Question

The filament in an incandescent light bulb is made from tungsten. The resistivity of tungsten = 5.6e-8 Ω*m. The radius of the tungsten wire is 0.045 mm. If the bulb is plugged into a 120 V outlet and is to draw a current of 1.24 A, how long must the wire be?

Answer 1

11m

Step-by-step explanation:

Given:

Resistivity ρ = 5.6e-8 Ωm

Radius r = 0.045 mm
`=(0.045)/(1000)` = 4.5 x 10⁻⁵ m

Voltage V = 120V

Current I = 1.24A

From Ohm's law,
`R = (V)/(I)`

`R = (120)/(1.24)`

R = 96.77 Ω

Resistivity = (Resistance × Area)/ length

ρ = (RA)/L

Therefore, the length of a wire is given by;

L = (RA)/ρ

Calculating the area A of the wire;

A = πr²

A = π × (4.5 x 10⁻⁵)²

A = 6.36 x 10⁻⁹ m²

Substituting area of the wire A = 6.36 x 10⁻⁹ m² into the equation of the length of wire

L = (96.77 × 6.36×10⁻⁹ ) / 5.6×10⁻⁸

L = 10.9977m

L = 11m (approximately)