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Unit 3 Notes

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Unit 3 Notes

  1. 1. Electricity
  2. 2. What is current electricity? <ul><li>Electricity is the flow of electrical power or charge. It is a secondary energy source which means that we get it from the conversion of other sources of energy, like coal, natural gas, oil, nuclear power and other natural sources, which are called primary sources. The energy sources we use to make electricity can be renewable or non-renewable, but electricity itself is neither renewable or non-renewable. </li></ul>
  3. 4. Producing Electricity
  4. 5. E.M.F. <ul><li>Five sources of Electromotive Forces (continuous current) </li></ul><ul><li>emf is the ability of certain devices to produce areas of potential difference </li></ul><ul><li>reworded that means, the ability to produce an electric current </li></ul>
  5. 6. Producing Electricity <ul><li>Chemical Energy </li></ul><ul><li>Thermoelectric Energy </li></ul><ul><li>Photoelectric Energy </li></ul><ul><li>Piezoelectric Energy </li></ul><ul><li>Electromagnetic Energy </li></ul>
  6. 7. Electromagnetism <ul><li>In a generator , moving water, rushing steam, the wind, etc. contain kinetic energy that is converted into electric energy. This is accomplished through the principle of electromagnetic induction where a conducting loop of wire rotating in a magnetic field causes free electrons in the conductor to move around the loop and produce an electrical current. </li></ul><ul><ul><li>A generator is an example </li></ul></ul>
  7. 8. Electromagnetic Energy
  8. 9. Photoelectric Cells <ul><li>In a photoelectric cell , or solar cell, light energy is converted directly into electric energy through the photoelectric effect where electrons are emitted by a substance when electromagnetic radiation of sufficiently short wavelength falls on the substance. </li></ul><ul><ul><li>a silicon solar cell is an example </li></ul></ul>
  9. 10. Photoelectric Energy
  10. 11. Thermoelectric <ul><li>In a thermocouple , an electric circuit is produced in a wire consisting of two different metals with two junctions placed at two different temperatures thus producing an electric current. The thermoelectric effect produces a potential difference and current when two different metals at two different junctions experience a temperature difference. </li></ul><ul><ul><li>a temperature gauge in a car is an example </li></ul></ul>
  11. 12. Piezoelectric <ul><li>In a piezoelectric cell , mechanical pressure on a crystal such as Rochelle salt or quartz is converted into a potential difference. This occurs due to the piezoelectric effect which is a property of certain natural and synthetic crystals to develop a potential difference between opposite surfaces when subjected to mechanical stress and vice versa. </li></ul><ul><ul><li>example is creating a spark in a barbecue </li></ul></ul>
  12. 13. Chemical <ul><li>In an electrochemical cell , chemical energy is converted into electric energy by a spontaneous chemical reaction in which electrons are transferred from one reactant to another. </li></ul><ul><li>Certain chemical reactions will produce a transfer of electrons from one reactant to another </li></ul><ul><ul><li>an example is the reaction in a battery </li></ul></ul>
  13. 14. Electric Current & Circuits <ul><li>Benjamin Franklin advocated a one-fluid model of electricity where the electrical “fluid” would move from a region where there was more of it to a region where there was less fluid. He called the more plentiful region positive and the less plentiful area negative . According to this theory, electricity moves from positive to negative and is called the conventional current of electricity . Years later, the actual flow of electricity was determined to be negative electrons moving from a negative region to a positive region (opposite to Franklin’s theory). This movement was called the electron flow . </li></ul>Unit 3 –Electricity
  14. 15. Electric Current & Circuits <ul><li>Electric current is described as the flow of charged particles (+ or -) </li></ul><ul><li>negative electron flow; ie. from - to + </li></ul><ul><li>positive flow; ie. From + to - (conventional current flow) </li></ul>Unit 3 –Electricity
  15. 16. Electric Current & Circuits <ul><li>Current is an indication of the # of electrons (amount of charge) passing through a wire per unit time </li></ul><ul><li>The unit for charge is the coulomb (C) and the unit for time is the second (s). The SI unit for current is the coulomb per second (C/s). One coulomb per second is referred to as an ampere  (A). </li></ul>Unit 3 –Electricity
