Here is a simple electric circuit:
This is the sort of circuit you would find in an old-style hand-held torch. It has an incandescent lamp, a battery to provide the power, and a switch to turn it on and off. We will use this to explain some basic points about electricity.
Atoms are made of neutrons and protons (the nucleus) and electrons. Every proton has a fixed amount of positive charge, and every electron have the same fixed amount of negative charge, and neutrons have no charge at all. An atom normally has the same number of protons and electrons, so it is electrically neutral.
If you rub a party balloon against your jumper, the balloon will strip some of the electrons away from the atoms in your jumper, leaving the balloon with a net negative charge (it has more electrons than protons, in total). This is called static electricity. If you charge two balloons in this way they will repel each other (you will feel a small force pushing them apart when you bring them close together). That is because like charges repel.
On the other hand, if you put the charged balloon close to a wall, it will stick to the wall. That is because the wall is neutral (no overall charge), which make it more positive that the balloon - if the balloon has a charge of -1 and the wall has a charge of 0, the wall is more positive. Opposite charges attract, so the balloon sticks.
An electric current is when electrons flow continuously along a conductor (usually a thin metal wire). A common analogy, that works quite well, is to think of electricity flowing through wires as being a bit like water flowing through pipes. It isn't a perfect analogy but it works in quite a few cases.
To make electrons flow continuously as an electric current, we need two things. First we need a power source, such as a battery. The battery creates a voltage difference that forces the electrons to flow round the circuit. The second thing we need is a closed circuit. There must be a route for the current to flow all the way back to the other side of the battery.
In the diagram above, when the switch is closed there is a complete circuit so the current flows. When the switch is open, the circuit has a break in it so the current can't flow. Air is an insulator, electricity cannot flow through the air to complete the circuit.
Using the water analogy, for the water to flow there needs to be a pressure difference (equivalent to a voltage). This is provided by a pump (equivalent to the battery). The water pipes must also provide a route back to the inlet of the pump so that continuous flow is possible. If we turn off the valve (the equivalent of the electric switch), the pipe will be closed off so the flow will stop. Here is the water circuit:
Unfortunately, flowing water can't create light, at least, not directly. Instead of a light bulb we have used a water wheel so we can at least see that our imaginary water is flowing.
The electric and water circuits have something else in common. They take potential energy (voltage/pressure), transport it to somewhere else, and then convert it to a different form of energy (radiated light in the bulb, or kinetic energy in the case of the water wheel).
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