A.Why Can T the Transformer Directly Convert 12-V DC Into 120-V DC?

Cases – Chapter 11 1. An uninterruptible power supply (UPS) allows a computer system to operate during a brief power outage. Most personal computer UPS systems use an electronic device to convert 12-V DC power from a battery into 120-V AC power for the computer. The UPS circuitry first converts the 12-V DC into 12-V AC and then uses a transformer to increase the voltage to 120 V, as required by the computer. In Europe, the final voltage is 230 V. a. Why can’t the transformer directly convert 12-V DC into 120-V DC? b. An electronic switching system converts the 12-V DC from the batteries into 12-V AC for the transformer. What is different about the current flowing through the two wires attached to the battery and the current flowing through the two wires attached to the transformer? c. How does power move from the 12-V AC side of the transformer to the 120-V AC side of the transformer? *d. Energy is conserved. If there is an average current of about 20 A in the 12-V primary circuit of the transformer, what is the average current in the 120-V secondary circuit of that transformer? e. The length of time that the UPS can deliver power to the computer is limited by the battery’s chemical potential energy. Suppose you wish to extend that time by adding a second 12-V battery to the system. How should you connect the two batteries together so that the current arriving at the pair of batteries will still experience a 12-V rise in voltage and yet be able to extract power from both batteries? 2. A recycling plant is trying to separate metals from other trash automatically. It grinds the trash up into small pieces and then sends these pieces past the poles of a strong electromagnet. a. Iron and steel scraps in the trash are attracted to the poles of the electromagnet but aluminum scraps are not. Why do these metals behave so differently? b. If they’re moving fast enough, aluminum scraps experience a magnetic drag force that separates them from nonmetallic trash. What is the origin of this force? c. To look for metal hidden inside bundles of paper, the recycling plant exposes the bundles to an alternating magnetic field (one that reverses directions many times a second). If it finds that something inside a bundle creates another alternating magnetic field in response, it knows that the bundle contains metal. How can metal inside the trash create this second alternating magnetic field? 3. A home burglar alarm uses various sensors to detect an intruder. These sensors are connected to the alarm’s control unit by wires. The control unit determines when a break-in has occurred, sounds an alarm, and notifies the authorities. a. Each sensor is attached to the control unit via two wires rather than just one. It’s very hard to signal a break-in electrically with only one wire. Why do two wires make it so much easier for a sensor to indicate that a break-in has occurred? b. One of the simplest sensors is just a thin strip of metal foil that runs along the edge of a window. If a burglar breaks the window, the foil strip will be severed. How can the control unit determine if the strip has broken, using its two wires? c. A more sophisticated sensor can tell when a door is opened. It uses a magnet attached to the door and a small device called a reed switch attached to the doorframe. This switch contains two iron strips that are arranged head to tail in a line, but normally don’t quite touch—they’re bent slightly apart and must bend together to make contact. When the magnet’s north pole is near the end of one of the iron strips, that strip becomes magnetic. Why? d. The first iron strip, now magnetic, attracts the other strip and they pull together and touch. Why does the first strip attract the second strip? e. When the door is closed, the magnet is near the reed switch. But as the door opens, the magnet moves away from the reed switch and the two iron strips spring apart. How can the control unit tell when the door opens? 4. A ground fault interrupter is a device that senses when some of the current flowing out one side of an electric outlet isn’t returning through the other side of that outlet. The only way such an imbalance can occur is if some current is returning to the electric company through the ground. Because that accidental current path might include your body, the interrupter shuts off current as soon as it senses trouble. a. Inside the interrupter, the two wires from the electric company pass together around the iron core of a single transformer, forming two identical primary coils. If the alternating current passing through each coil is equal in magnitude but opposite in direction, how does the magnetization of the transformer’s core change with time? b. If the alternating current passing through each coil isn’t equal (perhaps because some current is escaping from a hair dryer plugged into the outlet), how does the magnetization of the transformer’s core change with time? c. The transformer’s core has a secondary coil wrapped around it. If all of the current flowing to the hair dryer through one wire returns from it through the other wire, current passing through this secondary coil will experience no change in voltage. But if some of the current flowing to the hair dryer doesn’t return, current in the secondary coil will experience a change in voltage. Explain. d. The current from the secondary coil is used to trigger a switch that disconnects the outlet from the electric company. This switch has manual “test” and “reset” buttons. To test the ground fault interrupter, you press the “test” button. What can this button do to simulate a real current accident? 5. The needle of a magnetic compass is a permanent magnet. When the compass is level, the needle rotates easily about a vertical axis so that its north magnetic pole points toward the earth’s north geographic pole. a. What type of magnetic pole is located near the earth’s north geographic pole? b. The compass needle is sensitive to any nearby steel or iron. Whenever a piece of iron is held near the compass, one end of its needle turns toward that iron. Why is either end of the needle attracted to pieces of iron? c. The needle is also disturbed by nearby electric currents. Why? d. Some compasses have mechanisms that can prevent their needles from turning. If you lock a compass’s needle in place and pass its north pole near the north pole of a very strong permanent magnet, you will spoil the compass. When you release the needle, it will point toward the earth’s south geographical pole. What will have happened to the needle? 