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### 5.2

1. 1. Electricity and Magnetism Topic 5 . 2 Electric Circuits
2. 2. Electromotive Force <ul><li>Defining potential difference </li></ul><ul><li>The coulombs entering a lamp have electrical potential energy; </li></ul><ul><li>those leaving have very little potential energy. </li></ul><ul><li>There is a potential difference (or p.d.) across the lamp, because the potential energy of each coulomb has been transferred to heat and light within the lamp. </li></ul><ul><li>p.d. is measured in volts (V) and is often called voltage. </li></ul>
3. 3. <ul><li>The p.d. between two points is the electrical potential energy transferred to other forms, per coulomb of charge that passes between the two points. </li></ul>
4. 4. <ul><li>Resistors and bulbs transfer electrical energy to other forms, but which components provide electrical energy? </li></ul><ul><li>A dry cell, a dynamo and a solar cell are some examples. </li></ul><ul><li>Any component that supplies electrical energy is a source of electromotive force or e.m.f. </li></ul><ul><li>It is measured in volts. </li></ul><ul><li>The e.m.f. of a dry cell is 1.5 V, that of a car battery is 12 V </li></ul>
5. 5. <ul><li>A battery transfers chemical energy to electrical energy, so that as each coulomb moves through the battery it gains electrical potential energy. </li></ul><ul><li>The greater the e.m.f. of a source, the more energy is transferred per coulomb. In fact: </li></ul><ul><li>The e.m.f of a source is the electrical potential energy transferred from other forms, per coulomb of charge that passes through the source. </li></ul><ul><li>Compare this definition with the definition of p.d. and make sure you know the difference between them. </li></ul>
6. 6. Internal Resistance
7. 7. <ul><li>The cell gives 1.5 joules of electrical energy to each coulomb that passes through it, </li></ul><ul><li>but the electrical energy transferred in the resistor is less than 1.5 joules per coulomb and can vary. </li></ul><ul><li>The circuit seems to be losing energy ‑ can you think where? </li></ul>
8. 8. <ul><li>The cell itself has some resistance, its internal resistance. </li></ul><ul><li>Each coulomb gains energy as it travels through the cell, but some of this energy is wasted or `lost' as the coulombs move against the resistance of the cell itself. </li></ul><ul><li>So, the energy delivered by each coulomb to the circuit is less than the energy supplied to each coulomb by the cell. </li></ul>
9. 9. <ul><li>Very often the internal resistance is small and can be ignored. </li></ul><ul><li>Dry cells, however, have a significant internal resistance. </li></ul><ul><li>This is why a battery can become hot when supplying electric current. </li></ul><ul><li>The wasted energy is dissipated as heat. </li></ul>
10. 10. Resistance Combinations
11. 11. Resistors in series
12. 12. <ul><li>The diagram shows three resistors connected in series </li></ul><ul><li>There are 3 facts that you should know for a series circuit: </li></ul><ul><ul><li>the current through each resistor in series is the same </li></ul></ul><ul><ul><li>the total p.d., V across the resistors is the sum of the p.d.s across the separate resistors, so: V = V l + V 2 + V 3 </li></ul></ul><ul><ul><li>the combined resistance R in the circuit is the sum of the separate resistors </li></ul></ul>
13. 13. <ul><li>R = R l + R 2 + R 3 </li></ul><ul><li>Suppose we replace the 3 resistors with one resistor R that will take the same current I when the same p.d. V is placed across it </li></ul>
14. 15. <ul><li>This is shown in the diagram. Let's calculate R. </li></ul><ul><li>We know that for the resistors in series: </li></ul><ul><ul><li>V = V l + V 2 + V 3 </li></ul></ul><ul><li>But for any resistor: p.d. = current x resistance (V = I R). </li></ul><ul><li>If we apply this to each of our resistors, and remember that the current through each resistor is the same and equal to I, we get: </li></ul><ul><li>IR = IR l +IR 2 +IR 3 </li></ul><ul><li>If we now divide each term in the equation by I, </li></ul><ul><li>we get: </li></ul><ul><ul><li>R = R 1 + R 2 + R 3 </li></ul></ul>
