Ohm's Law for a Circuit (EMF)

A real current source has not only an EMF ($\varepsilon$) but also an internal resistance ($r$). Ohm's law for the whole closed circuit is:

$I=\frac{\varepsilon}{R+r}$

where $R$ is the external resistance (the load). The terminal voltage of the source is smaller than the EMF by the drop across the internal resistance:

$U=I\,R=\varepsilon-I\,r$

The larger the current drawn, the more voltage is "lost" inside the source. At a short circuit ($R=0$) the terminal voltage falls to zero and the current reaches its maximum $\varepsilon/r$. This is why an old battery (large $r$) powers a load poorly.