The last lesson left charge sitting in a field, pushed by a force. Force is a clumsy thing to track around a circuit, because it points in a direction and changes from place to place. Energy is far easier, because it is a single number, and the quantity a circuit is really organised around is not force but energy per unit charge, which is called voltage. Voltage is the most used word in the subject and the most often misunderstood, so it is worth building from the ground up, because once it is clear the rest of the theory falls into place around it.
Potential energy, then energy per charge
Lift a rock and you store gravitational potential energy in it, energy that gravity will give back as motion if you let the rock fall. Push a positive charge toward another positive charge, against their repulsion, and you store electric potential energy in exactly the same way, energy the field will give back if you release the charge. So far this is Coulomb's law seen through energy rather than force. The step that makes it useful for circuits is to divide out the charge. The electric potential at a point is the potential energy a charge would have there, per unit of its charge:
Dividing by the charge strips away how much charge you happen to be carrying and leaves a property of the location alone, the way the height of a hill is a property of the hill and not of the particular rock you carry up it. Potential is measured in volts, and one volt is one joule of energy per coulomb of charge. A point at 5 V will give up 5 joules to every coulomb that falls from it to zero.
Only differences matter
Potential, like height, has no absolute zero that nature cares about. What drives anything is a difference in it, a potential difference, and this is what everyday language calls a voltage across something. A 9 V battery does not mean its terminals hold some absolute nine volts; it means one terminal sits nine volts higher than the other, so each coulomb that travels from the high terminal to the low one through a circuit gives up nine joules along the way. Because only differences matter, one point in any circuit is chosen as the reference and called ground or zero volts, and every other voltage is quoted relative to it. Choosing where ground sits is free and changes no current, exactly as choosing to measure heights from the sea or from the valley floor changes no waterfall.
The gravitational picture is worth holding onto because it is not merely an analogy but the same mathematics with a different force. Voltage is electrical height. A battery is a pump that lifts charge to a high potential. A wire is level ground the charge coasts along. A resistor is a slope the charge tumbles down, giving up energy as it goes. Charge flows downhill in voltage exactly as water flows downhill in height, and a circuit that goes nowhere, with both ends at the same potential, drives no current for the same reason a lake with a level surface has no stream.
Example. A battery raises 3 coulombs of charge through a potential difference of 12 V. How much energy does it give them?
Energy is charge times potential difference, J. Each coulomb gains 12 J, and three coulombs gain 36 J, which the circuit will spend as the charge flows back down to the low terminal.
Now you. A 1.5 V cell pushes 4 coulombs through a torch. How much energy does it deliver to them?
Answer
J.
Electromotive force, the source that keeps lifting
Charge flowing downhill in voltage loses energy, so a circuit that only ran downhill would stop the moment its charge reached the bottom, like a waterfall that drains its lake. Something has to lift the charge back up, and that something is a source, a battery or a generator, whose defining ability is to push charge from low potential to high, against the field, by spending some other kind of energy. A battery spends chemical energy; a generator spends mechanical energy. The measure of how hard a source lifts is its electromotive force, or EMF, which despite the name is not a force but a voltage, the energy per coulomb the source adds. The EMF is the height of the pump. A real source also has a small internal resistance that eats a little of that lift as current flows, which is why a battery's terminal voltage sags under load, an effect met already in the quadcopter's power system and explained fully a few lessons on.
Why voltage is where circuits begin
The reason voltage, not force or field, is the natural language of circuits is that a circuit is an energy machine. A source lifts charge to a high potential, the charge flows around the loop through wires and components, and at each component it gives up some of its energy per coulomb, its share of the voltage, doing work: heating a resistor, lighting a lamp, spinning a motor. Add up the voltage the charge gains at the source and the voltages it loses around the loop and they must balance, because the charge returns to where it started with the energy it started with, a bookkeeping rule that becomes one of the two great laws of circuit analysis a few lessons from here. Everything from here is charge moving through voltage differences, and the first thing to quantify is the moving itself: how much charge passes, how fast, which is the current of the next lesson.