It may seem strange to say that a negatively charged particlegoing one way creates a current going the other way, but this isquite ordinary. As we will see, currents flow through metal wiresvia the motion of electrons, which are negatively charged, so thedirection of motion of the electrons in a circuit is always opposite tothe direction of the current. Of course it would have been convenientof Benjamin Franklin had defined the positive and negative signs ofcharge the opposite way, since so many electrical devices are basedon metal wires.Number of electrons flowing through a lightbulb example 2⊲ If a lightbulb has 1.0 A flowing through it, how many electronswill pass through the filament in 1.0 s?⊲ We are only calculating the number of electrons that flow, so wecan ignore the positive and negative signs. Solving for (charge) =It gives a charge of 1.0 C flowing in this time interval. The numberof electrons isnumber of electrons = coulombs × electronscoulomb= coulombs/ coulombselectron= 1.0 C/eThat’s a lot of electrons!= 6.2 × 10 18g / 1. Static electricity runsout quickly. 2. A practical circuit.3. An open circuit. 4. How anammeter works. 5. Measuringthe current with an ammeter.5.3 CircuitsHow can we put electric currents to work? The only method ofcontrolling electric charge we have studied so far is to charge differentsubstances, e.g., rubber and fur, by rubbing them against eachother. Figure g/1 shows an attempt to use this technique to lighta lightbulb. This method is unsatisfactory. True, current will flowthrough the bulb, since electrons can move through metal wires, andthe excess electrons on the rubber rod will therefore come throughthe wires and bulb due to the attraction of the positively chargedfur and the repulsion of the other electrons. The problem is thatafter a zillionth of a second of current, the rod and fur will both haverun out of charge. No more current will flow, and the lightbulb willgo out.Figure g/2 shows a setup that works. The battery pushes chargethrough the circuit, and recycles it over and over again. (We willhave more to say later in this chapter about how batteries work.)This is called a complete circuit. Today, the electrical use of theword “circuit” is the only one that springs to mind for most people,but the original meaning was to travel around and make a roundtrip, as when a circuit court judge would ride around the boondocks,dispensing justice in each town on a certain date.102 Chapter 5 Electricity
Note that an example like g/3 does not work. The wire willquickly begin acquiring a net charge, because it has no way to getrid of the charge flowing into it. The repulsion of this charge willmake it more and more difficult to send any more charge in, andsoon the electrical forces exerted by the battery will be canceledout completely. The whole process would be over so quickly thatthe filament would not even have enough time to get hot and glow.This is known as an open circuit. Exactly the same thing wouldhappen if the complete circuit of figure g/2 was cut somewhere witha pair of scissors, and in fact that is essentially how an ordinarylight switch works: by opening up a gap in the circuit.The definition of electric current we have developed has the greatvirtue that it is easy to measure. In practical electrical work, onealmost always measures current, not charge. The instrument usedto measure current is called an ammeter. A simplified ammeter, g/4,simply consists of a coiled-wire magnet whose force twists an ironneedle against the resistance of a spring. The greater the current,the greater the force. Although the construction of ammeters maydiffer, their use is always the same. We break into the path of theelectric current and interpose the meter like a tollbooth on a road,g/5. There is still a complete circuit, and as far as the battery andbulb are concerned, the ammeter is just another segment of wire.Does it matter where in the circuit we place the ammeter? Couldwe, for instance, have put it in the left side of the circuit insteadof the right? Conservation of charge tells us that this can make nodifference. Charge is not destroyed or “used up” by the lightbulb,so we will get the same current reading on either side of it. What is“used up” is energy stored in the battery, which is being convertedinto heat and light energy.5.4 VoltageThe volt unitElectrical circuits can be used for sending signals, storing information,or doing calculations, but their most common purpose byfar is to manipulate energy, as in the battery-and-bulb example ofthe previous section. We know that lightbulbs are rated in units ofwatts, i.e., how many joules per second of energy they can convertinto heat and light, but how would this relate to the flow of charge asmeasured in amperes? By way of analogy, suppose your friend, whodidn’t take physics, can’t find any job better than pitching bales ofhay. The number of calories he burns per hour will certainly dependon how many bales he pitches per minute, but it will also be proportionalto how much mechanical work he has to do on each bale.If his job is to toss them up into a hayloft, he will got tired a lotmore quickly than someone who merely tips bales off a loading dockSection 5.4 Voltage 103
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ContentsMomentum compared to kineti
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Chapter 1Conservation of Mass andEn
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1.2 Conservation of MassWe intuitiv
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masses on the spring, and they both
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A common source of confusion is the
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Discussion questionA Each of the fo
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l / Galileo Galilei was the first p
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that this wasn’t really an argume
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the girl on the left goes up a cert
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1. kinetic energy2. gravitational e
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In fact, your body uses up even mor
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kinetic energy is twice as much. Bu
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ather than flying off straight. New
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of mass?Actually they’re not even
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ecause the square of the speed of l
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ProblemsKey√∫⋆A computerized
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13 How high above the surface of th
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Chapter 2Conservation ofMomentumFan
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win the Martian version of the Nobe
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a / How can we prove that this coll
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all.This is exactly like the rules
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Unequal masses example 4⊲ Suppose
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ForceDefinition of forceWhen moment
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DLocate the images formed by the pe
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Problem 2.4 In this chapter we’ve
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signals to travel between you and t
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“The Great Wave Off Kanagawa,”
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amplitude, A. The definition of amp
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a single hump or trough. If you hit
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Surfing example 3The incorrect beli
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Sound wavesThe phenomenon of sound
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do they signify in the case of a wa
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⊲ Solving for wavelength, we have
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Appendix 1: Photo CreditsExcept as
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Appendix 2: Hints and SolutionsAnsw
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cm, and the distance from the axis
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Foucault, Léon, 17frame of referen
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twin paradox, 83units, conversion o