You have seen that you can store energy in a capacitor. The equivalent in a water system would be a bottle that could fill up or provide water to the system. When the capacitor is charged to 3 V, it contains about 1 Joule (equivalent to raisinging an egg 1 m).

The diagram for a capacitor tries to describe what is inside. Some capacitors actually look like this: a pair of conducting plates with a small separation between them. Even though there is no conducting path through the capacitor, it can play a role in a circuit. The two plates are so close together and so large in area that when the current first starts to flow it doesn't realize it isn't connected. It's a bit like blowing through a straw that has a balloon on the end -- you can blow some air through it, but if you stop trying, all the air comes back out your end. Just as a balloon can store air, a capacitor can store energy.

Energy and power

Because energy has many forms, there are many ways to measure it, and this has led to the definition of many units for it: calories, therms, watt-hours, ergs, BTU, ... . The best unit to use is the metric unit, which is called the Joule. One joule is roughly the amount of energy it takes to raise an egg from the bottom of the refrigerator to the top. It takes 84,000 J to turn 250 ml (1 cup) of room-temperature water into water that is about to boil. A fresh flashlight battery contains 63,000 J.

Sometimes we are interested in the rate that energy is delivered or converted into another form. For example, we use a certain amount of energy every day to keep our house warm -- this is quite different from getting one lump of energy for the house when you build it. This new concept is power, which is the rate of delivery or use of energy (amount of energy divided by the time interval). Power can be measured in Kilowatts (1000 Joule/second) or horsepower (3/4 Kilowatt). A stick of dynamite releases less energy than burning a pint of gasoline, but the dynamite explosion is a high power event because the time interval is small. For a car to change its speed quickly, it must change its energy quickly, which requires a high power engine (200 horsepower!). A bright light bulb (200 Watts) is rapidly converting electrical energy into heat and light -- 200 Joules in every second.

Voltage and power

We should distinguish carefully between the electrical potential (measured in volts), electrical current (measured in amperes), and power (measured in watts).

To understand the distinctions, think of a water mill. As water goes through the mill, it leaves behind energy, but all the water continues going. There has to be both a stream leading to the mill and a stream to carry the water away, or the water mill will not work. The flow rate of the water is the same in the arriving stream and in the arriving stream. What is different is that the water has decreased in height -- it has given up gravitational potential energy. Power is the rate of delivery of energy -- the amount of energy per second. The amount of power delivered to the mill is determined by the rate that water flows through the mill, but it also depends on the height difference at the mill.

In the same way, consider a light bulb. As electrical current goes through the light bulb, it leaves behind energy, but all of the current continues going. There has to be both a wire leading to the light bulb and a wire to carry it away, or the light bulb will not work. The current is the same in the two wires. What is different is that the voltage is different on the two sides of the light bulb. The electrical power delivered to the light bulb is determined by both this voltage difference and by the current through the light bulb. The energy that is delivered to the light bulb comes from inside the battery. This is energy that is stored until we want to use it, and so it is called potential energy. The quantity that corresponds to the height of the water wheel is the voltage of the battery, which is sometimes called the potential of the battery. It tells us how much energy the battery will release for each unit of charge that moves through the circuit.

The lake behind a dam exerts pressure on the dam. When water flows into the turbines, the potential energy of the water in the lake is converted into mechanical energy. Similarly, a battery stores energy for an electrical system. The battery has a voltage whether it is in use or not; only when there is a current is the battery supplying power. The voltage and current both play a role in determining how much power is supplied, according to the relationship

For example, two fresh D cells in series give 3.2 V; when connected to a standard flashlight bulb, the current is 0.33 A. The power delivered is the product of these two numbers: 1.06 Watts. According to the manufacturer, a pair of alkaline D cells contain 126,000 J; then we can calculate that they can keep the bulb bright for 119,000 seconds (33 hours), since 126,000 J = 1.06 Watt x 119,000 seconds.

This relationship explains why electrical power is moved from generating plant to the city using high voltage lines: a very large amount of energy is transmitted every second, so the voltage must be large (the alternative of using a large current would require thick wires, just as moving a lot of water requires large pipes).

Ordinary household voltage ranges from 110 V to 120 V. It is the equivalent of about 75 flashlight batteries in series.

Electrical safety

There is a discussion of electrical safety in the first module. The major points made there are

• Electricity delivers energy, and so it can cause fires. Circuit breakers detect when there is too much power being delivered to a circuit, and turn it off.
• The nervous system makes use of electrical signals, and that is why we get electrical shocks. The current required to cause a shock is rather small -- 1/100 of the current it takes to operate a light bulb! The most important part of electrical safety is to avoid becoming part of a circuit.

Check the box when you are done:  

Discussion of electrical concepts