D.C. Circuits

Current and Potential Difference in Circuits
Series and Parallel Circuits

1. D.C. Circuits Current and Potential Difference in Circuits Series and Parallel Circuits

2. Electric Ciruit An electric circuit is a complete or closed path through which charge can flow from one terminal of an electrical source to the other. It consists of four main parts or components: One that drives the electric charge round the circuit, e.g. a battery; One on which the moving charge can do a useful job, e.g. a lamp; Conductors to join them together, e.g. copper wire; Switches to break or complete the circuit.

3. Symbols in Drawing Circuit a.c . supply cell battery d.c. supply switch ammeter voltmeter lamp resistor variable resistor light dependent resistor (LDR)

4. thermistor fuse capacitor bell buzzer magnetising coil transformer diode

5. 330 Ω

6. A C B D

7. B A

8. Current in a Series Circuit In figure below, ammeters A 1 , A 2 and A 3 measure the current at various points in the circuit. All the ammeters record the same reading. This conclude that: The current at every point in a series circuit is the same .

9. Potential Difference in a Series Circuit In figure below, voltmeters V 1 and V 2 measure the potential differences across R 1 and R 2 respectively. Voltmeter V measures the potential difference across the whole circuit. The sum of the potential differences in a series circuit is equal to the potential difference across the whole circuit, i.e. V = V 1 + V 2 .

10. Figure below shows a simple circuit consisting of a battery connected by copper wires to two resistors having resistor R 1 and R 2 . For any individual resistor in the circuit, the current, potential difference and resistance are related by the equation V = IR Thus, V 1 = IR 1 and V 2 = IR 2 .

11. In a series circuit, the component with largest resistance has the highest potential difference across it. If the internal resistance of cell is neglected, the e.m.f. E of the cell equals to the potential difference across the whole circuit V . In series circuit, the current will cease to flow if there is a break anywhere in the circuit.

12. Example 1 Determine the reading of the ammeter marked by ‘?’ Determine the reading of the voltmeter marked by ‘?’

13. Example 2 Two resistors valued 30 Ω and 15 Ω are connected in series. Calculate its effective resistance. Calculate the current which a 4.5 V battery supplies to each combination. Calculate the potential difference across each separate resistor when the 4.5 V battery is connected across each combination. In a circuit four resistors valued 8 Ω , 20 Ω , 24 Ω and 30 Ω are connected in series to a 60 V cell. Find The combined resistance, The current , The potential difference across the 20 Ω resistor. Three resistors are connected in series to a 24 V battery, and an ammeter in the circuit reads 0.5 A. The first resistor is rated at 22 Ω , and the second at 8 Ω . Find The total resistance, The resistance of the third resistor, The potential difference across the third resistor.

14. Current in a Parallel Circuit Figure below shows how the current from dry cell is shared in the separate branches of a parallel circuit. The current from the source I the sum of the currents in the separate branches of a parallel circuit, i.e. I = I 1 +I 2 .

15. Potential Difference in a Parallel Circuit Figure below shows a voltmeter V 1 and V 2 measure the potential differences across resistor R 1 and R 2 respectively. All the voltmeters record the same reading. We can conclude that: the potential differences across the separate branches of a parallel circuit are the same .

16. In parallel circuit, the component with the smallest resistance has the highest current flowing through it. The current flowing out from the cell, I , is the same as the current flowing back to the cell, I 3 . Any breakdown in one of the parallel branches does not affect the current flow in the other branches of the circuit.

17. Example 3 Determine the reading of the ammeter marked by ‘?’ Determine the reading of the voltmeter marked by ‘?’ (a) (b) (c) (d) (e) (a) (b) (c)

18. Example 4 A 12 Ω and 4 Ω resistor is connected in parallel to a 12 V battery. Calculate the effective resistance. Calculate the current flowing through the 12 Ω resistor, the 4 Ω and the battery. Four resistors with resistance 8 Ω , 20 Ω , 24 Ω and 30 Ω are connected in parallel to a 60 V dry cell. Find The combined resistance, The current in the battery, The current in the 8 Ω resistor.

19. Example 5

20. This question refers to the circuit below in which the current is 100 mA: (a) What is 100 mA in amps? (b) What is the current in each resistor? (c) What is the voltage across each resistor? (d) What is the total resistance? (e) What is the battery voltage? Example 6

21. Refer the circuit below (a) What is the single resistor equivalent? (b) What is the total current? (c) What is the voltage across  the 6 ohm resistor? (d) What is the current in each resistor?

