Let's say I have a closed circuit with 1 resistor. Lets say the EMF is between points c and a, the resistor between points a and b, and then between b and c there is nothing but the circuit wire. According to my textbook, the voltage at c is V1, increases by EMF to V2, where V2 = V1+EMF, and then V2 decreases by IR to return to V1 which implies that IR = EMF. I understand all this. I understand that the voltage must return to V1 after completing the loop. But as you move along the wire where the voltage is a constant V1, deltaV must be 0 which implies that E must be 0 along the circuit path as deltaV is the work done by E. But since a current exists and is the same throughout the circuit, this implies that E must exist. So my question is how can deltaV be zero but the E not be 0?