Question

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

Answer 1

Answer:

L = 6.032 m

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