The filament of a 100 W (120 V) light bulb is a tungsten wire 0.035 mm...

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The filament of a 100 W (120 V) light bulb is a tungsten wire 0.035 mm...

The filament of a 100 W (120 V) light bulb is a tungsten wire 0.035 mm in diameter. At the filament's operating temperature, the resistivity is 5.0×10−7Ω⋅m.

How long is the filament? L=? m

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Answer 1

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Answer #1

apply the formula for resistance R = rho L/A

where rho is resisitivity = 5 e -7 ohm m

L is length = ? m

A is area = pi r^2 where r is radius = d/2 = 0.035/2 = 0.0175 mm

use ohms law and power relation as Power P = V^2/R

so
Resistance R = V^2/P

R = 120*120/100 = 144 ohms

so

now from R = rho L/A

L = RA/rho

L = 144 *3.14 * 0.0175 e -3 * 0.0175 e -3/(5 e -7)

L = 0.277 m

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Answer 2

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