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In the last chapter, we developed some intuition about electric fields and electric potentials, so in this chapter we will apply this intuition to electric circuits. A simple electric circuit consists of a voltage source, wires, and resistors, so that charge flows in a closed path or circuit. This flow of charge is called a current. In this chapter the concepts to watch are current and electric potential, two related but distinct concepts. Whenever you see a circuit diagram, you should imagine seeing currents and potentials. By doing this as you read this chapter, you will find that this subject becomes fairly straightforward.


A voltage source (often a DC cell or battery) is a potential difference enforcer, its one job being to ensure that the potential difference between the two terminals remains constant. It does this by chemically transporting electrons from the positive terminal to the negative terminal. When the potential between the terminals becomes the rated voltage (6 volts, or whatever), the chemical reaction in the cell reaches equilibrium and the electron transport stops. The symbols for a cell are shown in Figure 15-1, where the long bar is the positive end, the end with higher potential.

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Figure 15-1


A wire is simply a long, long cylinder of metal. Because it is a piece of metal, however, the potential difference between any two points in it is zero. That is to say, all along its length, a wire has one potential. In our analogy with Sisyphus and the mountain (Chapter 14), a wire is like a plateau, all of it at one height. The reason for this is simple: If it were not so, that is, if one end of the wire were at a higher potential, then electrons, being free to move, would rush toward the higher potential and lower it. Perhaps a better analogy is a mountain lake which is, of course, flat. If one end were higher than the other, the water, free to move, would flow away from that end into the lower one.
For this reason also the electric field inside a piece of metal is always zero. If it were not so, then the electric field would push electrons to one side, and the shifting electrons would cancel the electric field.
At any rate, you should remember that inside a metal, the electric field is zero, and if the potential at one point in the wire is V0, then the potential all along the wire is V0.
Electric current may flow through a resistor as well, but the charge does not flow freely as it does in a wire. For current to flow through a resistor, there must be a potential difference across it. A simple example of a resistor is a piece of graphite (pencil lead). Other examples include a light bulb and a toaster. The symbols for these are shown in Figure 15-2.


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Figure 15-2

In order to think about circuits, it is helpful to think of an analogy. The electric current is like a current of water, and the electric potential is like the height of the water. Wires are like level streambeds (level because they have one potential). Resistors are like rocky waterfalls, and a voltage source is like a pump which pumps water from one height to another.
Let’s look at the example of a 6-V battery connected to a light bulb. This is shown in Figure 15-3, and the circuit diagram is shown in Figure 15-4. The battery pumps the charge from one electric potential to another. The charge flows through a wire to the light bulb, through the light bulb, and back to the battery. The analogy is shown in Figure 15-5, in which the water flows in a circuit. Note the following very important idea: The current in the upper trough is the same as the current in the lower trough. If the current in the upper trough were larger, then more water would be going into the waterfall than coming out of it, and the waterfall would overflow. That is not what happens. Think about this scenario until it is intuitive.
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Figure 15-4 Figure 15-3
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Figure 15-5


Also, energy flow is not the same as water flow. The energy starts in the pump and becomes the energy of flowing water. As the water falls, however, the energy becomes heat. Similarly, the chemical energy of the battery is transformed into electrical energy and then into heat and light.
Whereas in the last chapter we were often interested in the absolute potential, in circuits we are interested only in changes in potential from one position to another. Therefore, we are free to choose a standard 0 volts, relative to which other potentials are measured. In this circuit, we can label the low end of the battery 0 volts. The other end of the battery is then 6 volts (Figure 15-6).

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Figure 15-6

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