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Resistors in series and in parallel

Resistors in series and in parallel. Warm-up. 1 Margaret connects 10 bulbs in a circuit and the light of the bulbs is not visible. . Do you agree with Margaret that total resistance of the circuit . (a) increases with the number of bulbs, (b) is equal to 10 times the resistance of a bulb?.

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Resistors in series and in parallel

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  1. Resistors in series and in parallel

  2. Warm-up 1 Margaret connects 10 bulbs in a circuit and the light of the bulbs is not visible. Do you agree with Margaret that total resistance of the circuit (a) increases with the number of bulbs, (b) is equal to 10 times the resistance of a bulb? Agree Agree

  3. Warm-up 2 Flow of charge in a conductor vs. students walking on a road. (a) If the road is narrow, how will the no. of students walking on it be affected? Fewer students can walk on it at a time. (b) How should the road be changed to let more students walk on it at a time? To make the road wider.

  4. 1 Bulbs in series and in parallel bulb 1 bulb 1 bulb 2 bulb 2 bulb 1 Bulbs are connected in series. Bulbs are connected in parallel. -- The bulb glows brightly. The bulbs glow dimmer. The bulbs glow brightly.

  5. 1 Bulbs in series and in parallel bulb 1 bulb 1 bulb 2 bulb 2 bulb 1 -- in series in parallel Remove bulb 1  breaks circuit & bulb 2 goes out Remove bulb 1 NOT break circuit & bulb 2 glows -- Vbattery=Vbulb 1 Vbattery = Vbulb 1+Vbulb 2 Vbattery=Vbulb 1=Vbulb 2

  6. 1 Bulbs in series and in parallel bulb 1 bulb 1 bulb 2 bulb 2 bulb 1 -- in series in parallel I0 Ibulb 1 = Ibulb 2 (= 0.5I0) Ibulb 1 = Ibulb 2 =I0 (= 0.5  Itotal) same current  same brightness

  7. V R2 R1 R3 V3 V1 V2 2 Resistors in series R1, R2 and R3 are connected in series. I I = current through R1, R2 and R3 V = V1 + V2 + V3 IR2 IR3 =I (R1 + R2 + R3) IR1 Equivalent resistance

  8. V R2 R1 R3 V R (= R1 + R2 + R3) 2 Resistors in series I.e. =I (R1 + R2 + R3) I =IR I

  9. 2 Resistors in series If 2 or more resistors are connected in series, the equivalent resistance of resistors > resistance of each resistor. Analogy — joining wires... ...to give a longer wire (of higher resistance).

  10. V R1 V V R2 R2 R1 • • 1 1 1 R3 R3 R1 R2 V R3 3 Resistors in parallel R1, R2 and R3 are connected in parallel. V = voltage across R1, R2 and R3 I1 I I = I1 + I2 + I3 I2 I3 =V ( + + ) V = (R1–1 + R2–1 + R3–1)–1 Equivalent resistance

  11. V R1 V R2 R • • R3 V R [= (R1–1 + R2–1 + R3–1)–1] 3 Resistors in parallel I.e. I1 I =I1 + I2 + I3 I2 I3 = I

  12. 3 Resistors in parallel If 2 or more resistors are in parallel, the equivalent resistance of resistors < resistance of each resistor. Analogy — putting wires side by side... ...to give a wider wire (of lower resistance).

  13. 9 V 3  6  Example 4 Equivalent resistance (a) (i) What is the equivalent resistance of the circuit? 3- and 6- resistors are in series. Equivalent resistance = = 9  3 + 6

  14. 9 V V R 3  6  9 9 Example 4 Equivalent resistance (a) (ii) What is the voltage across the 6- resistor? equivalent resistance = 9  Current through each resistor = = 1 A equivalent resistance of the series circuit 1  6 Voltage across 6- resistor = IR 6 V

  15. 9 V 3  • • 6  Example 4 Equivalent resistance (b) (i) What is the equivalent resistance of the circuit? 3- and 6- resistors are in parallel. (R1–1 + R2–1)–1 Equivalent resistance = 3 6 = 2 

