The force per unit charge $E_c$ is equivalent to the electric field strength. Thus, the work done per unit charge by the force on a section $l$ of the circuit is $W=E_cl$, which is the same as the potential difference between the two endpoints of this section. The graphs show potential difference between each point in the circuit and point $A$. When the circuit is open (shown in red), the only change in potential is across the section of length $l$. When the circuit is closed (shown in green), there is also potential drop of $-E_cl$ across the resistor. (Note the discontinuity in the potential between points $C'$ and $A$ in the open circuit.
