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# Ee1 chapter3 resistors_inseries

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### Ee1 chapter3 resistors_inseries

1. 1. IT2001PAEngineering Essentials (1/2)Chapter 3 - Resistors in Series CircuitsLecturer Namelecturer_email@ite.edu.sg Jul 18, 2012Contact Number
2. 2. Chapter 3 - Resistors in Series CircuitsNumber of slides for today 33 Including this useless slide 2 IT2001PA Engineering Essentials (1/2)
3. 3. Chapter 3 - Resistors in Series CircuitsLesson ObjectivesUpon completion of this topic, you should be able to: Apply Ohm’s Law to calculate voltages, currents and resistances in a series circuit. 3 IT2001PA Engineering Essentials (1/2)
4. 4. Chapter 3 - Resistors in Series CircuitsSpecific Objectives • State the characteristics of series-connected resistors. • Calculate the total resistance for series- connected resistors • Calculate the current flow, voltage drops across the various resistors for series-connected resistors. • Use the voltage divider rule to calculate the voltage drops across series-connected resistors. 4 IT2001PA Engineering Essentials (1/2)
5. 5. Chapter 3 - Resistors in Series CircuitsIntroduction Connecting Line R1 R2 Two resistors in series Resistors in series are connected end to end or in a string as shown. Three resistors in series R1 R2 R3 5 IT2001PA Engineering Essentials (1/2)
6. 6. Chapter 3 - Resistors in Series CircuitsTwo Resistors Connected in Series R1 R2 Apply Ohm’s Law, I V1 = I x R1 V2 = I x R2 V1 V2 VT = I x RT Where RT is the total resistance of the circuit. VT VT = V1 + V2 RT = I x R1 + I x R2 I = I x(R1+ R2) = I x RT VT 6 IT2001PA Engineering Essentials (1/2)
7. 7. Chapter 3 - Resistors in Series CircuitsTwo Resistors Connected in Series R1 R2 RT I I V1 V2 VT VT Total resistance of the circuit, RT = (R1+ R2) 7 IT2001PA Engineering Essentials (1/2)
8. 8. Chapter 3 - Resistors in Series CircuitsCharacteristics of a Series Circuit Three resistors are connected in series. R1 R2 R3 I V1 V2 V3 V The current (I) is the same in all parts of a series circuit. 8 IT2001PA Engineering Essentials (1/2)
9. 9. Chapter 3 - Resistors in Series CircuitsCharacteristics of a Series Circuit R1 R2 R3 I V1 V2 V3 VT The voltage applied to the circuit (VT) is equal the sum of the voltages across each individual parts. VT = V1 + V2 + V3 9 IT2001PA Engineering Essentials (1/2)
10. 10. Chapter 3 - Resistors in Series CircuitsCharacteristics of a Series Circuit R1 R2 R3 I V1 V2 V3 VT Applying Ohm’s Law V1 = I R1 Individual Voltage drop = current x Individual resistance V2 = I R2 V3 = I R3 10 IT2001PA Engineering Essentials (1/2)
11. 11. Chapter 3 - Resistors in Series CircuitsCharacteristics of a Series Circuit Example R1 R2 R3 I V1 V2 V3 VT Given I =2A V1 = I x R1 = 2 x 2 = 4 V R1 = 2 Ω V2 = I x R2 = 2 x 4 = 8 V R2 = 4 Ω V3 = I x R3 = 2 x 6 = 12 V R3 = 6 Ω VT = 4 + 8 + 12 = 24 V 11 IT2001PA Engineering Essentials (1/2)
