Question

If the 0.09-mm-diameter tungsten filament in a light bulb is to have a resistance of 0.11 Ω at 20∘C, how long should it be?

Answer 1

Length L=0.0125 m

Step-by-step explanation:

Given data

Resistance R=0.11Ω

Temperature T=20°C

Resistivity of tungsten at 20°C p=5.6×10⁻⁸Ω.m²

Radius of filament r=0.09/2 =0.045 mm =0.045×10⁻³m

To find

Length of filament L

Solution

The Cross section of area of filament is given as:

`A=\pi r^(2)\\ A=\pi (0.045*10^(-3))^(2)\\A=6.3585*10^(-9)m^(2)`

The Resistance of a material is given as:

`R=p(L)/(A) \\L=(AR)/(p)\\ L=((6.3585*10^(-9))(0.11))/(5.6*10^(-8))\\L=0.125m`