  16. 17. Electric Current I = q/t
  17. 18. Number of Electrons and Energy Gain <ul><li>Recall that the charge on an electron is </li></ul><ul><li>e = 1.60 x 10 -19 C </li></ul><ul><li>This value can be used to determine the number of electrons that flow in a circuit in a given time. For example, the charge that passes through a circuit is; q = It </li></ul><ul><li>If the unit of current is amperes, and the unit of time is in second, then the charge is in coulombs. The number of electrons is therefore given by </li></ul>Unit 3 –Electricity
  18. 19. Potential Difference <ul><li>Recall, potential difference is the difference in electric potential between 2 points </li></ul><ul><li>indicates the force with which the electrons are moving </li></ul><ul><li>measured in volts (V) </li></ul>Unit 3 –Electricity
  19. 20. Potential Difference V = Ed Unit 3 –Electricity
  20. 21. Instruments <ul><li>Voltmeter </li></ul><ul><ul><li>emf of a circuit is measured using a voltmeter </li></ul></ul><ul><ul><li>must be placed in parallel with circuit </li></ul></ul><ul><li>Ammeter </li></ul><ul><ul><li>Current is measured using an ammeter </li></ul></ul><ul><ul><li>must be hooked up in series </li></ul></ul>Unit 3 –Electricity
  21. 22. Resistance and Ohm's Law <ul><li>To help understand the ideas involved in electric currents moving in circuits, an analogy with water flowing through pipes is sometimes helpful. In an electrical circuit, a battery causes electrons to flow through wires. This is analogous to a pump forcing water through pipes. Just as greater battery voltages create greater electrical currents, so do stronger water pumps create greater water currents flowing through pipes. </li></ul>Unit 3 –Electricity
  22. 23. Resistance and Ohm's Law <ul><li>In a water pipe, the flow rate is not only determined by the pump pressure, but it is also affected by the length and diameter of the pipe. Longer and narrower pipes offer a higher resistance to the moving water and lead to a smaller flow rate for a given pump pressure. A similar situation exists in electrical circuits. </li></ul>Unit 3 –Electricity
  23. 24. Resistance Unit 3 –Electricity
  24. 25. Ohm's Law <ul><li>Ohm's law is the most important and basic law of electricity and electronics. </li></ul><ul><li>It defines the relationship between the three fundamental electrical quantities: current, voltage and resistance. </li></ul>Unit 3 –Electricity
  25. 26. Ohm's Law <ul><li>Ohm's law defines the way current, voltage and resistance. are related. </li></ul><ul><li>The law was discovered by a German physicist, George Simon Ohm. </li></ul><ul><li>Ohm found that a current flowing through a conductor is directly proportional to the electric force that produces it. </li></ul>Unit 3 –Electricity
  26. 27. Ohm’s Law Unit 3 –Electricity
  27. 28. Basic Definition <ul><li>Ohm's Law states that the ratio V/I is a constant, where V is the voltage applied across a piece of material (such as a wire) and I is the current through the material: </li></ul><ul><li>= constant or V = IR </li></ul><ul><li>R is the resistance of the material. The SI unit of resistance is the volt/ampere (V/A)  = ohm (Ω) </li></ul><ul><li>The SI unit for resistance is the volt per ampere which is called the ohm. The ohm is represented by the Greek capital letter  (Ω). </li></ul>Unit 3 –Electricity
  28. 29. Equation <ul><li>Current is directly proportional to voltage and inversely proportional to resistance . </li></ul>V = IR Unit 3 –Electricity
  29. 30. Example In any circuit, the higher the voltage, the higher the current will be. Conversely, the lower the voltage, the lower the current will be. This assumes that the resistance remains constant. However current is also determined by resistance. Resistance is the opposition to current flow. So, assuming that voltage is constant, the higher the resistance is the lower the current will be. Also, the lower the resistance the higher the current will be. Unit 3 –Electricity
  30. 31. Equivalent Equations I = V/R R = V/I Unit 3 –Electricity
  31. 32. Resistors, a Circuit Diagram, and Ohm's Law <ul><li>A resistor is an electrical device that offers resistance to the flow of electric charges. Resistors can have a wide range of resistance values. </li></ul><ul><li>In drawing electric circuits, the convention is to use a zigzag line to represent a resistor and a straight line to represent an ideal conducting wire with negligible resistance. </li></ul>Unit 3 –Electricity
  32. 33. Resistors, a Circuit Diagram, and Ohm's Law <ul><li>A flashlight is a simple example of an electric circuit. If two 1.5 V batteries are placed in a flashlight, the total voltage is equivalent to 3.0 V. A typical current for such a circuit could be 0.40 A. A possible diagram for such a simple circuit is as shown below. </li></ul>Unit 3 –Electricity