15. 16. Resistors in parallel
16. 17. <ul><li>We now have three resistors connected in parallel: </li></ul><ul><li>There are 3 facts that you should know for a parallel circuit: </li></ul><ul><ul><li>the p.d. across each resistor in parallel is the same </li></ul></ul><ul><ul><li>the current in the main circuit is the sum of the currents in each of the parallel branches, so: </li></ul></ul><ul><ul><li> I = I 1 + I 2 + I 3 </li></ul></ul><ul><ul><li>the combined resistance R is calculated from the equation: </li></ul></ul>
17. 18. <ul><li>Suppose we replace the 3 resistors with one resistor R that takes the same total current I when the same p.d. V is placed across it. </li></ul>
18. 20. <ul><li>This is shown in the diagram. Now let's calculate R. </li></ul><ul><li>We know that for the resistors in parallel: </li></ul><ul><li>I = I 1 +I 2 +I 3 </li></ul><ul><li>But for any resistor, current = p.d. = resistance (I = V/R ). </li></ul><ul><li>If we apply this to each of our resistors, and remember that the </li></ul><ul><li>p.d. across each resistor is the same and equal to V, </li></ul><ul><li>we get:V/ R=V/R 1 + V/R 2 + V/R 3 </li></ul><ul><li>Now we divide each term by V, to get: </li></ul><ul><li>1/ R=1/R 1 + 1/R 2 + 1/R 3 </li></ul>
19. 21. <ul><li>You will find that the total resistance R is always less than the smallest resistance in the parallel combination. </li></ul>
20. 22. Circuit Diagrams <ul><li>You need to be able to recognize and use the accepted circuit symbols included in the Physics Data Booklet </li></ul>
21. 23. Ammeters and Voltmeters <ul><li>In order to measure the current, an ammeter is placed in series, in the circuit. </li></ul><ul><li>What effect might this have on the size of the current? </li></ul><ul><li>The ideal ammeter has zero resistance, so that placing it in the circuit does not make the current smaller. </li></ul><ul><li>Real ammeters do have very small resistances ‑ around 0.01 Ω . </li></ul>
22. 24. <ul><li>A voltmeter is connected in parallel with a component, in order to measure the p.d. across it. </li></ul><ul><li>Why can this increase the current in the circuit? </li></ul><ul><li>Since the voltmeter is in parallel with the component, their combined resistance is less than the component's resistance. </li></ul><ul><li>The ideal voltmeter has infinite resistance and takes no current. </li></ul><ul><li>Digital voltmeters have very high resistances, around 10 M Ω , and so they have little effect on the circuit they are placed in. </li></ul>
23. 25. Potential dividers <ul><li>A potential divider is a device or a circuit that uses two (or more) resistors or a variable resistor (potentiometer) to provide a fraction of the available voltage (p.d.) from the supply. </li></ul>
24. 26. <ul><li>The p.d. from the supply is divided across the resistors in direct proportion to their individual resistances. </li></ul>
25. 27. <ul><li>Take the fixed resistance circuit - this is a series circuit therefore the current in the same at all points. </li></ul><ul><li>I supply = I 1 = I 2 </li></ul><ul><li>Where I 1 = current through R 1 </li></ul><ul><li> I 2 = current through R 2 </li></ul>
26. 28. <ul><li>Using Ohm’s Law </li></ul>
27. 29. Example
28. 30. With sensors <ul><li>A thermistor is a device which will usually decrease in resistance with increasing temperature. </li></ul><ul><li>A light dependent resistor, LDR, will decrease in resistance with increasing light intensity. ( L ight D ecreases its R esistance). </li></ul>
29. 31. Example <ul><li>Calculate the readings on the meters shown below when the thermistor has a resistance of </li></ul><ul><li>a) 1 k W ( warm conditions) and b) 16 k W. ( cold conditions ) </li></ul>