1. We’ll show you how you can determine the voltage supplied by different arrangements of cells in an electrical circuit.

2. We’ll start out by looking at cells arranged in series Cells in Series

3. The rule is, the total voltage supplied by a battery of cells in series is the sum of the voltages supplied by each cell. The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. 6.0 V 9.0 V V total = V 1 + V 2 + … V ? V

4. The equation we can use is V total equals V1 + V2 etc. The voltage of each cell is added up. The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. 6.0 V 9.0 V V total = V 1 + V 2 + … V ? V

5. Here are two cells in series, a 9 volt cell and a 6 volt cell. 6.0 V 9.0 V V total = V 1 + V 2 + … Two cells in series The total voltage supplied by cells in series is the sum of the voltages supplied by each cell.

6. Cells in series are in the same loop or pathway. Each electron has to pass through both cells. 6.0 V 9.0 V Two cells in series The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

7. As an electron passes through the 6 volt cell, its electrical potential increases by 6 volts. 6.0 V 9.0 V Two cells in series e–e– The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

8. Then as it goes through the 9 volt cell, its electrical potential increases by another 9 volts. 6.0 V 9.0 V Two cells in series e–e– The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

9. So passing through both cells, its electrical potential goes up by a total of 6 + 9, or 15 volts. The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. 6.0 V 9.0 V Two cells in series e–e– The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

10. V A voltmeter measures the difference in electrical potential of electrons, or what is called potential difference between different points in a circuit. The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. 6.0 V 9.0 V The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

11. In this location, the leads from the voltmeter touch the circuit at point A and point B, so it measures the potential difference between point A and point B The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. 6.0 V 9.0 V V A B The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

12. The reading on the voltmeter is 6.0 volts. 6.0 V 9.0 V 6.0 V A B The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

13. When the leads from the voltmeter touch point B and point C, it measures the potential difference between points B and C 6.0 V 9.0 V V A B C The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

14. So it reads 9.0 volts. The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. 6.0 V 9.0 V A B C The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

15. So what do you think the voltmeter will read if its leads touch point A and point C? 6.0 V 9.0 V ? V A B C The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

16. The total potential difference is 6 + 9, or 15 volts, so the voltmeter reads 15 volts. 6.0 V 9.0 V 15.0 V A B C The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

17. To find the total voltage supplied by cells in series, the given equation can also be used. 6.0 V 9.0 V V V total = ? The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

18. And because we have only 2 cells, we can say that the total voltage, V total is equal to V1 + V2 6.0 V 9.0 V V V total = ? The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

19. We’ll call the voltage of the 6 volt cell, V1 6.0 V 9.0 V V V total = ? The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

20. And the voltage of the 9 volt cell, V2 6.0 V 9.0 V V V total = ? The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

21. So V total equals V1 + V2, or 6 + 9 6.0 V 9.0 V V V total = ? The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

22. Which is equal to 15 volts. 6.0 V 9.0 V V V total = ? The total voltage supplied by cells in series is the sum of the voltages supplied by each cell. V total = V 1 + V 2 + …

23. We can represent cells in series in a more compact way. (click) We bring the cells together… 6.0 V 9.0 V

24. And represent them with alternating short lines for the negative terminals 6.0 V – 9.0 V –

25. And alternating longer lines for the positive terminals. 6.0 V + 9.0 V +

26. So its positive to negative (click) 6.0 V 9.0 V

27. To positive (click) 6.0 V 9.0 V

28. To negative (click) 6.0 V 9.0 V

29. And we can replace the 6 volts and 9 volts (click) by 15 volts, for the total battery. 6.0 V 9.0 V 15.0 V

30. A very common voltage for cells is 1.5 volts, so two 1.5 volt cells in series can be depicted like this. 1.5 V

31. And because they are series, the total voltage (click) of this battery is 3 volts 1.5 V 3.0 V

32. A group of four 1.5 volt cells in series would have a total of four times 1.5… 1.5 V

33. Which is equal to 6 volts 1.5 V 6.0 V

34. Cells in parallel behave differently than cells in series.. Cells in Parallel

35. The rule is, the total voltage supplied by cells of equal voltage in parallel is the same as the voltage supplied by each cell. The total voltage supplied by cells of equal voltage in parallel is the same as the voltage supplied by each cell.

36. Just a note here, in this course, any cells that are in parallel to each other, will be of equal voltage. The total voltage supplied by cells of equal voltage in parallel is the same as the voltage supplied by each cell.

37. The equation we can use for cells in parallel is V total = V1 = V2 etc. V total = V 1 = V 2 = … The total voltage supplied by cells of equal voltage in parallel is the same as the voltage supplied by each cell.

