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A 60 W lightbulb has a resistance of 240 ohms. At the operating temperature of the tungsten filament, the resistivity is approximately5.0x10^-7 ohms. If the wire used to make the filament is 0.040 mm in diameter (a typical value), how long must the filament be

User MindHacks
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1 Answer

7 votes

Answer:

L = 6.032 m

Step-by-step explanation:

The resistance of a wire is given by

R = ρ L / A

done ρ is the resistivity of matter, L is the length and A is the area

L = R A /ρ

the area of ​​a circle is

A = π r² = π d² / 4

L = R π d² / 4ρ

in the problem they indicate the resistance of 240 Ω, the diameter of 0.040 mm and the resistivity of 5 10⁻⁷ Ω / m

Let's reduce the diameter to SI units

d = 0.040 mm (1 m / 1000 mm) = 4 10⁻⁵ m

let's calculate

L = 240 π (4 10⁻⁵) 2 / (4 5 10⁻⁷)

L = 6.0319 m

L = 6.032 m

User Abarisone
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