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

Answer:

Length L=0.0125 m

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:

$R=p\frac{L}{A} \\L=\frac{AR}{p}\\ L=\frac{(6.3585*10^{-9})(0.11)}{5.6*10^{-8}}\\L=0.125m$