  33. 34. Ohm's Law Unit 3 –Electricity
  34. 35. Resistance and Resistivity <ul><li>In a water pipe, the length and cross-sectional area of the pipe determine the amount of resistance that the pipe offers to the flow of water. The greatest resistance comes from water pipes that are long and have a small cross sectional area. </li></ul><ul><li>A similar situation occurs for electrical current. </li></ul>Unit 3 –Electricity
  35. 36. Resistance and Resistivity <ul><li>For many materials, the resistance of a piece of material of length  L and cross-sectional area  A is </li></ul><ul><li>The symbol ρ is a proportionality constant known as the resistivity of the material. The unit for the resistivity is the ohm·metre (Ω·m). </li></ul>Unit 3 –Electricity
  36. 37. Resistance and Resistivity Unit 3 –Electricity
  37. 38. Resistance and Resistivity <ul><li>Resistance depends on the resistivity of the material and the geometry (length and cross sectional area) of the material. </li></ul><ul><li>So for example, two copper wires will always have the same resistivity. But a short wire with a large cross-sectional area has a smaller resistance than a long, thin wire. Power cables carry a large current so they are thick rather than thin to keep the resistance of the wires as small as possible. </li></ul>Unit 3 –Electricity
  38. 39. Resistance and Power <ul><li>Recall: </li></ul><ul><li>Therefore: </li></ul>Unit 3 –Electricity ΔPE = qΔV
  39. 40. Resistance and Power <ul><li>Thus, when there is an electric current I in a circuit as a result of a voltage V, the electric power delivered to the circuit is </li></ul><ul><li>P = IV </li></ul><ul><li>  </li></ul><ul><li>The SI unit of power is the watt. </li></ul>Unit 3 –Electricity
  40. 41. Resistance and Power <ul><li>Many electrical devices become hot when provided with sufficient power. Such devices might be toasters, irons, space heaters, heating elements on electric stoves, and incandescent light bulbs. In cases such as these, it is possible to obtain two additional equivalent expressions for the power. </li></ul><ul><li>  </li></ul><ul><li>From Ohm's Law, V = IR or </li></ul>Unit 3 –Electricity
  41. 42. Resistance and Power <ul><li>From Ohm's Law, </li></ul><ul><li>V = IR or </li></ul><ul><li>P = IV = I(IR) = I 2 R </li></ul>Unit 3 –Electricity
  42. 43. Series & Parallel Circuits <ul><li>Some circuits contain basic combinations of resistors, the series combination and the parallel combination. </li></ul><ul><li>We will examine the idea of an equivalent resistance for these two types of circuits, and learn how currents and voltages exist in different parts of the circuit. </li></ul>Unit 3 –Electricity
  43. 44. Series & Parallel Circuits Unit 3 –Electricity
  44. 45. Series Circuits <ul><li>A series circuit is one in which electrical current flows through each component one after the other so that there is a single conducting path. </li></ul><ul><li>The diagram below shows a circuit in which two resistors, R 1 and R 2 are connected in series with a battery. </li></ul>Unit 3 –Electricity
  45. 46. Series Circuits <ul><li>Because the two resistors are connected this way, one after the other, if the current in one resistor is interrupted, the current in the other is also interrupted. </li></ul><ul><li>When the current is flowing through a series circuit, the amount of current is the same through each resistor. </li></ul>Unit 3 –Electricity
  46. 47. Series Circuits <ul><li>Because of the series wiring, the voltage supplied by the battery is divided between the two resistors. The voltage across R 1 is V 1 and the voltage across R 2 is V 2 . Using Ohm's Law ( V=IR ), we can say that </li></ul><ul><li>V = V 1 + V 2 = IR 1 + IR 2 = I( R 1 + R 2 ) = IR T where R T is the equivalent resistance of the circuit. </li></ul>Unit 3 –Electricity
  47. 48. Series Circuits <ul><li>The equivalent resistance for a circuit could be defined as the single resistance that could replace several resistors. </li></ul><ul><li>Thus two resistors in series are equivalent to a single resistor whose resistance is R T  =  R 1  +  R 2 . This means that there is the same current running through R T as there is through the series combination of R 1 and R 2 . This line of reasoning can extend to any number of resistors in series with the result that for resistors in series, </li></ul><ul><li>R T = R 1 + R 2 + R 3 + … </li></ul>Unit 3 –Electricity
  48. 49. Series Circuits <ul><li>For the example discussed with two resistors in a circuit, a circuit with the equivalent resistance could be drawn as follows. </li></ul>Unit 3 –Electricity
