Why use water to think about a circuit? You cannot see the charges moving in a wire, and you cannot see their energy. Water in pipes is something you can picture, and it behaves in a very similar way. A model like this is a good way to think about a circuit, but it is not the circuit itself, so it is important to know where it works and where it does not.

Energy per drop is voltage. The pump does work on the water, lifting each drop up to the top. The higher it lifts a drop, the more gravitational potential energy the drop has (E = mgh). In the same way, a battery does work on the charges. Voltage is the energy given to each unit of charge:

V = E / Q (volts = joules per coulomb)

A 6 V battery gives 6 joules of energy to every coulomb of charge that passes through it. A pump that lifts the drops twice as high gives each drop twice the energy: twice the voltage.

Flow is current. The number of drops that pass a point each second is the flow of water. For a circuit it is the current, the charge that passes a point each second:

I = Q / t (amperes = coulombs per second)

The water is not used up as it goes round, and neither is the charge. In a loop with no branches the same flow passes every point, so the current is the same everywhere. What is used up is the energy.

The restriction is resistance. It is hard to push water through a narrow pipe. The pump has to do work against this, and the energy of the drops ends up as heat. A narrower restriction lets less water through for the same lift. In a circuit, a resistor (or a lamp, or a heater) transfers the electrical energy to heat and light. The resistance is how much voltage you need for each ampere:

R = V / I, so I = V / R (Ohm’s law)

Lift the water higher (more voltage) and more flows. Make the pipe narrower (more resistance) and less flows. The energy used each second, the power, is the energy per drop times the drops per second: P = VI.

Measuring. A standpipe shows the energy of the drops at one place: the higher the water in the tube, the more energy per drop. A voltmeter connected across a component measures the difference between two places, the energy each coulomb loses in that component (the potential difference). A flow meter is in the pipe so that all the water goes through it, like an ammeter, which is connected in series.

Series and parallel. With two restrictions in series the drops have to go through both, so the same current passes through each. Each takes some of the energy: the voltages add up to the supply voltage (V = V₁ + V₂), and the resistances add up (R = R₁ + R₂). With two restrictions in parallel the water has two pipes to choose from. Each pipe has the full lift across it (the same voltage), the flow splits between them (more in the wider pipe), and the currents add up (I = I₁ + I₂). Two pipes are easier than one, so the total resistance is less than either.

Where the model does not work. (1) In a wire the charges are already there and the whole wire is full of them, so a lamp lights as soon as you switch it on. In the water model the pipes are full too, which is why the flow starts everywhere at once (try it). (2) Water drops fall because of gravity, but the charges are pushed by the electric field in the wire, which the battery sets up. The “height” is a way to picture the energy, not a real height. (3) In real pipes, resistance increases very rapidly as the pipe gets narrower. Here the width is only a picture of the resistance that you choose. (4) The water model does not show the direction of the current or the electrons, which move the other way (the conventional current is drawn from positive to negative).

Things to try. (1) Double the pump setting. What happens to the flow? (2) Double the resistance. What happens to the flow? (3) With two restrictions in series, find the energy lost in each. Do they add up to the pump setting? (4) With two in parallel, which restriction takes more flow, and why? (5) In the second tab, take readings of I for different pump settings and draw the graph. What does the gradient tell you? (6) Use the mystery restriction to find an unknown resistance.