Question

A motorist switches on their headlights. If the distance along the copper connecting wires between the car battery and the one of the light is 1.5m, what is the average time an individual electron will take to drift between the battery and the light ? Take the current in the wire to be 3A and the cross section area of the wire to be 3x10^-7m

Answer 1

Let's first find the drift velocity of electrons:

$$v=\dfrac{I}{nqA},$$ $$v=\dfrac{3\ A}{8.5\cdot10^{28}\ \dfrac{el}{m^3}\cdot1.6\cdot10^{-19}\cdot3\cdot10^{-7}\ m^2}=7.35\cdot10^{-4}\ \dfrac{m}{s}.$$

Finally, we can find the average time an individual electron will take to drift between the battery and the light:

$$t=\dfrac{s}{v}=\dfrac{1.5\ m}{7.35\cdot10^{-4}\ \dfrac{m}{s}}=2041\ s=0.57\ h.$$