  49. 50. Series Circuits <ul><ul><ul><li>Current in a series circuit travels along only one path so current through each resistor is equal. I T = I 1 = I 2 = I 3 … </li></ul></ul></ul><ul><li>In addition, the voltage dropped across all resistors must be equivalent to the total voltage supplied. V T = V 1 + V 2 + V 3 ... </li></ul>Unit 3 –Electricity
  50. 51. Series Circuits <ul><li>Three Cardinal Rules for Resistances in Series   </li></ul><ul><ul><li>1. The current in all parts of a series circuit has the same magnitude. </li></ul></ul><ul><ul><li>I T = I 1 = I 2 = I 3 = … </li></ul></ul><ul><ul><li>2. The sum of all the separate drops in potential around a series circuit is equal to the potential rise of the battery (or any other applied emf). </li></ul></ul><ul><ul><li>V T = V 1 + V 2 + V 3 + … </li></ul></ul><ul><ul><li>3. The total resistance in a series circuit is equal to the sum of all the separate resistances. </li></ul></ul><ul><ul><li>R T = R 1 + R 2 + R 3 + … </li></ul></ul>Unit 3 –Electricity
  51. 52. Series Circuits – An Example <ul><li>A 6.00 Ω and a 4.00 Ω resistor are connected in series with a 12.0 V battery. We assume that the battery itself does not offer any resistance to the circuit. a) Find the equivalent resistance for this circuit. b) Find the current delivered to each resistor. c) Find the power dissipated in each resistor. d) Find the total power delivered to the resistors by the battery. e) Find the potential difference across each resistor. </li></ul>Unit 3 –Electricity
  52. 53. Series Circuits – An Example <ul><li>A 6.00 Ω and a 4.00 Ω resistor are connected in series with a 12.0 V battery. We assume that the battery itself does not offer any resistance to the circuit. a) Find the equivalent resistance for this circuit. b) Find the current delivered to each resistor. c) Find the power dissipated in each resistor. d) Find the total power delivered to the resistors by the battery. e) Find the potential difference across each resistor. </li></ul>Unit 3 –Electricity
  53. 54. Parallel Circuits <ul><li>In a parallel circuit , there are two or more paths for the current to flow. </li></ul><ul><li>In a parallel circuit the resistors are wired in such a way that the same potential drop is applied to each resistor. The current passing through each resistors is not the same as the total current in the circuit. </li></ul>Unit 3 –Electricity
  54. 55. Parallel Circuits <ul><li>The diagram below shows two resistors connected in parallel. </li></ul>Unit 3 –Electricity
  55. 56. Parallel Circuits <ul><li>Just as in a series circuit, it is possible to replace a combination of resistors with an equivalent resistor that results in the same total current and power for a given voltage as the original combination. To determine the equivalent resistance for the two resistors, note once again that the total current I T from the battery is the sum of the individual currents I 1 and I 2 where I 1 is the current through R 1 and I 2 is the current through R 2 . </li></ul><ul><li>where R T is the total or equivalent resistance. </li></ul>Unit 3 –Electricity
  56. 57. Parallel Circuits <ul><li>Hence when two resistors are connected in parallel, they are equivalent to a single resistor whose resistance R T is given by 1/R T = 1/R 1 + 1/R 2 . </li></ul><ul><li>In general, for resistors connected in parallel, </li></ul>Unit 3 –Electricity
  57. 58. Parallel Circuits <ul><li>Three Cardinal Rules for Resistances in Parallel   </li></ul><ul><ul><li>1. The total current in a parallel circuit is equal to the sum of the currents in the separate branches. </li></ul></ul><ul><ul><li>I T = I 1 + I 2 + I 3 + … </li></ul></ul><ul><ul><li>2. The potential difference across all branches of a parallel circuit must have the same magnitude. </li></ul></ul><ul><ul><li>V T = V 1 = V 2 = V 3 = … </li></ul></ul><ul><ul><li>3. The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the separate resistances in parallel. </li></ul></ul>Unit 3 –Electricity
  58. 59. Parallel Circuits – An Example <ul><li>A 6.00 Ω and a 4.00 Ω resistor are connected in parallel with a 12.0 V battery. We assume that the battery itself does not offer any resistance to the circuit. a) Find the equivalent resistance for this circuit. b) Find the potential difference across each resistor. c) Find the current delivered to each resistor. d) Find the power dissipated in each resistor. e) Find the total power delivered to the resistors by the battery. </li></ul>Unit 3 –Electricity
  59. 60. Parallel Circuits – An Example Unit 3 –Electricity
