How Many Electrons Move through a Headlight Each Second?

To find the number of electrons, we must first find the charge that moved in 1.00 s. The charge moved is related to voltage and energy through the equation $\text{ΔPE}=q\mathrm{\Delta }V$. A 30.0 W lamp uses 30.0 joules per second. Since the battery loses energy, we have $\text{ΔPE}=\text{–30.0 J}$ and, since the electrons are going from the negative terminal to the positive, we see that $\mathrm{\Delta }V=\text{+12.0 V}$.

To find the charge $q$ moved, we solve the equation $\text{ΔPE}=q\mathrm{\Delta }V$:

Entering the values for $\text{Δ}\text{PE}$ and $\text{Δ}V$, we get

The number of electrons ${\text{n}}_{\text{e}}$ is the total charge divided by the charge per electron. That is,

This is a very large number. It is no wonder that we do not ordinarily observe individual electrons with so many being present in ordinary systems. In fact, electricity had been in use for many decades before it was determined that the moving charges in many circumstances were negative. Positive charge moving in the opposite direction of negative charge often produces identical effects; this makes it difficult to determine which is moving or whether both are moving.