12. 12. Chapter 3 - Resistors in Series Circuits Characteristics of a Series Circuit R1 R2 R3I VT = V1 + V2 + V3 V1 V2 V3 I RT = I R1 + I R2 + I R3 I RT = I ( R1 + R2 + R3) VT RT = ( R1 + R2 + R3) Total resistance = sum of Individual resistance RT = R1 + R2 + R3 12 IT2001PA Engineering Essentials (1/2)
13. 13. Chapter 3 - Resistors in Series CircuitsCharacteristics of a Series Circuit Example R1 R2 R3 I V1 V2 V3 VT Given I =2A RT = R1 + R2 + R3 R1 = 2 Ω R2 = 4 Ω R3 = 6 Ω = 2+4+6 = 12 Ω 13 IT2001PA Engineering Essentials (1/2)
14. 14. Chapter 3 - Resistors in Series CircuitsCharacteristics of a Series Circuit R1 R2 R3 I V1 V2 V3 VT RT = R1 + R2 + R3 Total resistance is greater than the larger individual resistance. 14 IT2001PA Engineering Essentials (1/2)
15. 15. Chapter 3 - Resistors in Series CircuitsCharacteristics of a Series CircuitExample R1 R2 R3 Given I I =2A V1 V2 V3 R1 = 2 Ω R2 = 4 Ω R3 = 6 Ω VT RT = R1 + R2 + R3 Larger Individual Resistance = R3 = 6 Ω = 2+4+6 = 12 Ω RT > R3 12 Ω > 6 Ω 15 IT2001PA Engineering Essentials (1/2)
16. 16. Chapter 3 - Resistors in Series CircuitsCharacteristics of a Series Circuit (Summary) 1. The current through all the resistors is the same. 2. The voltage applied to the circuit = the sum of the voltages across the individual parts. 3. Individual voltage drop = current x individual resistances. 4. Total resistance = sum of individual resistances. 5. Total resistance is greater than the largest individual resistance. 16 IT2001PA Engineering Essentials (1/2)
17. 17. Chapter 3 - Resistors in Series Circuits Example 3-1 R1= 1Ω R2= 2 Ω R3= 3 Ω Determine I the total V1 V2 V3 resistance of the circuit? V= 10 VCombine threeresistors intoone single RT RT = R1 + R2 + R3resistor = 1 + 2 + 3 = 6Ω 10 V 17 IT2001PA Engineering Essentials (1/2)
18. 18. Chapter 3 - Resistors in Series CircuitsExample 3-1 R1= 1Ω R2= 2 Ω R3= 3 Ω I Determine V2 the current V1 V3 flow of the circuit? V= 10 V RT = 1 + 2 + 3 = 6 Ω I = V / RT = 10 / 6 = 1.667 A 18 IT2001PA Engineering Essentials (1/2)
19. 19. Chapter 3 - Resistors in Series CircuitsExample 3-1 R1= 1Ω R2= 2 Ω R3= 3 Ω DetermineI the voltage V1 V2 V3 across resistor R1 of the circuit? V= 10 V V1 = I R1 = 1.667 X 1 = 1.667 V 19 IT2001PA Engineering Essentials (1/2)
20. 20. Chapter 3 - Resistors in Series CircuitsExample 3-1 R1= 1Ω R2= 2 Ω R3= 3 Ω Determine I the voltage V1 V2 V3 across resistor R2 of the circuit? V= 10 V V2 = I R2 = 1.667 X 2 = 3.334 V 20 IT2001PA Engineering Essentials (1/2)
21. 21. Chapter 3 - Resistors in Series CircuitsExample 3-1 R1= 1Ω R2= 2 Ω R3= 3 Ω Determine I the voltage V1 V2 V3 across resistor R3 of the circuit? V= 10 V V3 = I R3 = 1.667 X 3 = 5 V 21 IT2001PA Engineering Essentials (1/2)
22. 22. Chapter 3 - Resistors in Series Circuits Example 3-1 (Summary) R1= 1Ω R2= 2 Ω R3= 3 ΩI V1 V2 V3 V1 = I R1 = 1.667 X 1 V= 10 V V = = I 1.667 V 2 R 2 RT = 1 + 2 + 3 = 6 Ω = 1.667 X 2 = 3.334 V I = V / RT V3 = I R3 = 10 / 6 = 1.667 X 3 = 1.667 A = 5 V 22 IT2001PA Engineering Essentials (1/2)
