Introduction

Circuits are collections of batteries, resistors, wires, and other things through which current will flow. A circuit must provide one closed path, or else a steady current will not flow.
Real circuit and schematic representation. Maybe also a broken circuit. Also, another representation of the same circuit.

When you build a circuit in a lab, it may look rather messy, with wires going in various directions and the like. On paper, it's easier to represent circuits as schematic diagrams, such as the one shown in the figure. Wires are represented by lines, and are usually assumed to be ideal wires Ideal wires have zero resistance, and so there is no potential drop across them: their potential is assumed to be the same everywhere, even when current flows through them. (We'll discuss later when this assumption breaks down.) The shape of the schematic diagram doesn't matter, only the order of connections: the fact that a wire connects the battery to the resistor, and another wire connects the resistor back to the battery.

Consider the following circuit. The potential at the negative terminal of the battery is 0V. Assume the resistor is a light bulb.
Find the potential V at points A, B, and C. If you don't know the exact numbers, at least rank them: e.g. which is largest?
Through which point does more current flow in this circuit, B or C?
Point B has more current through it
Point C has more current through it
The same current flows through B and C.

The principle of current conservation   TBD   says that the current into the resistor is equal to the current out of the resistor. Thus the current through point B is the same as the current through C.

If the second answer in the example above surprised you, you're not alone! (And if you skipped the example, go back and read it!) Many people feel like current should be used up by the light bulb, and so the current should be smaller coming out than going in. But remember that current is the flow of charge. If more charge flows in than out, that means that charge is either being stored up in the light bulb (which would bring the current to a halt) or is being emitted by the light bulb into the environment somehow.

Light bulbs don't emit charge, though; they emit energy, and that's what's being "used up" as the current passes through the light bulb. Charges pick up potential energy as they pass through the battery, and then they release that energy when they fall down the resistor.

Fountain analogy: one waterfall, and then two (with matching schematic diagrams)

It's convenient to think of the electric current as the flow of water in a fountain, with no evaporation. In this analogy, the battery acts as a pump, lifting the water to a higher potential. The water then flows along a short watercourse until it reaches a waterfall (the resistor), where the water drops back down to "ground level" to start over again. As the water falls it might turn a waterwheel which can power a light bulb or other electric device, but otherwise the energy is dissipated into the environment. If there are two waterfalls (resistors), then the total drop (potential)over both waterfalls is equal to the total distance (potential) the water rises in the pump.