38. Here is an arrangement of two 6 volt cells in parallel V total = V 1 = V 2 = … Two cells in parallel The total voltage supplied by cells of equal voltage in parallel is the same as the voltage supplied by each cell. 6.0 V

39. If we attach the leads of a voltmeter across the first cell, the voltage reads 6 volts V total = V 1 = V 2 = … The total voltage supplied by cells of equal voltage in parallel is the same as the voltage supplied by each cell. 6.0 V

40. And if we attach the leads across the second cell, it also reads 6 volts. V total = V 1 = V 2 = … The total voltage supplied by cells of equal voltage in parallel is the same as the voltage supplied by each cell. 6.0 V

41. What do you think the voltmeter will read if we attach it to the whole combination, like this? V total = V 1 = V 2 = … The total voltage supplied by cells of equal voltage in parallel is the same as the voltage supplied by each cell. ? V 6.0 V

42. We see it also reads 6 volts. V total = V 1 = V 2 = … The total voltage supplied by cells of equal voltage in parallel is the same as the voltage supplied by each cell. 6.0 V

43. If we use the given equation, we have just two cells in parallel, so we can say V total = V1 = V2 V total = V 1 = V 2 = … The total voltage supplied by cells of equal voltage in parallel is the same as the voltage supplied by each cell. 6.0 V

44. V1 and V2 are both 6 volts V total = V 1 = V 2 = … The total voltage supplied by cells of equal voltage in parallel is the same as the voltage supplied by each cell. 6.0 V

45. V total equals V1 equals V2, so V total is also 6 volts. V total = V 1 = V 2 = … The total voltage supplied by cells of equal voltage in parallel is the same as the voltage supplied by each cell. 6.0 V

46. Now, you may be wondering why one would put more than one cell in parallel when the voltage stays exactly the same? WHY ? 6.0 V

47. The simple reason is, putting cells in parallel will make them last longer than having an individual cell. And the more cells there are in parallel, the longer they will last, given a certain load. Putting cells in parallel makes them last longer 6.0 V

48. Look at this simulation for a while. We’ve coloured the electrons that go through the left cell green, and the ones that go through the right cell blue. Here, we’re showing electron flow rather than conventional current. e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– 6.0 V e–e– e–e– e–e– e–e–

49. All of the electrons pass though the resistor, where some of their potential energy is converted to heat. You can see that half of the electrons that pass through in a given time interval are green and half are blue e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– resistor 6.0 V e–e– e–e– e–e–

50. We can see that half of the electrons that go through the resistor (the green ones), get potential energy from the cell on the left. e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– The green electrons get their energy from this cell. 6.0 V e–e– e–e– e–e–

51. And half of the electrons that go through the resistor (the blue ones), get potential energy from the cell on the right. e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– The blue electrons get their energy from this cell. 6.0 V e–e– e–e– e–e–

52. So half of the energy converted to heat in the resistor came from the cell on the left, carried by the green electrons, and half came from the cell on the right, carried by the blue electrons. e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– Half of the energy converted to heat in the resistor came from the cell on the left, and half came from the cell on the right. 6.0 V e–e– e–e– e–e–

53. So the two cells are sharing the work. e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– These two cells are sharing the work 6.0 V e–e– e–e– e–e–

54. You can see that each cell is supplying energy at half the rate the resistor is using the energy. e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– Each cell is supplying energy at half the rate the resistor is using the energy. 6.0 V e–e– e–e– e–e–

55. Now we’ll cut the wire from the cell on the right, closing off this loop of the circuit. e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– 6.0 V e–e– e–e–

56. In order for the resistor to convert energy to heat at the same rate as it was before, e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– In order for the resistor to convert energy to heat at the same rate as it was before, the green electrons must extract energy from the cell on the left twice as quickly as it did when both cells were working 6.0 V e–e– e–e–

57. the green electrons must extract energy from the cell on the left twice as quickly as they did when both cells were working e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– In order for the resistor to convert energy to heat at the same rate as it was before, the green electrons must extract energy from the cell on the left twice as quickly as they did when both cells were working 6.0 V e–e– e–e–

58. The cell on the left is doing all the work now, and losing energy faster, so it will burn out much more quickly than it would if both cells were sharing the work. 6.0 V e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– This cell will burn out much faster than it would if both cells were working e–e– e–e–

59. You can see that when two cells in parallel are both operating, this cell loses its energy more slowly, so it will last longer. e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– e–e– When two cells in parallel are both operating, this cell loses its energy more slowly, so it will last longer 6.0 V e–e– e–e– e–e–

60. Having more cells in parallel will share the load even more, making each cell last even longer! 6.0 V Having more cells in parallel will share the load even more, making each cell last even longer!

61. Now we’ll look at some cases where some cells are in series and some are in parallel. Cells in Series and Parallel

62. In the following examples, we’ll assume that each individual cell, shown by one short line and one long line, has a voltage of 1.5 volts. Each single cell is 1.5 V

63. Let’s say we’re asked to determine the reading on the voltmeter for this arrangement of cells V Each single cell is 1.5 V V = ? V

64. We see that the group of cells on the red (click) line on the left has three 1.5 volt cells in series V Each single cell is 1.5 V V = ? V Three 1.5 V cells in series

65. When cells are in series, their voltages add up, so the total voltage of this (click) group of three cells is 3 times 1.5, which is 4.5 volts V Each single cell is 1.5 V V = ? V 3 × 1.5 = 4.5 V

66. This group of 3 cells in series on the second red line, (click) will also have a total of 4.5 volts. V Each single cell is 1.5 V V = ? V 3 × 1.5 = 4.5 V 4.5 V