6. A magnetic resonance imaging (MRI) machine uses an enormous and extremely strong magnet to study a patient’s body. The magnet, which has its north pole at the patient’s head and its south pole at the patient’s feet, is actually a coil of superconducting wire through which electric charges flow. a. This fancy electric system seems unnecessary. Why can’t the technicians simply put a large number of north magnetic poles near the patient’s head and an equal number of south magnetic poles near the patient’s feet? b. The needle of your magnetic compass has its north magnetic pole painted red and its south pole painted white. If you stand a few meters from the MRI machine, at the end where the patient’s head is, why does the white end of the compass turn toward the patient’s head? c. The compass is a magnetic dipole, with no net magnetic pole. So why do you feel it pulled toward the patient’s head more and more strongly as you get closer to the magnet? d. Aluminum isn’t normally magnetic, but as you carry a large aluminum tray toward the magnet, you find that the magnet repels the aluminum. Explain. e. You eventually manage to get the aluminum tray up to the magnet. As long as the tray doesn’t move, it experiences no magnetic forces. But when you drop it, it falls past the magnet remarkably slowly. What slows down its fall? 7. Your neighborhood is experiencing an electric power outage. You have a huge box of 1.5 V flashlight batteries (“D” cells) in your garage and you decide to use them to operate some of your appliances until the power is restored. a. You form a complete circuit that includes one “D” battery and a 120 V incandescent light bulb. Why doesn’t the bulb light up? b. You replace the single “D” battery in that circuit with 80 ”D” batteries that are connected in a chain. You arrange these batteries alternately one way then the other, so that positive terminals touch positive terminals and negative terminals touch negative terminals. Why doesn’t this arrangement light the bulb? c. Now you rearrange the 80 ”D” batteries in the chain so that they all point in the same direction, and the bulb finally lights. Why is this chain able to light the bulb? d. You take another chain of 80 ”D” batteries, like the one in c, and connect it to the AC induction motor in your refrigerator’s compressor. Why doesn’t the motor begin to turn? e. After an hour, the 80 ”D” batteries in c stop lighting the 120 V light bulb. Use energy considerations to describe what has happened to the batteries and the bulb. 8. In the United States, most electric outlets accept either two- or three-prong plugs. The two slot-shaped openings in the outlet permit electric current to flow to and from an appliance while the semicircular opening can electrically connect the appliance’s frame to the earth itself. a. Why must an appliance make connections to both slots? Why can’t the appliance obtain electric power through just one of the slots? b. The current provided by the two slots is alternating current. Describe how the current flowing through those two slots varies with time. c. One of the slots in the outlet is usually wider than the other, just as one of the prongs on a power cord is usually wider than the other. The wider slot is called neutral because it has roughly zero net electric charge on it. If you were to touch neutral (which is attached to white wires to indicate relative safety), no current should flow into your hand even if you were also touching something connected to the earth. To make sure that neutral remains uncharged, it’s connected to the ground as it enters your home. The outlet’s narrow slot is called power because its net electric charge fluctuates above and below zero and it can propel current through an appliance. If you were to touch power (which is attached to black wires to indicate danger) and simultaneously to touch something connected to the earth, you would receive a serious and potentially life-threatening shock. Why must you also be connected to the earth to receive this shock? d. Most appliances with plastic surfaces use two-prong plugs and keep power as far from your hands as possible. But appliances with metal surfaces often use three-prong plugs and connect their metal surfaces to the earth through the outlet’s third opening. This third opening is called ground because it’s connected to the ground (by a green wire to indicate its association with the earth). If the power wire in such a “grounded” appliance comes loose and touches the appliance’s metal surface, current will begin to flow. Through what path will current go from power to neutral in this case? e. If a metal appliance weren’t “grounded” and power accidentally touched a metal surface, you would receive a shock if you touched the appliance and something connected to the earth at the same time. Why? 9. A treadmill is an exercise machine that allows you to walk or jog without actually going anywhere. Your feet land on a wide fabric belt that moves between two rollers, one in front of you and the other behind you. An electric motor turns these rollers at a steady pace so that the top of the belt keeps moving toward you. You step forward on the belt, but because it’s moving toward you, you stay in one place with respect to the room. a. What is the net force on you as you walk on the treadmill? *b. The tilt of the belt is adjustable. Suppose for the moment that the belt is exactly horizontal. How much work are you and the treadmill doing on one another? c. If you tilt the belt so that it rises in front of you, it becomes a much harder exercise. Why does it take so much more work to step forward on the tilted treadmill, even though you are not moving anywhere? d. The motor provides the power necessary to keep the belt moving at a steady pace. When the belt is horizontal, the motor compensates for friction by pulling the belt along. But when the belt is tilted far enough, the motor begins to act as a brake, preventing the belt from turning too quickly. The motor is then extracting energy from the belt (and from you). What is the motor doing with the energy it receives?