Question

he current in a tungsten filament lamp is 0.25 A. The filament has a radius o

f 5.4 × 10

−6

m

2

.

Tungsten has 3.4 × 10

28

electrons per cubic metre. Show that the mean drift velocity of the

electrons in this very thin filament is about 0.5 m s

−1

Answer 1

By the definition of the drift velocity, we have:

$$v_d=\dfrac{I}{nAq}=\dfrac{I}{n\pi r^2q},$$ $$v_d=\dfrac{0.25\ A}{3.4\times10^{28}\ \dfrac{el}{m^3}\times\pi\times(5.4\times10^{-6}\ m)^2\times1.6\times10^{-19}\ C},$$ $$v_d=0.5\ \dfrac{m}{s}.$$