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### 12.2

1. 1. Electromagnetism Topic 12.2 Alternating Current
2. 2. Rotating Coils <ul><li>Most of our electricity comes from huge generators in power stations. </li></ul><ul><li>There are smaller generators in cars and on some bicycles. </li></ul><ul><li>These generators, or dynamos, all use electromagnetic induction. </li></ul><ul><li>When turned, they induce an EMF (voltage) which can make a current flow. </li></ul>
3. 3. <ul><li>The next diagram shows a simple AC generator. </li></ul><ul><li>It is providing the current for a small bulb. </li></ul><ul><li>The coil is made of insulated copper wire and is rotated by turning the shaft. </li></ul><ul><li>The slip rings are fixed to the coil and rotate with it. </li></ul><ul><li>The brushes are two contacts which rub against the slip rings and keep the coil connected to the outside part of the circuit. </li></ul><ul><li>They are usually made of carbon. </li></ul>
4. 4. AC Generator
5. 5. <ul><li>When the coil is rotated, it cuts magnetic field lines, so an EMF is generated. </li></ul><ul><li>This makes a current flow. </li></ul><ul><li>As the coil rotates, each side travels upwards, downwards, upwards, downwards... and so on, through the magnetic field. </li></ul><ul><li>So the current flows backwards, forwards... and so on. </li></ul><ul><li>In other words, it is AC. </li></ul>
6. 6. <ul><li>The graph shows how the current varies through one cycle (rotation). </li></ul><ul><li>It is a maximum when the coil is horizontal and cutting field lines at the fastest rate. </li></ul><ul><li>It is zero when the coil is vertical and cutting no field lines. </li></ul>
7. 7. AC Generator Output
8. 8. The Sinusoidal Shape <ul><li>As the emf can be calculated from </li></ul><ul><li>ε = - N Δ ( Φ / Δ t) </li></ul><ul><li>and Φ = AB cos θ </li></ul><ul><li>It can be clearly seen that the shape of the curve must be sinusoidal. </li></ul>
9. 9. <ul><li>The following all increase the maximum EMF (and the current): </li></ul><ul><li>increasing the number of turns on the coil </li></ul><ul><li>increasing the area of the coil </li></ul><ul><li>using a stronger magnet </li></ul><ul><li>rotating the coil faster. </li></ul><ul><li>( rotating the coil faster increases the frequency too!) </li></ul>
10. 11. Alternating Current <ul><li>The graph shows the values of V and I plotted against time </li></ul><ul><li>Can you see that the graphs for both V and I are sine curves? </li></ul><ul><li>They both vary sinusoidally with time. </li></ul><ul><li>Can you see that the p.d. and the current rise and fall together? </li></ul><ul><li>We say that V and I are in phase. </li></ul>
11. 12. <ul><li>The time period T of an alternating p.d. or current is the time for one complete cycle. This is shown on the graph </li></ul><ul><li>The frequency f of an alternating pd or current is the number of cycles in one second. </li></ul><ul><li>The peak values V 0 and I 0 of the alternating p.d. and current are also shown on the graph </li></ul>
12. 13. Root Mean Square Values <ul><li>How do we measure the size of an alternating p.d. (or current) when its value changes from one instant to the next? </li></ul><ul><li>We could use the peak value, but this occurs only for a moment. </li></ul><ul><li>What about the average value? </li></ul><ul><li>This is zero over a complete cycle and so is not very helpful! </li></ul>
13. 14. <ul><li>In fact, we use the root‑mean‑square (r.m.s.) value. </li></ul><ul><li>This is also called the effective value. </li></ul><ul><li>The r.m.s. value is chosen, because it is the value which is equivalent to a steady direct current. </li></ul>
14. 15. <ul><li>You can investigate this using the apparatus in the diagram </li></ul><ul><li>Place two identical lamps side by side. </li></ul><ul><li>Connect one lamp to a battery; the other to an a.c. supply. </li></ul><ul><li>The p.d. across each lamp must be displayed on the screen of a double‑beam oscilloscope. </li></ul>
15. 17. <ul><li>Adjust the a.c. supply, so that both lamps are equally bright </li></ul><ul><li>The graph shows a typical trace from the oscilloscope We can use it to compare the voltage across each lamp. </li></ul>
16. 19. <ul><li>Since both lamps are equally bright, the d.c. and a.c. supplies are transferring energy to the bulbs at the same rate. </li></ul><ul><li>Therefore, the d.c. voltage is equivalent to the a.c. voltage. </li></ul><ul><li>The d.c. voltage equals the r.m.s. value of the a.c. voltage. </li></ul><ul><li>Notice that the r.m.s. value is about 70% (1/ √2) of the peak value. </li></ul>
17. 20. <ul><li>In fact: </li></ul>
18. 21. Why √2 <ul><li>Why The power dissipated in a lamp varies as the p.d. across it, and the current passing through it, alternate. </li></ul><ul><li>Remember power,P = current,( I) x p.d., (V) </li></ul><ul><li>If we multiply the values of I and V at any instant, we get the power at that moment in time, as the graph shows </li></ul>
19. 23. <ul><li>The power varies between I 0 V 0 and zero. </li></ul><ul><li>Therefore average power = I 0 V 0 / 2 </li></ul><ul><li>Or P = ( I 0 / √ 2) x (V 0 / √ 2) </li></ul><ul><li>Or P = I rms x V rms </li></ul>
20. 24. Root Mean Square Voltage
21. 25. Root Mean Square Current
22. 26. Calculations <ul><li>Use the rms values in the normal equations} </li></ul><ul><li>V rms = I rms R </li></ul><ul><li>P = I rms V rms </li></ul><ul><li>P = I rms 2 R </li></ul><ul><li>P = V rms 2 / R </li></ul>
23. 27. Transformers <ul><li>A transformer changes the value of an alternating voltage. </li></ul><ul><li>It consists of two coils, wound around a soft‑iron core, as shown </li></ul>
24. 29. <ul><li>In this transformer, when an input p.d. of 2 V is applied to the primary coil, the output p d . of the secondary coil is 8V </li></ul>
25. 30. <ul><li>http://www.allaboutcircuits.com/worksheets/trans1.html </li></ul><ul><li>Transformer simulation </li></ul>
26. 31. How does the transformer work? <ul><li>An alternating current flows in the primary coil. </li></ul><ul><li>This produces an alternating magnetic field in the soft iron core. </li></ul><ul><li>This means that the flux linkage of the secondary coil is constantly changing and so an alternating potential difference is induced across it. </li></ul><ul><li>A transformer cannot work on d.c. </li></ul>
27. 32. An Ideal Transformer <ul><li>This is 100% efficient </li></ul><ul><li>Therefore the power in the primary is equal to the power in the secondary </li></ul><ul><li>P p = P s </li></ul><ul><li>i.e. I p V p = I s V s </li></ul>
28. 33. Step-up Step-down <ul><li>A step‑up transformer increases the a.c. voltage, because the secondary coil has more turns than the primary coil. </li></ul><ul><li>In a step‑down transformer, the voltage is reduced and the secondary coil has fewer turns than the primary coil. </li></ul>
29. 35. The Equation
30. 36. <ul><li>Note: </li></ul><ul><li>• In the transformer equations, the voltages and currents that you use must all be peak values or all r.m.s. values. </li></ul><ul><li>Do not mix the two. </li></ul><ul><li>Strictly, the equations apply only to an ideal transformer, which is 100 % efficient. </li></ul>