22. The battery in a circuit has an e.m.f. of 6.0 V and negligible resistance. If two resistors R 1 and R 2 with resistance 12 Ω and 6 Ω are connected in parallel while resistance R 3 with resistance 8 Ω is connected in series with them. Calculate the combined resistance of the resistors connected in parallel. Calculate the current in the R 3 . Three resistors are connected in parallel to a 24 V battery, and the battery current is 3.0 A. The first resistor is rated 20 Ω and the second at 40 Ω . Find The total resistance, The resistance of the third resistor, The current in the third resistor.

23. The diagram shows the components of a lighter for a gas cooker.

24. Which circuit diagram for this lighter is correct? A

25. Which circuit contains a cell, a light-emitting diode and a fixed resistor? A

26. Which electrical component would not normally be found in a battery-operated torch (flashlight)? D

27. The diagram shows a torch containing two 2 V cells, a switch and a lamp.

28. What is the circuit diagram for the torch? A

29. Which symbol represents an electrical component used to store energy? A

30. The diagram shows an electric circuit.

31. Which pair of readings is obtained when a suitable power supply is connected between X and Y ? C

32. A 3.0  lamp and a 6.0  lamp are connected in series. What is the total resistance of the combination? 0.5  2.0  9.0  18.0 

33. A circuit is set up as shown in the diagram .

34. Assuming that the ammeter has negligible resistance, what is the value of the resistor R ? 0.5 Ω 1.5 Ω 5 Ω 6 Ω

35. A 1.0 resistor and a 2.0 resistor are connected in series across a 12 V d.c. supply. What is the current in the circuit? 0.25 A 4.0 A 6.0 A 12 A

36. A student sets up the circuit shown.

37. The currents measured with the ammeters are shown. Which equation is correct? I 1 = I 2 + I 3 + I 4 I 1 = I 2 = I 3 = I 4 I 2 + I 3 = I 4 + I 1 I 4 = I 3 + I 2 + I 1

38. The diagram shows a circuit with three ammeters, X, Y and Z.

39. Which set of readings is possible? D

40. Two resistors of 6 Ω and 12 Ω are arranged in parallel. A p.d . is connected across the terminals X and Y. The current through the 6 Ω resistor is 4 A.

41. What is the current in the ammeter? 4 A 6 A 8 A 12 A

42. Diagram 1 shows a resistor connected to a battery, an ammeter and a voltmeter. The ammeter reading is 0.5 A and the voltmeter reading is 3.0 V. A second identical resistor is now connected in parallel with the first resistor, as shown in diagram 2.

43. What are the ammeter and voltmeter readings in the circuit shown in diagram 2? A

44. The diagram shows part of an electric circuit.

45. What is the current in the 2 Ω resistor ? 0.6 A 1.2 A 3.0 A 6.0 A

46. At which point in the circuit is the current the smallest? D

47. In the circuit shown, at which point is the current the smallest? B

48. The following circuit is set up.

49. What is the reading on the ammeter? 0.33 A 0.50 A 0.67 A 1.0 A

50. Four resistors and an ammeter are connected to a battery as shown. The ammeter reads 2 A. Which of the four labelled points in the circuit is the only one where the current is less than 2 A? C

51. In the circuit shown, the reading on ammeter 1 is 2 A.

52. What is the reading on ammeter 2? 0 A 1 A 2 A 4 A

53. The circuit diagram shows a parallel arrangement of resistors. P , Q, R and S represent the current at the points shown.

54. Which statement is correct? P is greater than Q. Q is equal to R. R is greater than S. S is equal to P.

55. The diagram shows four different circuits.

56. What is the order of increasing resistance of these circuits? C

57. In the circuits shown, all the resistors are identical. Which circuit has the least resistance? C

58. In the circuit shown, the switches S 1 and S 2 may be open (off) or closed (on).

59. Which line in the table shows the voltmeter reading for the switch positions given? B

60. Circuit Diagram

61. B A

62. R 1 R 2 A B

63. A B

64. 1000 Ω A B C

65. A B

66. A B

67. D.C. Circuits Current and potential difference in circuits Series and parallel circuits

68. Current and Potential Difference in Circuits *draw circuit diagrams with power sources (cell, battery or a.c . mains), switches (closed and open), resistors (fixed and variable), light-dependent resistors, thermistors, lamps, ammeters, voltmeters, magnetising coils, bells, fuses, relays, light-emitting diodes and rectifying diodes. State that the current at every point in a series circuit is the same, and use this in calculations. State that the sum of the potential differences in a series circuit is equal to the potential difference across the whole circuit and use this in calculations.

69. Series and Parallel Circuits State that the current from the source is the sum of the currents in the separate branches of a parallel circuit. Do calculations on the whole circuit, recalling and using formulae including R = V/ I and those for potential differences in series, resistors in series and resistors in parallel.