  16. V R 9 V 9 3  6 • • 6  Example 4 Equivalent resistance (b) (ii) What is the current passing the 6- resistor? Voltage across each resistor = 9 V Current passing 6- resistor = = = 1.5 A

  17. V R 9 V 9 3  3 • • 6  Example 4 Equivalent resistance (b) (iii) What is the total current in the main circuit? I6- = 1.5 A Current passing 3- resistor = = = 3 A Total current in the main circuit = I3- + I6- = 4.5 A = 3 + 1.5

  18. 12 V B = 6  A = 8  • • C = 12  Example 5 Circuit analysis (a) What is the total resistance of the circuit? Equivalent resistance of B and C = (R1–1 + R2–1)–1 = 4  6 12 Total resistance = RA + RB // C = 8 + 4 = 12 

  19. 12 V B = 6  A = 8  • • V C = 12  R 12 12 Example 5 Circuit analysis (b) What is the current passing A? total resistance = 12  = 1 A = Total current from battery =  Current passing A = 1 A

  20. 12 V B = 6  A = 8  • • C = 12  Example 5 Circuit analysis (c) What is the voltage across A? I = 1 A Voltage across A = IR = 1  8 = 8 V

  21. 12 V B = 6  A = 8  • • C = 12  8 V Example 5 Circuit analysis (d) What is the voltage across the parallel combination of B and C? Voltage across the combination of B & C = 12 – 8 = 4 V

  22. 12 V B = 6  A = 8  • • V V C = 12  R R 4 V 4 4 6 12 Example 5 Circuit analysis (e) What is the current passing (i) B and (ii) C? = 0.667 A = (i) Current passing B = = 0.333 A = (ii) Current passing C =

  23.  4 Short circuit When the key is open... ...the bulb lights. When the key is closed... shorting key ...a large current passes the key (~ 0 ) and the wires become very hot. Also, the bulb goes out. The bulb is short-circuited.

  24.  4 Short circuit In this case, the battery goes ‘flat’ quickly. In a mains circuit, a short circuit overheats the cables and may cause a fire. shorting key

  25. Q1 Which circuit is NOT... Which circuit is NOT equivalent to the others? AB CD

  26. Q2 Find I1 and I2. Find I1 and I2. 6 V 1  2  6 A 3 A I1 =____ I2 =____

  27. Q3 Fill in the values of... Fill in the values of resistance in the blanks. A 1 A 6  B 12 V 6 ____ 

  28. Q3 Fill in the values of... Fill in the values of resistance in the blanks. equivalent to B (6 ); RC = RD A 1 A 6  C D 12 V 12 ___  12 ___ 

  29. Q3 Fill in the values of... Fill in the values of resistance in the blanks. equivalent to D (12 ); RE = RF A 1 A 6  E 6 ___  C 12 V F 12  6 ___ 

  30. Q3 Fill in the values of... Fill in the values of resistance in the blanks. equivalent to D (12 ); RG = 2RH A 1 A 6  G 8 ___  C 12 V H 12  4 ___ 

  31. Q3 Fill in the values of... Fill in the values of resistance in the blanks. A 1 A 6  G C 12 V equivalent to H (4 ); RK = RL 12  L K 8 RK = ___ , RL = ___  8

  32. Q4 Which circuit in Q3... Which circuit in Q3 has the highest equivalent resistance? All circuits in Q3 have the same equivalent resistance.

  33. A 5 Resistance of ammeters, voltmeters and cells a Resistance of ammeter Ammeter connected in series to a resistor gives the current passing the resistor. I Rcircuit = Rammeter + Rresistor  I in the circuit <I without ammeter Resistance of ammeter should be very low.

  34.  V 5 Resistance of ammeters, voltmeters and cells b Resistance of voltmeter Voltmeter connected in parallel to a resistor gives the voltage across the resistor. I V R// branch = (Rvoltmeter–1 + Rresistor–1)–1  V across resistor V without voltmeter Resistance of voltmeter should be very high.

