AET 3a DC Calculations

7/18/2019 AET 3a DC Calculations

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DC CALCULATIONSAET 3

Ohm’s Law and Kirchhoff's Law as it appliesto DC circuits

Courtesy of the United States Air Force



2

INTRODUCTION

In this unit you will learn how tocalculate circuit operatingparameters. We will expand on

Ohm’s Law and Kirchhoff’s Laws,and learn some new formulas.



3

Ohm’s Law and Kirchhoff’s Laws,along with many other electronicformulas, will give you the knowledge

to help you become proficient introubleshooting electronic circuits.

INTRODUCTION



4

If needed, we will take some time toanswer any questions or clear upany areas from the previous unit,

DC Theory.

INTRODUCTION



5

Objective 5aGiven formulas, calculate values fora resistive DC circuits IAW the PCchecklist Meas: PC

• Series

• Parallel

• Series-Parallel•Voltage Dividers

INTRODUCTION



6

Objective 5bGiven formulas, calculate parameterchanges on a resistive DC circuitsIAW the PC checklist Meas: PC

• Series

• Parallel

• Series-Parallel• Voltage Dividers

INTRODUCTION



7

Let’s start by taking a quick look atwhy we need to calculate circuitparameters or values.

INTRODUCTION



8

DC CALCULATIONS

Purpose of Calculations:

Mathematics is an integral part ofelectronics. By using the formulas ofthe laws governing electronics (Ohmsand Kirchhoff), we can calculate allcircuit parameters mathematically.



9


For example, the filament in a lightbulb has a positive temperaturecoefficient. This means that its’

resistance increases as temperatureincreases. The resistance of thetungsten cannot be measured under

normal operating conditions(resistance cannot be measured whilea circuit is in operation).

DC CALCULATIONS



10


However, we can calculate theresistance of the tungsten duringnormal operating conditions if we

know the voltage applied to the bulband the amount of current through it.

Remember the Ohm’s Law andKirchhoff’s Laws formulas we used inthe last unit. Well dust them off,

because we are going to use themagain.

DC CALCULATIONS



11


The first law that we will look at is Ohm’sLaw. We can use Ohm’s Law to calculatethe following circuit parameters: Current,

Source (applied) Voltage, Voltage “drops”,Resistance, and Power.

DC CALCULATIONS



12

Ohm’s Law: In 1827, Georg Simon

Ohm, a Germanteacher, discovered the

relationship betweenvoltage, current, andresistance.

DC CALCULATIONS



13

Ohm’s Law:Current is directly proportional to source voltage and inverselyproportional to circuit resistance.

I = R

E

E = IR

R = I

E

DC CALCULATIONS



14

Kirchhoff’s Laws: In 1854, a Russian

physicist, GustavRobert Kirchhoff,

announced hisvoltage and currentslaws that extend the

theory of GeorgSimon Ohm.

DC CALCULATIONS



15

Terms Applicable to Kirchhoff’s Laws:

• Element

• Node

• Branch

• Loop

DC CALCULATIONS



16

nodes

elements

branches

loops

2 nodes (connection points-three or more)3 loops (current or voltage)3 branches (connects adjacent nodes)4 elements (resistances and voltage sources)

DC CALCULATIONS



17

Kirchhoff’s Current Laws:

No matter how many branchesor paths into and out of a pointor node all the current leavingthat point or node must equalthe current arriving at thatpoint or node.

DC CALCULATIONS



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No matter how many branches or paths into andout of a point or node all the current leaving thatpoint or node must equal the current arriving at

that point or node.

3 mA 3 mA

3 mA3 mA

IT=IR1=IR2=IR3

DC CALCULATIONS



19

Kirchhoff’s Voltage Laws:

The sum of the voltage dropsin a closed loop equals theapplied voltage.

DC CALCULATIONS



20

Voltage: The sum of the voltage drops in aclosed loop equals the applied voltage.

20 V

30 V80 V

? V

Ea=ER1+ER2+ER3

DC CALCULATIONS



21

Circuit and Component Identification:

Ea = applied voltage

E or V = voltage

ER# or VR# = voltage drop of resistance #

I = current

IT = total circuit current

IR# = current of resistance #

R = resistanceR# = specific resistance #

Let’s properly label the circuit!

DC CALCULATIONS



22

Series Circuits Review:Voltage: Current:

DC CALCULATIONS



23

RT = R1 + R2 + R3 + …Calculating Total Resistance for a Series Circuit

OR RT = Ea / IT

α ρ

l=

Why?