67. As well as (click) this group V Each single cell is 1.5 V V = ? V 3 × 1.5 = 4.5 V 4.5 V

68. And (click) this one V Each single cell is 1.5 V V = ? V 3 × 1.5 = 4.5 V 4.5 V

69. This is just like having four 4.5 V cells in parallel V Each single cell is 1.5 V V = ? V 4.5 V Four 4.5 V cells in parallel

70. When cells are in parallel, (click) the total voltage is the same as the voltage of each cell, V Each single cell is 1.5 V V = ? V 4.5 V Four 4.5 V cells in parallel When cells are in parallel, the total voltage is the same as the voltage of each cell

71. When cells are in parallel, (click) the total voltage is the same as the voltage of each cell, V Each single cell is 1.5 V V = ? V 4.5 V Four 4.5 V cells in parallel When cells are in parallel, the total voltage is the same as the voltage of each cell

72. So the total voltage of this combination of cells is 4.5 volts V Each single cell is 1.5 V V = 4.5 V 4.5 V Four 4.5 V cells in parallel When cells are in parallel, the total voltage is the same as the voltage of each cell

73. Here’s another example. We’re given this arrangement of 1.5 volt cells and we’re asked to determine the voltage on the voltmeter. V Each single cell is 1.5 V V = ? V

74. Looking at these two cells on the left, (click) we see that they are two 1.5 volt cells in parallel V Each single cell is 1.5 V V = ? V Two 1.5 V cells in parallel

75. Remember, for a group of cells in parallel, the total voltage of the group is the same as the voltage of each cell in the group. V Each single cell is 1.5 V V = ? V Two 1.5 V cells in parallel When cells are in parallel, the total voltage is the same as the voltage of each cell

76. So as far as voltage is concerned, (click) this combination of cells is like a single 1.5 volt cell V Each single cell is 1.5 V V = ? V 1.5 V

77. Now, we’ll consider this group of cells up here (click) they are three 1.5 volt cells in series. V Each single cell is 1.5 V V = ? V 1.5 V Three 1.5 V cells in series

78. Remember, when cells are in series, their voltages add up.. V Each single cell is 1.5 V V = ? V 1.5 V In series, voltages add up

79. So the total voltage of three 1.5 volts in series is 3 times 1.5, which is 4.5 volts V Each single cell is 1.5 V V = ? V 1.5 V 3 × 1.5 = 4.5 V

80. We can consider these two groups of cells as being in series with each other. V Each single cell is 1.5 V V = ? V 1.5 V 4.5 V

81. If we replace the voltmeter with a resistor so current can flow, (click) every electron that goes through a cell on the left, must then go through the cells on the top. Each single cell is 1.5 V 1.5 V 4.5 V e–e– e–e–

82. Adding up the voltages of these two groups in series, Each single cell is 1.5 V 1.5 V 4.5 V V V = ? V Adding up the voltages of these two groups in series, V total = 1.5 V + 4.5 V = 6.0 V

83. We get V total is equal to… Each single cell is 1.5 V 1.5 V 4.5 V V V = ? V Adding up the voltages of these two groups in series, V total = 1.5 V + 4.5 V = 6.0 V

84. 1.5 volts Each single cell is 1.5 V 1.5 V 4.5 V V V = ? V Adding up the voltages of these two groups in series, V total = 1.5 V + 4.5 V = 6.0 V

85. Plus 4.5 volts Each single cell is 1.5 V 1.5 V 4.5 V V V = ? V Adding up the voltages of these two groups in series, V total = 1.5 V + 4.5 V = 6.0 V

86. Which equals 6 volts Each single cell is 1.5 V 1.5 V 4.5 V V V = ? V Adding up the voltages of these two groups in series, V total = 1.5 V + 4.5 V = 6.0 V

87. So the voltage on the voltmeter will read 6.0 volts Each single cell is 1.5 V 1.5 V 4.5 V V V = 6.0 V Adding up the voltages of these two groups in series, V total = 1.5 V + 4.5 V = 6.0 V

88. Another way we can look at it is, an electron will pass through one of the cells on the left, increasing its potential by 1.5 volts, then through the cells on top, increasing its potential by another 4.5 V, so this electron has increased its electrical potential by a total of 6 volts. Each single cell is 1.5 V 1.5 V 4.5 V e–e– Has increased its electrical potential by 6.0 volts

89. A different electron will pass through the other cell on the left, increasing its potential by 1.5 volts, then through the cells on top, increasing its potential by another 4.5 V, so this electron has also increased its electrical potential by a total of 6 volts. Each single cell is 1.5 V 1.5 V 4.5 V e–e– Has increased its electrical potential by 6.0 volts

90. So every electron that passes through this arrangement of cells, increases its electrical potential by a total of 6.0 volts Each single cell is 1.5 V 1.5 V 4.5 V Every electron that goes through this arrangement of cells, increases its electrical potential by a total of 6.0 V

91. So again, the voltage supplied by this arrangement is 6.0 volts. Each single cell is 1.5 V 1.5 V 4.5 V V V = 6.0 V