Chapter 16: DC Circuits

Transcription

1 Chapter 16: DC Circuits Why might all the electrical devices in your house suddenly turn off if you simultaneously turn too many on? How can you use an electric circuit to model the circulatory system? Why is it dangerous to use a hair drier while taking a bath? Make sure you know how to: 1. Apply the concept of the electric field to understand electric interactions. 2. Define the V-field (electric potential) and electric potential difference V. 3. Explain the differences in internal structure between conducting materials and non-conducting materials. On a cold Sunday morning you turn on an extra heater in the kitchen and put a waffle in the toaster oven. You are heading for a Frisbee game on the snow and remember your uniform is dirty you start the washing machine. Then you see that the dishwasher is full of dirty dishes, so you turn on the dishwasher. Now you are ready to make coffee. You turn on the coffee bean grinder and all of a sudden the lights in the kitchen go off. The dishwasher stops bubbling and the red heating element in the toaster oven dims. All the lights go out. What happened? Why did turning on a coffee grinder make the lights and all of the appliances go off? When you turn on too many appliances, a device called a circuit breaker disconnects the house from the external supply of electric energy to save the house from a potential fire. We will learn in this chapter how the circuit breaker knows when to turn off the energy supply to your house. In Chapters 14 and 15 we learned about electric force and energy and how to explain them using the idea of electric fields. We were mostly interested in phenomena involving macroscopic objects with electric charge, such as your body after you have rubbed your shoes on carpet. However, much of our modern technology involves processes when the charged objects are microscopic and moving. This is what is happening internally inside cell phones, computers, light bulbs, and nearly every other electrical device. It is also what happens inside the human body s nervous system. In this chapter we will learn how to explain some of what is happening in these situations Electric charge flow In the previous chapter we studied processes that occurred when one charged conducting object was connected with a wire to another non-charged conductor. We found that the excess Van Heuvelen/Etkina Process Physics 1/e, Chapter

2 electrical charge on the charged object redistributed itself until the electric potential or V -field on the surfaces of both conductors became equal. This phenomenon relates closely to the subject of this chapter electric circuits. Let s repeat this type of experiment using two electroscopes and a light bulb. Causing a neon bulb to flash Place the two identical electroscopes near each other and change electroscope 1 by rubbing it with a plastic rod that was rubbed vigorously with felt (Fig.16.1a). The leaves of electroscope 1 separate because of excess negative charge on them. If we touch a wire from charged electroscope 1 to uncharged electroscope 2, the leaves of 1 instantly separate less and the leaves of 2 instantly separate more (but not as much as the original separation of the leaves of 1) see Fig. 16.1b. Evidently, the excess negative charge originally on 1 redistributed itself on the two electroscopes so they reached the same electric potential V, at which point charge transfer stopped. Figure 16.1(a)(b) Transferring charge between electroscopes Now repeat the experiment only this time, connect the charged electroscope 1 to the uncharged electroscope 2 by the leads of a neon light bulb (Fig. 16.1c). The leaves behave the same way as in the previous experiment. As the leaves of electroscope 1 move closer and of electroscope 2 move apart, the neon bulb produces a quick flash of light. An explanation for this brief flash is that light is produced in a neon bulb when electric charge moves through the neon bulb due to a potential difference across its leads. Figure 16.1(c) Van Heuvelen/Etkina Process Physics 1/e, Chapter

3 Water analogy To understand the process, think of the following analogy. You have two containers with water A and B. A is almost full, and B is almost empty. You connect a hose between the two containers (Fig. 16.2a). Water starts flowing from A to B until the levels are the same (Fig. 16.2b), at which point the water flow stops. Here the amount of water in the container A is similar to the excess charge on the electroscope 1, and the difference in water pressure in the hose is similar to the potential difference between the electroscopes. The water flows till the pressure on both sides of the hose is the same; the electric charge flows till the potentials are the same. Figure 16.2(a)(b) Water flow analogy for electric charge flow It is the pressure difference and not the amount of water that makes the water flow. Imagine a large container A full of water with the water level the same as in small container B the water will not flow (Fig. 16.3a). Similarly, it is not the total charge difference between the electroscopes or metal spheres on their tops but the potential difference that makes the charge flow. Imagine big charged sphere A and small charged sphere B. Suppose the charge on A is large and on B is small; but, if the V fields on the surfaces of these two spheres (electric potentials) are the same (V k q ), there will be no charge flow through the wire conducting R them (Fig. 16.3b). Figure 16.3(a)(b) Get flow only in P A > P B of V A > V B Now, think of how you can make the process go on for a long time. You can manually take water from container B and move it back to A, thus causing the levels in the containers to differ; the water starts flowing again from A to B. Or you can connect the containers with another hose with a pump in the middle that moves water from B back to A (Fig. 16.4). Both you moving the water manually from B back to A or pumping water from B back to A maintains a pressure Van Heuvelen/Etkina Process Physics 1/e, Chapter