Remember the resistance formula:

Resistance in series effects the LENGTH factor.

DC CALCULATIONS

5Ù

10Ù

15Ù

30V

R1

R2

R3



24

Calculating Total Current for a Series Circuit

IT = IR1 = IR2 = IR3 … OR IT = Ea / RT

Kirchhoff Ohm

DC CALCULATIONS

5Ù

10Ù

15Ù

30V

1A

1A

1A

1A

R1

R2

R3

25



25

Ea = ER1 + ER2 + ER3 + …

Calculating Ea for a Series Circuit

OR Ea = IT x RT

Kirchhoff Ohm

DC CALCULATIONS

5Ù

10Ù

15Ù

30V

1A

5V

10V

15V

1A

1A

1A

1A

R1

R2

R3

26



26

IT = IR1 = IR2 = IR3 = …

Ea = ER1 + ER2 + ER3 + …

IT = Ea / RT

Ea = IT x RT

Current

Is

Common

Voltage

Is

Divided

Total Resistance is always Higher or Larger Than Largest Resistance

DC CALCULATIONS

27



27

Power: The rate of Doing Work, measured in Watts

DC CALCULATIONS

P = I x E

P = E2 x R

P = I2 x R

PT = IT x Ea

PT = Ea2 x RT

PT = IT2 x RT

PT = PR1+ PR2+ PR3+…

We’ll use these

formulas the most.

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28

P = I x E P = IT x Ea PT = PR1+ PR2+ PR3

Power Calculations

DC CALCULATIONS

5W5Ù

10Ù

15Ù

30V

5V

10V

15V

30W

10W

15W

1A

1A

1A

1A

R1

R2

R3

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29

DC CALCULATIONS

Total Current: IT = Ea / RT

Given:Ea=30V

R1=5ÙR2=10ÙR3=15ÙER1=5V

RT = R1+R2+R3

RT = 5Ù+10Ù+15Ù

RT = 30Ù

IT = Ea / RT

IT = 30V / 30Ù

IT = 1A OR

I = E / R

IR1

= ER1

/ R1IR1 = 5V / 5Ù

IR1 = 1ACurrent is common

IT = IR1

IT = 1A

R1

R2

R3

ER1

30



30

DC CALCULATIONS

Total Resistance: RT = Ea / IT

Given:Ea=165V

R1=?ÙR2=?ÙR3=?ÙIR1=15A

Current is common

IT = IR1

IT = 15A

RT = Ea / ITRT = 165V / 15A

RT = 11Ù

15A

11Ù

R1

R2

R3

IR1

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31

DC CALCULATIONS

R1

R2

R3

Find: RT, IT, ER1, ER2, ER3, PT, PR1, PR2, PR3

Given:

Ea=100VR1=20ÙR2=5ÙR3=25Ù

RT = R1+R2+R3

RT = 20Ù+5Ù+25ÙRT = 50Ù

IT = Ea / RT

IT = 100V / 50Ù

IT = 2AIT = IR1 = IR2 = IR3

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32

DC CALCULATIONSFind: RT, IT, ER1, ER2, ER3, PT, PR1, PR2, PR3

E = I x R

ER1 = IR1 x R1

ER2 = IR2 x R2

ER3 = IR3 x R3

ER1 = 2A x 20Ù ER1 = 40V

ER2 = 2A x 5Ù ER2 = 10V

ER3 = 2A x 25Ù ER3 = 50V

R1

R2

R3

Given:

Ea=100VR1=20ÙR2=5ÙR3=25Ù

RT = 50ÙIT = 2A

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33

DC CALCULATIONSFind: RT, IT, ER1, ER2, ER3, PT, PR1, PR2, PR3

P = I x E

PT = IT x Ea

PR1 = IR1 x ER1

PR2 = IR2 x ER2

PR3 = IR3 x ER3

PT = 2A x 100V PT = 200W

PR1 = 2A x 40V PR1 = 80W

PR2 = 2A x 10V PR2 = 20W

PR3 = 2A x 50V PR3 = 100W

R1

R2

R3

Given:

Ea=100VR1=20ÙR2=5ÙR3=25Ù

RT = 50Ù

IT = 2A

ER1 = 40V

ER2 = 10V

ER3 = 50VPT = 200W

PR1 = 80W

PR2 = 20W

PR3 = 100W

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34

DC CALCULATIONSR1 R2

R3

R4R5

IR1

Given:R1=2ÙR2=6Ù

R3=4ÙR4=10ÙR5=8ÙIR1=2A

Find: Ea

RT = R1+R2+R3+R4+R5

RT = 2Ù+6Ù+4Ù+10Ù+8ÙRT = 30Ù

Ea = IT x RTIT = IR1

IT = 2AEa = IT x RT

Ea = 2A x 30ΩEa = 60V

Ea = ER1+ER2+ER3+ER4+ER5

ER# = IR# x R#

IR# = IT

ER1 = 2A x 2Ù ER1 = 4VER2 = 2A x 6Ù ER2 = 12VER3 = 2A x 4Ù ER3 = 8VER4 = 2A x 10Ù ER4 = 20V

ER5 = 2A x 8Ù ER5 = 16VEa = 4V+12V+8V+20V+16VEa = 60V

OR

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35

DC CALCULATIONS

Practice:

GIVEN:

Ea =ER1 =

ER2 =

ER3 =

RT =R1 =

R2 =

R3

=

IT =

IR1 =

IR2 =

IR3 =PT =

PR1 =

PR2 =

PR3 =

ANSWERS:

Ea =ER1 =

ER2 =

ER3 =

RT =R1 =

R2 =

R3

=

IT =

IR1 =

IR2 =

IR3 =PT =

PR1 =

PR2 =

PR3 =

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DC CA CU ATIONS



36

DC CALCULATIONSPractice:GIVEN:

Ea =ER1 =

ER2 =

ER3 =

RT =

R1 =

R2 =

R3 =IT =

IR1 =

IR2 =

IR3 =PT =

PR1 =

PR2 =

PR3 =

ANSWERS:

Ea =ER1 =

ER2 =

ER3 =

RT =

R1 =

R2 =

R3 =IT =

IR1 =

IR2 =

IR3 =PT =

PR1 =

PR2 =

PR3 =

R1 R2

R3

37

DC CALCULATIONS



37

Polarity of Voltage Drops

DC CALCULATIONS

- +

+

+ +

-

--

Polarity of components is referenced to negative side of the battery.

38

DC CALCULATIONS



38

Circuit Reference Point: Ground

DC CALCULATIONS

Voltage drops are referenced to circuit ground.

39

DC CALCULATIONS



Voltages with respect to ground:

DC CALCULATIONS

TP TP

TP

TPTP

40

DC CALCULATIONS



Voltages with Non-ground References:

DC CALCULATIONS

TP

TP TP

TP

TP

Voltage between TP B & D = +14V

41

DC CALCULATIONS



Voltages with Non-ground References:

DC CALCULATIONS

TP

TP TP

TP

TP

Voltage between TP B & D = +14V

VBD =+14V

42

DC CALCULATIONS



Multiple Voltage Sources

DC CALCULATIONS

Series-aiding

43

DC CALCULATIONS



DC CALCULATIONS


Series-opposing

44

DC CALCULATIONS



DC CALCULATIONS


Complex

45TRANSITION



What’s next ?

Parallel Circuits

TRANSITION

46

DC CALCULATIONS



Parallel Circuit Review:

Remember Ohm’s and Kirchhoff’s Laws

DC CALCULATIONS

Voltage in a parallel circuit is common.

90V 90V 90V 90V

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DC CALCULATIONS



DC CALCULATIONS

Current in a parallel circuit is divided.

6A 3A2A

5A

1A

6A 5A

Parallel Circuit Review:

Remember Ohm’s and Kirchhoff’s Laws

48

DC CALCULATIONS



Parallel Circuits: Multiple current paths (loops)

DC CALCULATIONS

Branch currents are inversely proportional to branch resistances.Branch currents are independent:Gain or loss of a branch resistance doesn’t effect other branches.

49

DC CALCULATIONS



Parallel Circuits: Current in, Current out

DC CALCULATIONS

Current entering node considered positive polarity.Current exiting node considered negative polarity.

Label

With theCorrect

Polarity

50

DC CALCULATIONS



Calculating Total Resistance for a Parallel Circuit

DC CALCULATIONS

321

111

1

R R R

RT

++

=21

21

R R

R R R

T

+=

N

R R

N

T =OR OR

Why?

α ρ

l=Remember the resistance formula:

Resistance in parallel effects the cross-sectional area.

