The tungsten filament light bulb is rated for 220 V and 40 W. Determine the length of the filament

The tungsten filament light bulb is rated for 220 V and 40 W. Determine the length of the filament of this light if the filament diameter is 0.01 mm? The resistivity of tungsten is 5.5 10 Ohm m.

d = 0.01 mm = 1 * 10^-5 m.

U = 220 V.

ρ = 5.5 * 10^-8 Ohm * m.

N = 40 W.

L -?

The current power N in the conductor is determined by the formula: N = U ^ 2 / R, where U is the current voltage at the ends of the conductor, R is the resistance of the conductor.

The resistance R of a cylindrical homogeneous conductor is determined by the formula: R = ρ * L / S, where ρ is the resistivity of the material from which the conductor is made, L is the length of the conductor, S is the cross-sectional area of ​​the conductor.

The power formula N will take the form: N = S * U ^ 2 / ρ * L.

The cross-sectional area of ​​the conductor S is expressed by the formula: S = P * d ^ 2/4.

N = P * d ^ 2 * U ^ 2/4 * ρ * L.

The length of the wire L will be determined by the formula: L = P * d ^ 2 * U ^ 2/4 * ρ * N.

L = 3.14 * (1 * 10 ^ -5 m) 2 * (220 V) ^ 2/4 * 5.5 * 10 ^ -8 Ohm * m * 40 W = 1.727 m.

Answer: The length of the filament of the bulb is L = 1.727 m.