2. Chapter 3 - Resistors in Series Circuits
Number of slides for today
33
Including this useless slide
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IT2001PA Engineering Essentials (1/2)
3. Chapter 3 - Resistors in Series Circuits
Lesson Objectives
Upon completion of this topic, you should be able to:
Apply Ohm’s Law to calculate voltages, currents and
resistances in a series circuit.
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4. Chapter 3 - Resistors in Series Circuits
Specific 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.
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5. Chapter 3 - Resistors in Series Circuits
Introduction
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
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6. Chapter 3 - Resistors in Series Circuits
Two 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
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7. Chapter 3 - Resistors in Series Circuits
Two Resistors Connected in Series
R1 R2
RT
I I
V1 V2
VT
VT
Total resistance of the circuit,
RT = (R1+ R2)
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8. Chapter 3 - Resistors in Series Circuits
Characteristics 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.
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9. Chapter 3 - Resistors in Series Circuits
Characteristics 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
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10. Chapter 3 - Resistors in Series Circuits
Characteristics 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
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11. Chapter 3 - Resistors in Series Circuits
Characteristics 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
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12. Chapter 3 - Resistors in Series Circuits
Characteristics of a Series Circuit
R1 R2 R3
I 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
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13. Chapter 3 - Resistors in Series Circuits
Characteristics 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
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14. Chapter 3 - Resistors in Series Circuits
Characteristics 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.
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15. Chapter 3 - Resistors in Series Circuits
Characteristics of a Series Circuit
Example 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
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16. Chapter 3 - Resistors in Series Circuits
Characteristics 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.
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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 V
Combine three
resistors into
one single RT RT = R1 + R2 + R3
resistor = 1 + 2 + 3
= 6Ω
10 V
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18. Chapter 3 - Resistors in Series Circuits
Example 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
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19. Chapter 3 - Resistors in Series Circuits
Example 3-1
R1= 1Ω R2= 2 Ω R3= 3 Ω
Determine
I
the voltage
V1 V2 V3 across
resistor R1 of
the circuit?
V= 10 V
V1 = I R1
= 1.667 X 1
= 1.667 V
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20. Chapter 3 - Resistors in Series Circuits
Example 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
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21. Chapter 3 - Resistors in Series Circuits
Example 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
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22. Chapter 3 - Resistors in Series Circuits
Example 3-1 (Summary)
R1= 1Ω R2= 2 Ω R3= 3 Ω
I
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
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23. Chapter 3 - Resistors in Series Circuits
Example 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
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24. Chapter 3 - Resistors in Series Circuits
Example 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
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25. Chapter 3 - Resistors in Series Circuits
Example 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.
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26. Chapter 3 - Resistors in Series Circuits
Example 3-2 (Solution)
R1= 40Ω R2= 60 Ω R3= X Ω
I
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
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27. Chapter 3 - Resistors in Series Circuits
Voltage 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
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28. Chapter 3 - Resistors in Series Circuits
Voltage Divider Rx
Vx = Vs
R1 R2
RT
I R T = R 1 + R2
V1 V2
R1
V1 = Vs
Vs
RT
R2
V2 = Vs
RT
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29. Chapter 3 - Resistors in Series Circuits
Rx
Voltage 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
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30. Chapter 3 - Resistors in Series Circuits
Example 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
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31. Chapter 3 - Resistors in Series Circuits
Potentiometer as an Adjustable Voltage Divider
Potentiometer is a variable resistor with three terminals
A potentiometer connected to a voltage source is
shown:
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32. Chapter 3 - Resistors in Series Circuits
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.
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33. Chapter 3 - Resistors in Series Circuits
Next Lesson
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