160 CHAPTER 3 Logic Suppose you are sitting at your desk and want to turn on a lamp so you can read a book. If a wall switch controls the power to the outlet that the lamp is plugged into and the lamp has an on/off switch, what conditions must be true for the lamp’s bulb to light? The electrical wiring in our homes can be explained and described using logic. Switching Circuits SECTION 3.7 LEARNING GOALS Upon completion of this section, you will be able to: 7 Use symbolic statements to represent switching circuits. 7 Draw switching circuits that represent symbolic statements. 7 Determine whether two switching circuits are equivalent. Why This Is Important In this section we will show how electrical circuits can be represented using logic. Understanding these basic circuits can help us understand how logic is used in all modern electronic devices such as smartphones, computers, and appliances. Using Symbolic Statements to Represent Switching Circuits A common application of logic is switching circuits. To understand the basic concepts of switching circuits, let us examine a few simple circuits that are common in most homes. The typical lamp has a cord, which is plugged into a wall outlet. Somewhere between the bulb in the lamp and the outlet is a switch to turn the lamp on and off. A switch is often referred to as being on or off. When the switch is in the on position, the current flows through the switch and the bulb lights up. When the switch is in the on position, we can say that the switch is closed and that current will flow through the switch. When the switch is in the off position, the current does not flow through the switch and the bulb does not light. When the switch is in the off position, we can say that the switch is open, and the current does not flow through the switch. The basic configuration of a switch is shown in Fig. 3.12. Figure 3.12 Electric circuits can be expressed as logical statements. We represent switches as letters, using T to represent a closed switch (or current flow) and F to represent an open switch (or no current flow). This relationship is indicated in Table 3.37. Table 3.37 Switch Lightbulb T on (switch closed) F off (switch open) Occasionally, we have a wall switch connected to a wall outlet and a lamp plugged into the wall outlet (Fig. 3.13). We then say that the wall switch and the switch on the lamp are in series, meaning that for the bulb in the lamp to light, both switches must be on at the same time (Fig. 3.14). On the other hand, the bulb will not light if either switch is off or if both switches are off. In either of these conditions, the electricity will not flow through the circuit. In a series circuit, the current can take only one path. If any switch in the path is open, the current cannot flow. Figure 3.13 p q Outlet Wall switch Lamp switch Light Figure 3.14 To illustrate this situation symbolically, let p represent the wall switch and q the lamp switch. The letter T will be used to represent both a closed switch and the bulb lighting. The letter F will represent an open switch and the bulb not lighting. Thus, we have four possible cases as shown in Table 3.38. Lacheev/123RF
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