Induction and Alternating Current with teacher's notes

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$Holt Math Minnesota Test Prep Workbook for Grade 9$

$Math Skills: More Practice$

their orientation to each other. Because these properties are kept constant, it follows that a changing current in the secondary coil can also induce an emf in the primary circuit. The equation holds as long as the coils remain unchanged with respect to each other, so that the mutual inductance is constant. By changing the number of turns of wire in the secondary coil, the induced emf in the secondary circuit can be changed. This arrangement is the basis of an extremely useful electrical device: the transformer. TRANSFORMERS It is often desirable or necessary to change a small ac potential difference to a larger one or to change a large potential difference to a smaller one. The device that makes these conversions possible is the transformer. In its simplest form, an ac transformer consists of two coils of wire wound around a core of soft iron, like the apparatus for the Faraday experiment. The coil on the left in Figure 22-19 has N 1 turns and is connected to the input ac potential difference source. This coil is called the primary winding, or the primary. The coil on the right, which is connected to a resistor R and consists of N 2 turns, is the secondary. As in Faraday’s experiment, the iron core provides a medium for nearly all magnetic field lines passing through the two coils. Because the strength of the magnetic field in the iron core and the crosssectional area of the core are the same for both the primary and secondary windings, the potential differences across the two windings differ only because of the different number of turns of wire for each. The ac potential difference that gives rise to the changing magnetic field in the primary is related to that changing field by Faraday’s law of induction. ∆V1 =−N1⎯ ∆(AB cos q) ⎯ ∆t Similarly, the induced potential difference (emf) across the secondary coil is ∆V2 =−N2⎯ ∆(AB cos q) ⎯ ∆t Taking the ratio of ∆V 1 to ∆V 2 causes all terms on the right side of both equations except for N 1 and N 2 to cancel. This result is the transformer equation. TRANSFORMER EQUATION ∆V2 = ⎯ N2 ⎯ ∆V1 N1 potential difference in secondary = number of turns in secondary ⎯⎯⎯ potential difference in primary number of turns in primary Copyright © by Holt, Rinehart and Winston. All rights reserved. transformer a device that changes one ac potential difference to a different ac potential difference ∆V 1 Primary (input) Soft iron core N 1 N 2 R Induction and Alternating Current ∆V 2 Secondary (output) Figure 22-19 A transformer uses the alternating current in the primary circuit to induce an alternating current in the secondary circuit. NSTA TOPIC: Transformers GO TO: www.scilinks.org sciLINKS CODE: HF2224 815 SECTION 22-3 Demonstration 9 Induced potential difference Purpose Show that induced potential difference depends on the number of turns of wire. Materials 9 V battery, knife switch, 30 cm (or longer) iron bar, 2 flashlight bulbs (or more) in holders, three connecting wires (each about 1 m long) Procedure Set up the primary coil as in Demonstration 8. Set up two secondary coils, one with 25 turns of wire and one with 50 turns of wire. Close the switch, and have students compare the brightness of the two bulbs. You may wish to open and close the switch several times for repeated observations. 815
SECTION 22-3 Teaching Tip Some students may wonder whether dc transformers are possible. The dc produced by a battery would not work with a transformer. This is because a changing current is required, and a battery generates a steady direct current. However, as seen on page 811, a generator can produce a fluctuating direct current. Such a current could be used by a transformer. Teaching Tip Point out to students that spark plugs create a spark because the potential difference across the gap increases to 20 000 V. At such high potential differences, air is ionized and becomes a conductor. 816 816 Step-up transfomer (ignition coil) Ignition switch + Chapter 22 – 12 V battery Another way to express this equation is to equate the ratio of the potential differences to the ratio of the number of turns. ∆V2 ⎯⎯ = ⎯ ∆V1 N2 ⎯ N1 When N2 is greater than N1, the secondary potential difference is greater than that of the primary, and the transformer is called a step-up transformer. When N2 is less than N1, the secondary potential difference is less than that of the primary, and the transformer is called a step-down transformer. It may seem that a transformer provides something for nothing. For example, a step-up transformer can change an input potential difference from 10 V to 100 V. However, the power input at the primary must equal the power output at the secondary. An increase in potential difference at the secondary means that there must be a proportional decrease in current. If the potential difference at the secondary is 10 times that at the primary, then the current at the secondary is reduced by a factor of 10. Computer Crank angle sensor Spark plug Figure 22-20 The transformer in an automobile engine raises the potential difference across the gap in a spark plug so that sparking occurs. Real transformers are not perfectly efficient The transformer equation assumes that there are no power losses between the transformer’s primary and its secondary. Real transformers typically have efficiencies ranging from 90 percent to 99 percent. Power losses occur because of the small currents induced by changing magnetic fields in the iron core of the transformer and because of resistance in the wires of the windings. When electric power is transmitted over large distances, it is economical to use a high potential difference and a low current. This is because the power lost to resistive heating in the transmission lines varies as I 2 R. By reducing the current by a factor of 10, the power loss is reduced by a factor of 100. In practice, potential difference is stepped up to around 230 000 V at the generating station, then stepped down to 20 000 V at a regional distribution station, and finally stepped down to 120 V at the customer’s utility pole. The high potential difference in long-distance transmission lines makes them especially dangerous when they are knocked down by high winds. Coils in gasoline engines are transformers An automobile ignition system uses a transformer, or ignition coil, to convert the car battery’s 12 dc volts to a potential difference that is large enough to cause sparking between the gaps of the spark plugs. The diagram in Figure 22-20 shows the type of ignition system that has been Copyright © by Holt, Rinehart and Winston. All rights reserved.
Page 1 and 2: Chapter 22 Overview Section 22-1 in
Page 3 and 4: Section 22-1 Teaching Tip Remind st
Page 5 and 6: SECTION 22-1 Demonstration 1 Induce
Page 7 and 8: SECTION 22-1 Demonstration 2 Lenz
Page 9 and 10: SECTION 22-1 Teaching Tip Point out
Page 11 and 12: SECTION 22-1 Section Review ANSWERS
Page 13 and 14: SECTION 22-2 STOP 804 Misconception
Page 17 and 18: SECTION 22-2 Demonstration 6 Effect
Page 19 and 20: SECTION 22-2 PRACTICE GUIDE 22C Sol
Page 23: Section 22-3 Demonstration 8 Transf
Page 27 and 28: SECTION 22-3 PRACTICE GUIDE 22D Sol
Page 29 and 30: Chapter 22 Summary Teaching Tip Ask
Page 31 and 32: 22 REVIEW & ASSESS 12. −0.63 V 13
Page 33 and 34: 22 REVIEW & ASSESS 42. 1.03 × 10 5
Page 35 and 36: Chapter 22 Laboratory Exercise NOTE

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