  60. 61. Series & Parallel Circuits <ul><li>The physics of brightness and light bulbs connected to an electrical outlet. A number of lights are to be connected to a single electrical outlet. In which case will the bulbs provide more brightness, when they are connected in series, or in parallel? </li></ul>Unit 3 –Electricity
  61. 62. Series & Parallel Circuits <ul><li>2. The physics of Christmas tree lights and resistance. Seven 8.0 W Christmas tree lights are connected in series to a 120 V source. What is the resistance of each bulb? </li></ul>Unit 3 –Electricity
  62. 63. Series & Parallel Circuits <ul><li>3. The physics of stereo speakers connected in parallel. A 16 Ω loudspeaker and an 8.0 Ω loudspeaker are connected in parallel across the terminals of an amplifier. Assume that the speakers behave as resistors, determine the equivalent resistance of the two speakers. </li></ul>Unit 3 –Electricity
  63. 64. Series & Parallel Circuits <ul><li>4. The physics of a coffee cup and heater and a lamp connected in parallel. A coffee cup heater and a lamp are connected in parallel to the same 120 V outlet. Together they use a total of 84 W of power. The resistance of the heater is 6.0 x 10 2  Ω. Find the resistance of the lamp. </li></ul>Unit 3 –Electricity
  64. 65. Network Circuits <ul><li>Practical circuits can be quite complex compared to the series and parallel circuits we have considered. There can resistances in series and other resistances in parallel. </li></ul><ul><li>Such complex circuits which are combined series-parallel circuits, are commonly called networks . </li></ul>Unit 3 –Electricity
  65. 66. Network Circuits Unit 3 –Electricity
  66. 67. Network Circuits <ul><li>These kinds of circuits can be understood by analyzing them in steps. </li></ul><ul><ul><li>If any resistors are connected in parallel, calculate the single equivalent resistance that can replace them. </li></ul></ul><ul><ul><li>If any equivalent resistances are connected in series, calculate a single new equivalent resistance that can replace them. </li></ul></ul><ul><ul><li>By repeating steps 1 and 2, you can reduce the circuit to a single resistance. The total circuit current can now be found. The voltage drops and currents through individual resistors can then be calculated. </li></ul></ul>Unit 3 –Electricity
  67. 68. Network Circuits <ul><li>A 30.0 Ω resistor is connected in parallel with a 20.0 Ω resistor. The parallel connection is placed in series with a 8.0 Ω resistor. The entire circuit is placed across a 60.0 V difference of potential. </li></ul>Unit 3 –Electricity
  68. 69. <ul><li>What starts as a practical joke turns into a money-making venture for Dr. J. His after-school stint as a part-time electrician keeps him busier than he ever imagined. It all began at a party while he was just horsing around. Dressed up as a cowboy, he began singing &quot;ohm ohm on the range.&quot; He followed that with his own version of &quot;Watt's cookin' at the campfire?&quot; Not liking that series of songs, the other party goers turned on every noise-making appliance in the house, literally blowing a fuse. The resulting blackout could have been dangerous if it hadn't been for Dr. J's lightening-quick action. Tracing down the problem and restoring the power earned him the respect of all in attendance. Billing himself as The Circuit Rider, he has built a powerful reputation. Today's problem is a typical one. Dr. J needs to modify a 120-volt circuit so that it will carry a current of 15 amps. All he has in his repair kit are 40-ohm resistors. How many of these will he need to use? </li></ul>Unit 3 –Electricity
  69. 70. <ul><li>How many of these will he need to use? </li></ul><ul><li>5 resistors wired in parallel </li></ul>Unit 3 –Electricity
  70. 71. <ul><li>In this shocking episode, Dr. J and his crew invest in a new part-time business. With the high price of gasoline, many of the rental car companies have started renting motorcycles. Of course the leader in this field is Hertz (after all, a cycle per second is a fantastic rate of business). On the other hand, Avis and some of the other companies have shown a resistance to this current trend because of their concern over the potential business. Dr. J decides to go one step further and rent electric motorcycles. It seems like a natural: J. Jr. will handle the renting; Timex will serve as the mechanic (his specialty is timing engines); and even Tripod can show first-time customers how to keep their balance. Dr. J designs these electric motorcycles himself. The only drawback to them is the speed. Whereas a gas-guzzling Harley can reach 70 MPH and over, Dr. J's model can only reach 7 MPH (he names it a Hardly). A problem arises while assembling the first of these cycles. There are three 10-ohm resistors left, but the circuit diagram showing the proper way to wire them is blurred. After thinking a bit, Timex says, &quot;How many ways can you do this, anyway?&quot; Dr. J says that there are seven different combinations. (Not every combination need use all three resistors.) Find the total resistance for each of these seven combinations. </li></ul>Unit 3 –Electricity