  35.    V V 5 Resistance of ammeters, voltmeters and cells c Resistance of cells All power supplies (batteries, power packs, etc.) have some resistance — internal resistance. E.g. voltage =2.8 V voltage = 3 V < 3 V closed

  36. 5 Resistance of ammeters, voltmeters and cells c Resistance of cells ‘Lost volt’ is due to the resistance of the cells. In a complete circuit, a battery is like... battery Internal resistance of a cell is usually neglected if not otherwise indicated. I lost volt 3 V voltage supplied in a complete circuit < 3 V

  37. Example 6 Applying Ohm’s law A student uses this set-up to investigate Ohm’s law. voltmeter ammeter (a) (i) What are the 2 mistakes in the circuit? 1. Ammeter and voltmeter should be interchanged. 2. Rheostat is connected up as a fixed resistor, not a variable resistor.

  38. Example 6 Applying Ohm’s law A student uses this set-up to investigate Ohm’s law. voltmeter ammeter (a) (ii) Draw a correct circuit diagram for this set-up.

  39. V 1.8 4.8 I 0.6 1.2 Example 6 Applying Ohm’s law After fixing mistakes, the student obtains... (b) (i) What is the resistance of the wire when V is (1) 1.8 V (2) 4.8 V? R = (2) R = (1) R = = 4.0  = 3.0 

  40. V / V 5 4 3 2 1 I / A 0 0.2 0.4 0.6 0.8 1.0 1.2 Example 6 Applying Ohm’s law After fixing mistakes, the student obtains... (b) (ii) Plot V-I graph.

  41. V / V 5 4 3 2 1 I / A 0 0.2 0.4 0.6 0.8 1.0 1.2 Example 6 Applying Ohm’s law After fixing mistakes, the student obtains... (b) (iii) When is the voltage not  current? When V > 2.4 V

  42. V / V 5 4 3 2 1 I / A 0 0.2 0.4 0.6 0.8 1.0 1.2 Example 6 Applying Ohm’s law After fixing mistakes, the student obtains... (b) (iv) Why is the proportion not held there? The wire is heated up by the current and its resistance .

  43. A The effect of the resistance of ammeter, voltmeter and cell on the circuit. 1 (a) What would I and V be if resistance of ammeterR were... 1 V 3  Ibulb 6  Vbulb 111 mA 66.7 mA 0.166 mA 0.167 A 0.667 V 1.00 V 0.4 V 0.999 mV

  44. A The effect of the resistance of ammeter, voltmeter and cell on the circuit. 1 (a) 1 V 3  Ibulb 6  66.7 mA 0.166 mA 111 mA 0.167 A 1.00 V 0.667 V 0.999 mV 0.4 V Vbulb (b) A good ammeter should have a __________ resistance. low

  45. V The effect of the resistance of ammeter, voltmeter and cell on the circuit. 2 (a) What would I and V be if resistance of voltmeterR were... 1 V 3  Ibulb 6  Vbulb 0.111 A 83.3 mA 0.111 A 0.111 A 0.667 V 0.667 V 0.5 V 0.666 V

  46. V The effect of the resistance of ammeter, voltmeter and cell on the circuit. 2 (a) 1 V 3  Ibulb 6  88.3 mA 0.111 A 0.111 A 0.111 A 0.667 V 0.667 V 0.666 V 0.5 V Vbulb (b) A good voltmeter should have a __________ resistance. large

  47. The effect of the resistance of ammeter, voltmeter and cell on the circuit. 1 V 3 (a) What would I and V be if resistance of batteryR were... E 3  Ibulb 6  Vbulb 111 mA 66.7 mA 0.166 mA 0.167 A 0.667 V 1.00 V 0.4 V 0.999 mV

  48. The effect of the resistance of ammeter, voltmeter and cell on the circuit. 1 V 3 (a) 3  Ibulb 6  66.7 mA 0.166 mA 111 mA 0.167 A 1.00 V 0.667 V 0.999 mV 0.4 V Vbulb (b) A good battery should have a __________ resistance. low

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