4 difference between A and B and causes continuous flow through the hose from A to B. How do we create a continuous electric charge flow in an electrical system? Figure 16.4 Pump keeps pressure higher in A Causing the neon bulb to have a steady glow As we saw from the analogy, for steady water flow through the hose we need to maintain a steady difference in water pressure at the ends of the hose. For steady flow of electric charge, we need a device that can maintain steady potential difference between the ends of the neon bulb. Let s attach wires from the positive and negative terminals of a battery to the leads of the neon bulb (Fig. 16.5a). The bulb does in fact have a steady glow. Thus, it appears that the battery produces a steady potential difference across its terminals, which in turn causes a steady flow of electric charge passing through the neon bulb. The battery is the electric pump! Notice that the leads of the bulb are connected to the two terminals of the battery; we can draw a complete loop going through the battery and the bulb with the leads (Fig. 16.5b). This loop is called a complete circuit. Figure 16.5 (a)(b) A neon bulb and battery electric circuit Electric current Let us go back to the analogy with water and container A and B with different water levels. If there is no hose connecting the two, the water will not flow even if the levels are different. With the hose, the water will flow slowly through a narrow hose, and faster through the wide hose. Knowing the speed with which the water is going through the cross sectional area of the hose is important if we want to use this flowing water to turn a paddle wheel or do something Van Heuvelen/Etkina Process Physics 1/e, Chapter

5 else. The mass of water passing though a cross sectional area of a hose per unit time is called water current. The physical quantity water current characterizes the coordinated motion of water through the hose. Similarly, the electrically charged particles move through the wire between two locations that are at different electric potentials. This potential difference is produced briefly by the presence of two electroscopes whose spheres are at different potentials or continuously by a battery. When the two locations are connected with a conducting wire, the movable charged particles in the wire move in a continuous coordinated way similar to the water moving though the hoses in a coordinated way. The physical quantity electric current I characterizes this coordinated movement of charged particles. In most electric circuits, the charged particles that move in a coordinated way are free electrons in the wires and circuit elements (Fig. 16.6a). They flow toward the direction of higher V -field (towards the positive terminal of a battery.) However, traditionally, the direction of electric current I is defined to be in the opposite direction to the motion of the electrons. Imagine that positively charged particles are flowing from the terminal at a higher electric potential (labeled + on the battery) through the wires and electrical devices, to the terminal at lower electric potential (labeled ), then through the battery to the positive terminal, and then the cycle starts over (Fig. 16.6b). Figure 16.6(a)(b) Current in opposite direction to electron motion This definition of the direction of the electric current is a historical quirk. When scientists first studied electric processes, they did not know about electrons and instead thought that an invisible positively charged electric fluid flowed around the circuit (recall this from Chapter 14). For most situations involving electric circuits, it does not matter if we model the process in terms of electrons flowing one way or imaginary positive charges flowing the other way; so this historical convention is not a problem. Electric current The electric current I in a wire equals the magnitude of the electric charge Q that passes through a cross section of the wire divided by the time interval t needed for that amount of charge to pass: Q I (16.1) t Van Heuvelen/Etkina Process Physics 1/e, Chapter

6 The unit of current is the ampere A. A current of 1 A means that the charge of 1 C passes through a cross section of the wire every second. The direction of the current is in the direction positive charges would move (even though negative electrons usually are moving in the opposite direction). In the metric system it is the unit of current that is a basic unit similar to a meter, kilogram, and second, not the unit of charge, Coulomb. Unfortunately, we have not studied the phenomenon, which can be used to define the ampere this will be done in the magnetism chapter. The unit of electric charge (1 coulomb) is actually defined in terms of the ampere as 1 C = (1A)(1 s). Quantitative Exercise 16.1 Electric current calculation Each second, electrons flow from right to left past a cross section of a wire attached to the two terminals of a battery. Determine the magnitude and direction of the electric current in the wire. Represent Mathematically The electric charge of an electron is C. Since we know how many electrons ( N ) pass a cross section of the wire in one second, we can find the total electric charge passing that cross-section each second. To find the magnitude of the current, we use the definition Solve and Evaluate Q I t en t C en I t 1 s A 16 ma The direction of the current is from left to right, which is opposite to the direction of the electron flow. Try It Yourself: A current of 2.0 A flows in a circuit for 20 min. What is the total charge that moved through the battery during this time interval? Answer: 2400 C. Review Question 16.1 What condition(s) are needed for electric charge to travel from one place to another? 16.2 Batteries and emf Recall for a moment the water flow analogy. Water flows through a hose from one container to another if there is a difference in the water level in the two containers, thus causing a Van Heuvelen/Etkina Process Physics 1/e, Chapter