  71. 72. <ul><li>Hooking them in series, the following combinations are possible: </li></ul><ul><li>  </li></ul><ul><li>  </li></ul><ul><li>Hooking them in parallel can produce: </li></ul><ul><li>  </li></ul><ul><li>  </li></ul><ul><li>Using a series-parallel combination can produce: </li></ul><ul><li>  </li></ul>Unit 3 –Electricity
  72. 73. Electromagnetic Induction <ul><li>When most singers perform, they most likely use a microphone. Many microphones use magnetism and the phenomenon of electromagnetic induction. </li></ul><ul><li>Recall that an electric current produces a magnetic field, and that a magnetic field exerts a force on an electric current or a moving electric charge. These discoveries were made in the 1820's. Scientists began to wonder that if electric currents produce a magnetic field, then would it be possible for a magnetic field to produce an electric current. Ten years later, the American Joseph Henry (1797-1878) and the Englishman Michael Faraday (1791-1867) independently found that this was possible. It was actually Henry who made the discovery first, but Faraday published his results earlier and investigated the subject in more detail. </li></ul>Unit 3 –Electricity
  73. 74. Electromagnetic Induction Unit 3 –Electricity
  74. 75. Induced EMF and Faraday's Experiment <ul><li>The current in the coil in circuit Y is called an induced current because it is brought about (or “induced”) by a changing magnetic field. </li></ul><ul><li>Since a source of emf, like the battery in Faraday's experiment, is always needed to produce a current, the coil behaves as if it were a source of emf. This emf is known as the induced emf . </li></ul><ul><li>In general, we can define electromagnetic induction as the production of an induced current or emf in a conducting circuit brought about by a changing magnetic field. </li></ul>Unit 3 –Electricity
  75. 76. Inducing EMF and the North Pole of a Magnet Unit 3 –Electricity
  76. 77. Inducing EMF and the South Pole of a Magnet Unit 3 –Electricity
  77. 78. Induced EMF and the Area or Orientation of a Coil Unit 3 –Electricity
  78. 79. Motional EMF and Current Direction <ul><li>Another method of creating an induced emf is when a conducting rod moves through a constant magnetic field. </li></ul><ul><li>The separated charges on the ends of the moving rod give rise to an induced emf called the motional emf . </li></ul><ul><li>This is because it originates from the motion of charges through a magnetic field . The emf exists as long as the rod moves. </li></ul>Unit 3 –Electricity
  79. 80. Motional EMF and Magnitude of EMF <ul><li>The amount of motional emf, ξ, produced in a moving conductor of length, L, moving in a magnetic field, B, at a speed, v, is </li></ul><ul><li>ξ  = vBL . </li></ul><ul><li>The power delivered to a resistance in the circuit is </li></ul><ul><li>P = Iξ </li></ul><ul><li>and the energy delivered to the resistance </li></ul><ul><li>E = Pt </li></ul>Unit 3 –Electricity
  80. 81. Magnetic Flux <ul><li>Motional emf can be described in terms of a concept called flux. </li></ul><ul><li>Magnetic flux is defined as the product of the magnetic field strength and the surface area that the field lines pass through. Magnetic flux is represented by the Greek letter phi, Φ. Thus, </li></ul><ul><li>Φ =  BA </li></ul><ul><li>The unit for flux is the tesla · square metre (T·m 2 ). This unit is called a weber (Wb). </li></ul>Unit 3 –Electricity
  81. 82. Magnetic Flux <ul><li>Magnetic flux </li></ul><ul><li>Φ =  BA </li></ul><ul><li>Φ – Magnetic Flux (T·m 2 ) or weber (Wb) </li></ul><ul><li>B – Magnetic Field Strength (N/(A · m) </li></ul><ul><li>A – Area (m 2 ) weber (Wb). </li></ul>Unit 3 –Electricity
  82. 83. Magnetic Flux <ul><li>The magnitude of the induced emf in a loop of conductor is the change in flux Δ Φ  =  Φ  -  Φ o divided by the time interval Δ t = t - t o . </li></ul><ul><li>  </li></ul><ul><li>The induced emf equals the time rate of change of the magnetic flux. </li></ul><ul><li>Most of the time, this equation is written with a negative sign, </li></ul>Unit 3 –Electricity
