Question

A car headlight filament is made of tungsten and has a cold resistance of 0.451 ohms. If the filament is cylindrical in nature and is 3.6m long. What is its cross-sectional area?

Answer 1

Given

Resistance of wire is $R=0.451 \Omega$

Length of the wire is $L=3.6 m$

Resistivity of tungsten  is $\rho=5.6\times 10^{-8} \Omega .m$

The expression for the resistance of the wire is

$R=\frac{\rho l}{A}$

The area of cross section is

$A=\frac{\rho l}{R}=\frac{(5.6\times 10^{-8} \Omega .m)(3.6 m)}{0.451 \Omega}=4.470\times10^{-7} m^2$