Answer to Question #308658 in Physics for chan

Question

If the 0.100-mm-diameter tungsten filament in a light bulb is to have a resistance of 0.300 \OmegaΩ at 20.0 ^o

o

C , how long should it be?

Answer 1

The length is given as follows:

$$l = \dfrac{AR}{\rho}$$

where $A = \pi d^2/4$ is the area of the filament cross-section, $d = 0.1mm = 0.1\times 10^{-3}m$ is the diameter, $R = 0.3\Omega$ is the resistance, and $\rho = 5.6\times 10^{-8}\Omega \cdot m$ is electrical resistivity of tungsten. Thus, obtain:

$$l = \dfrac{\pi d^2R}{4\rho}\\ l = \dfrac{\pi \cdot (0.1\times 10^{-3})^2\cdot 0.3}{4\cdot 5.6\times 10^{-8}} \approx 0.0421m = 4.21cm$$

Answer. 4.21 cm.