  83. 84. Magnetic Flux and Magnetic Field Direction <ul><li>When the magnetic field is not perpendicular to the surface that it is interacting with, the flux is computed using only the component of the field that is perpendicular to the surface. </li></ul><ul><li>In this case, the component of the magnetic field that is perpendicular to the surface is given by B sin Θ . Therefore the flux is Φ = ( B  sin Θ)A or BA  sin Θ . </li></ul>Unit 3 –Electricity
  84. 85. Faraday's Law of Electromagnetic Induction <ul><li>Recall Faraday's discovery that there must be a changing magnetic field in a loop of wire before an emf will be induced in the loop. </li></ul><ul><li>Another way to state this is that there must be a change in flux through the loop of wire. In this context, the word “change” refers to the passage of time. A flux that is constant in time does not create an emf. </li></ul>Unit 3 –Electricity
  85. 86. Faraday's Law of Electromagnetic Induction <ul><li>Faraday's law of electromagnetic induction brings together the idea of magnetic flux and the time interval during which it changes. In fact Faraday found that the magnitude of the induced emf is equal to the time rate of change of the magnetic flux. </li></ul>Unit 3 –Electricity Notes Handout & Questions
  86. 87. Faraday's Law of Electromagnetic Induction <ul><li>Often the magnetic flux passes through a coil of wire containing more than one loop (or turn). If the coil consists of N loops, and if the same flux passes through each loop, it is found experimentally that the total induced emf is N times that induced in a single loop. </li></ul>Unit 3 –Electricity
  87. 88. Faraday's Law of Electromagnetic Induction <ul><li>For the general case of N  loops, Faraday's law of electromagnetic induction describes the total emf in the following way. </li></ul><ul><li>The average emf ξ induced in a coil of wire of N loops is </li></ul>Unit 3 –Electricity Notes Handout & Questions
  88. 89. Lenz’s Law <ul><li>An induced emf creates a current around a circuit but the location of the positive and negative terminals is not as obvious. We need a method to determine the polarity or algebraic sign of the induced emf so that the terminals can be identified. </li></ul><ul><li>Lenz's law states that the induced emf resulting from a changing magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original change in flux. </li></ul>Unit 3 –Electricity
  89. 90. Lenz’s Law Unit 3 –Electricity
  90. 91. Lenz’s Law <ul><li>One source of the magnetic flux is the original magnetic field that leads to the induced emf. For example, if the north pole of a magnet is approaching a coil of wire, then the magnet is the source of the magnetic field. </li></ul><ul><li>The other source of the magnetic flux is the induced current. Any current passing through a coil of wire creates a magnetic flux, and the induced current creates its own flux. The field created by the induced current is called the induced magnetic field . </li></ul>Unit 3 –Electricity
  91. 92. Lenz’s Law <ul><li>The Russian physicist Heinrich Lenz (1804-1865) discovered a method to determine the polarity of the induced emf. His discovery is known as Lenz's law . </li></ul><ul><li>  </li></ul><ul><li>The induced emf resulting from a changing magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original change in flux. </li></ul>Unit 3 –Electricity
  92. 93. The Electric Generator <ul><li>A generator is a device that converts mechanical energy into electrical energy. In its simplest form, an ac generator consists of a coil of wire that is rotated in a uniform magnetic field. </li></ul>Unit 3 –Electricity
  93. 94. The Electric Generator <ul><li>The wire forming the loop is usually wound around an iron core. The coil/iron combination is called an armature . </li></ul><ul><li>Each end of the wire forming the coil is connected to an external circuit by means of metal rings called slip rings that rotate with the coil. </li></ul><ul><li>Each ring slides against a stationary carbon brush to which the external circuit is connected. The armature rotates in a magnetic field produced by magnets. </li></ul><ul><li>Thus the four essential components of a generator are the armature, the slip rings, the brushes, and the magnets . </li></ul>Unit 3 –Electricity
  94. 95. The Electric Generator Unit 3 –Electricity
  95. 96. The Electric Generator <ul><li>In general, the shaft of the generator is rotated by some mechanical means such as water falling over a turbine. This causes the armature to rotate in the magnetic field. An emf is induced in the coil which is part of the armature. The ends of the coil are connected to slip rings that rotate as the armature is turned. A graphite (carbon) brush rides on each slip ring connecting the armature to the external circuit, thereby delivering the current to the circuit. </li></ul>Unit 3 –Electricity
