Question

A 2.1 cm length of tungsten filament in a small lightbulb has a resistance of 0.067 ω. find its diameter. the resistivity of the filament is 5.6 × 10−8 ω · m. answer in units of mm.

Answer 1

The resistance of an ohmic material is given by 
$R= \frac{ \rho l}{a}$
where l is the length and a is the cross sectional area.  For a circular wire, this area is that of a circle:
$R= \frac{\rho l}{ {d^2} } \frac{4}{\pi}=\frac{5.6\times10^-8 \times0.021m\times4}{\pi d^2} = \frac{1.497\times 10^-9}{d^2}$
Then solving for diameter, d:
$d^2=\frac{1.497\times 10^-9}{0.067}=2.235\times10^-8$
$d=0.1495mm$