot with temperature, and we don't know the temperature.

Wikipedia puts it at: typically 2000 K to 3300 K depending on the filament type, shape, size, and amount of current passed through.

I'll start with 2000K. The resistivity is 57 μΩ·cm.

Power is 120v x 1.24 a = 149 watts

Resistance is 120/1.24 = 97 ohms

Cross sectional area:

radius = 0.003mm = 0.0003 cm

A = πr² = π(0.0003)² = 2.8e-7 cm²

97 ohms = 57 μΩ·cm x L / 2.8e-7 cm²

L = 97 x 2.8e-7 / 57e-6 = 0.482 cm

Now try 3000K, resistivity = 88 μΩ·cm

L will be 97 x 2.8e-7 / 88e-6 = 0.309 cm

numbers seem low, but length is between 0.31 and 0.48 cm.

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