23. 23. Chapter 3 - Resistors in Series CircuitsExample 3-1 (Summary) RT = 1 + 2 + 3 = 6 Ω R1= 1Ω R2= 2 Ω R3= 3 Ω 1.667 A I 5 V 1.667 V 3.334 V V1 V2 V3 V= 10 V 23 IT2001PA Engineering Essentials (1/2)
24. 24. Chapter 3 - Resistors in Series CircuitsExample 3-1 (Summary) 1.667 V 3.334 V 5 V Voltage can be measured from a V V V voltmeter connected in parallel R1= 1Ω R2= 2 Ω R3= 3 Ω I V1 V2 V3 current can be measured from a A ammeter V= 10 V connected in series 1.667 A 24 IT2001PA Engineering Essentials (1/2)
25. 25. Chapter 3 - Resistors in Series CircuitsExample 3-2 R1= 40Ω R2= 60 Ω R3= X Ω I V1=16V V2 V3 V= 50 V Three resistors of 40 Ω, 60 Ω and X Ω respectively are connected in series. The combination is connected across the 50 V supply. If the voltage drop across the 40 Ω resistor is 16 V, determine the current in the circuit and the unknown resistor X. 25 IT2001PA Engineering Essentials (1/2)
26. 26. Chapter 3 - Resistors in Series CircuitsExample 3-2 (Solution) R1= 40Ω R2= 60 Ω R3= X ΩI V1=16V V2 V3 V3 = 50 – 16 – 24 V3 = 10 V V= 50 V V3 = I R3 10 = 0.4 x R3 I = V1 / R1 V2 = I R2 R3 = 10 / 0.4 I = 16 / 40 V2 = 0.4 x 60 R3 = 25 Ω I = 0.4 A V2 = 24 V 26 IT2001PA Engineering Essentials (1/2)
27. 27. Chapter 3 - Resistors in Series CircuitsVoltage Divider R1 R2 I V1 V2 Vs General Voltage divider Formula is Rx Vx = Vs Where RT RT is the total or equivalent series resistance Vx is the voltage across any resistor, Rx 27 IT2001PA Engineering Essentials (1/2)
28. 28. Chapter 3 - Resistors in Series CircuitsVoltage Divider Rx Vx = Vs R1 R2 RT I R T = R 1 + R2 V1 V2 R1 V1 = Vs Vs RT R2 V2 = Vs RT 28 IT2001PA Engineering Essentials (1/2)
29. 29. Chapter 3 - Resistors in Series Circuits RxVoltage Divider Vx = Vs RT I R T = R 1 + R2 + R 3 R1 V1 R1 V1 = Vs Vs RT R2 V2 R2 V2 = Vs R3 V3 RT R3 V3 = Vs RT 29 IT2001PA Engineering Essentials (1/2)
30. 30. Chapter 3 - Resistors in Series CircuitsExample 3-3 RT = 82+ 64=146 Ω R1= 82Ω R2= 64 Ω V1 = Vs x R1 / RT = 10 x 82 / (146) I = 5.617 V V1 V2 V2 = Vs x R2 / RT = 10 x 64 / (146) = 4.383 V Vs = 10V Or Determine the voltage across V2 = 10 – 5.617 R1 and R2 = 4.383 V 30 IT2001PA Engineering Essentials (1/2)
31. 31. Chapter 3 - Resistors in Series CircuitsPotentiometer as an Adjustable Voltage Divider Potentiometer is a variable resistor with three terminals A potentiometer connected to a voltage source is shown: 31 IT2001PA Engineering Essentials (1/2)
32. 32. Chapter 3 - Resistors in Series CircuitsSummary 1. The current through all the resistors is the same. 2. The voltage applied to the circuit = the sum of the voltages across the individual parts. 3. Individual voltage drop = current x individual resistances. 4. Total resistance = sum of individual resistances. 5. Total resistance is greater than the largest individual resistance. 32 IT2001PA Engineering Essentials (1/2)
33. 33. Chapter 3 - Resistors in Series CircuitsNext Lesson 33 IT2001PA Engineering Essentials (1/2)