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where I is traditionally used to represent current in amperes, E is used to represent voltage (it stands for electromotive force), and R is resistance.

For example, let's look at a battery that's just sitting around not connected to anything:

The voltage E is 1.5. That's a potential for doing work. But because the positive and negative terminals are connected solely by air, the resistance (the symbol R) is very, very, very high, which means the current (I) equals 1.5 volts divided by a large number. This means that the current is just about zero.

Now let's connect the positive and negative terminals with a short piece of copper wire (and from here on, the insulation on the wires won't be shown):

This is known as a short circuit. The voltage is still 1.5, but the resistance is now very, very low. The current is 1.5 volts divided by a very small number. This means that the current will be very, very high. Lots and lots of electrons will be flowing through the wire. In reality, the actual current will be limited by the physical size of the battery. The battery will probably not be able to deliver such a high current, and the voltage will drop below 1.5 volts. If the battery is big enough, the wire will get hot because the electrical energy is being converted to heat. If the wire gets very hot, it will actually glow and might even melt.

Most circuits are somewhere between these two extremes. We can symbolize them like so:

The squiggly line is recognizable to electrical engineers as the symbol for a resistor. Here it means that the circuit has a resistance that is neither very low nor very high.

If a wire has a low resistance, it can get hot and start to glow. This is how an incandescent lightbulb works. The lightbulb is commonly credited to America's most famous inventor, Thomas Alva Edison (1847–1931), but the concepts were well known at the time he patented the lightbulb (1879) and many other inventors also worked on the problem.

Inside a lightbulb is a thin wire called a filament, which is commonly made of tungsten. One end of the filament is connected to the tip at the bottom of the base; the other end of the filament is connected to the side of the metal base, separated from the tip by an insulator. The resistance of the wire causes it to heat up. In open air, the tungsten would get hot enough to burn, but in the vacuum of the lightbulb, the tungsten glows and gives off light.

Most common flashlights have two batteries connected in series. The total voltage is 3.0 volts. A lightbulb of the type commonly used in a flashlight has a resistance of about 4 ohms. Thus, the current is 3 volts divided by 4 ohms, or 0.75 ampere, which can also be expressed as 750 milliamperes. This means that 4,680,000,000,000,000,000 electrons are flowing through the lightbulb every second.

(A brief reality check: If you actually try to measure the resistance of a flashlight lightbulb with an ohmmeter, you'll get a reading much lower than 4 ohms. The resistance of tungsten is dependent upon its temperature, and the resistance gets higher as the bulb heats up.)

As you may know, lightbulbs you buy for your home are labeled with a certain wattage. The watt is named after James Watt (1736–1819), who is best known for his work on the steam engine. The watt is a measurement of power (P) and can be calculated as

P = E x I

The 3 volts and 0.75 amp of our flashlight indicate that we're dealing with a 2.25-watt lightbulb.

Your home might be lit by 100-watt lightbulbs. These are designed for the 120 volts of your home. Thus, the current that flows through them is equal to 100 watts divided by 120 volts, or about 0.83 ampere. Hence, the resistance of a 100-watt lightbulb is 120 volts divided by 0.83 ampere, or 144 ohms.

So we've seemingly analyzed everything about the flashlight—the batteries, the wires, and the lightbulb. But we've forgotten the most important part!

Yes, the switch. The switch controls whether electricity is flowing in the circuit or not. When a switch allows electricity to flow, it is said to be on, or closed. An