  96. 97. Producing the AC Current: The First Half Turn Unit 3 –Electricity
  97. 98. Producing the AC Current: The Second Half Turn Unit 3 –Electricity
  98. 99. The Electric Generator Unit 3 –Electricity
  99. 100. Calculating EMF <ul><li>In producing alternating current, the armature rotates in a circle. It would be useful to know what the induced emf would be in terms of the frequency of rotation of the armature. </li></ul><ul><li>The area of the coil is A = LW where “W” is the width of the coil. When the coil rotates in a circular fashion, the radius of the circle is r = W /2.The tangential speed “ v ” in m/s of a point on a circle is </li></ul><ul><li>v = d/t = 2 π R/T = 2 π Rf = 2π ( W /2) f = π Wf . </li></ul><ul><li>Substituting into the expression for the induced emf, the maximum emf produced by a rotating armature is </li></ul><ul><li>ξ = 2 N (π Wf)BL or ξ = NBA 2π f </li></ul>Unit 3 –Electricity
  100. 101. Calculating EMF <ul><li>ξ = 2 N (π Wf)BL or ξ = NBA 2π f </li></ul><ul><li>N – number of loops passing through magnetic field </li></ul><ul><li>W – width of coil </li></ul><ul><li>B – magnetic field strength </li></ul><ul><li>L – length of conductor </li></ul><ul><li>A – area of the coil </li></ul><ul><li>f – frequency of loop rotating </li></ul>Unit 3 –Electricity
  101. 102. Transformers <ul><li>In our technological world where voltages and currents passing through our various appliances often need to be higher or lower than what is available in a battery or wall plug, we need the transformer to make this increase or decrease. For example, whenever cordless appliances, such as cell phones, are plugged into a wall receptacle to recharge the batteries, a transformer plays a role in reducing the 120 V ac voltage to a much smaller value. Typically, between 3 and 9 V are needed to recharge batteries. Another example would be a picture tube in a television set which needs 15 000 V to accelerate an electron beam. A transformer is used to obtain this high voltage from the 120 V at a wall socket. </li></ul>Unit 3 –Electricity
  102. 103. Parts of the Transformer and Its Functioning <ul><li>A transformer consists of an iron core on which two coils are wound: the primary coil with N p turns, and a secondary coil with N s turns. The primary coil is connected to the ac generator. At the moment shown, the switch in the secondary circuit is open, so there is no current in this circuit. </li></ul>Unit 3 –Electricity
  103. 104. Parts of the Transformer and Its Functioning <ul><li>The alternating current in the primary coil establishes a changing magnetic field in the iron core. </li></ul><ul><li>The iron also carries the magnetic field lines to the secondary coil. </li></ul><ul><li>Since the magnetic field is changing, the flux through the primary and secondary coils is also changing. Consequently an emf is induced in both coils. </li></ul><ul><li>A transformer operates with ac electricity and not with dc. A steady direct current in the primary coil produces a flux but this flux does not change with time, so no emf is induced in the secondary coil. </li></ul>Unit 3 –Electricity
  104. 105. The Transformer Equation <ul><li>When the changing flux passes through the primary coil, the emf induced in this coil is given by Faraday's law. </li></ul><ul><li>  </li></ul><ul><li>In the secondary coil, the emf induced is </li></ul><ul><li>  </li></ul><ul><li>The term is the same in both of these equations since the same flux penetrates each turn of both coils. Diving the two equations gives us </li></ul><ul><li>  </li></ul>Unit 3 –Electricity
  105. 106. The Transformer Equation <ul><li>In high quality transformers, the resistances of the coils are negligible, so the magnitudes of the emfs, ξ s and ξ p are nearly equal to the terminal voltages, V s and V p across the coils. We can now write the transformer equation as </li></ul>Unit 3 –Electricity
  106. 107. The Transformer Equation <ul><li>According to the transformer equation, if N s is greater than N p , the secondary (output) voltage is greater than the primary (input) voltage. In this case the transformer is referred to as a step-up transformer . </li></ul><ul><li>On the other hand, if N s is less than N p , the secondary voltage is less than the primary voltage and we have a step-down transformer . </li></ul><ul><li>For example for a turns ratio of 5/1 (often written as 5:1), the secondary coil has five more turns than does the primary coil. Conversely, a turns ratio of 1:5 implies that the secondary coil has one-fifth as many turns as the primary coil. </li></ul>Unit 3 –Electricity
  107. 108. Transformers Unit 3 –Electricity