51

DC CALCULATIONS



Parallel Circuit Resistance

2nd 6 1 0 EE 3 1/X + 2 0 EE 3 1/X = 1/X

321

111

1

R R R

RT

++

=

DC CALCULATIONS

10kÙ 20kÙ

RT = 6.67kÙ

ReciprocalFormula

52

DC CALCULATIONS



DC CALCULATIONS


321

111

1

R R R

RT

++

=

10kÙ 20kÙ

RT

= 4kÙ

ReciprocalFormula

10kÙ

2nd 6 1 0 EE 3 1/X + 2 0 EE 3 1/X = 1/X1 0 EE 3 1/X+

53

DC CALCULATIONS



DC CALCULATIONS


10kÙ 20kÙ

21

21

R R

R R R

T

+

=

ProductOver

Sum

2nd 6 1 0 EE 3 + 2 0 EE 3 =1 0 EE 3 2 0 EE 3x ÷( () )

RT

= 6.67kÙ



55

DC CALCULATIONS



Like Value

Formula

N

R R

N

T =

DC CALCULATIONS


10kÙ 10kÙ

2nd 6 =1 0 EE 3 2÷

RT = 5kÙ

Let’s check this using the reciprocal or product over sum formulas.

56

DC CALCULATIONS



Like Value

Formula

N

R R

N

T =

DC CALCULATIONS


10kÙ 10kÙ 10kÙ

2nd 6 =1 0 EE 3 3÷

RT = 3.33kÙ

Let’s check this using the reciprocal or product over sum formulas.

57

DC CALCULATIONS



DC CALCULATIONSCalculating Total Current for a Parallel Circuit

IT

= IR1

+ IR2

+ IR3

+ … OR IT

= Ea / RT

6A 3A2A

5A

1A

6A 5A

10Ù 15Ù 6Ù18V

58

DC CALCULATIONS



DC CALCULATIONSCalculating Ea for a Parallel Circuit

6A 3A2A

5A

1A

6A 5A

10Ù 15Ù 6Ù18V

Ea = ER1

= ER2

= ER3

= … OR Ea = IT

x RT

59

DC CALCULATIONS



IT = IR1 + IR2 + IR3 + …

Ea = ER1 = ER2 = ER3 = …

IT = Ea / RT

Ea = IT x RT

Current

Is

Divided

Voltage

Is

Common

Total Resistance is always Lower or Smaller Than Smallest Resistance

DC CALCULATIONS

40V

40V40V40V

6A

3A2A1A

60

DC CALCULATIONS



Power: The rate of Doing Work, measured in Watts

DC CALCULATIONS

P = I x E

P = E2 x R

P = I2 x R

PT = IT x Ea

PT = Ea2

x RT

PT = IT2 x RT

PT = PR1+ PR2+ PR3+…

We’ll use these

formulas the most.

61

DC CALCULATIONS



P = I x E P = IT x Ea PT = PR1+ PR2+ PR3

Power Calculations

DC CALCULATIONS

40V40V40V40V

6A

3A2A1A

240W

120W80W40W

62

DC CALCULATIONS



DC CALCULATIONSTotal Current: IT = Ea / RT

Given:Ea=60V

R1=10ÙR2=15Ù

RT = 6Ù

IT = Ea / RT

IT = 60V / 6ÙIT = 10A

OR

IT = IR1+ IR2+ IR3+…

Voltage is common

IR1 = ER1 / R1

IR2 = ER2 / R2

IR1 = 60V / 10Ù

IR1 = 6A

IR2 = 60V / 15ÙIR2 = 4A

321

T

R1

R1

R1

1R

++

=

151

101

1RT

+

=

Current is divided

IT = 6A+4AIT = 10A

63

DC CALCULATIONS



DC CALCULATIONSTotal Resistance: RT = Ea / IT

Given:Ea=60V

R1=10ÙR2=15ÙR3=6Ù

Voltage is common

IT = IR1+ IR2+ IR3+…

IR1 = ER1 / R1

IR2 = ER2 / R2

IR3 = ER3 / R3IR1 = 60V / 10Ù IR1 = 6A

IR2 = 60V / 15Ù IR2 = 4A

IR3 = 60V / 6Ù IR3 = 10A

IT = 6A+4A+10A IT = 20A

321

T

R1

R1

R1

1R

++

=

61

151

101

1RT

++

=

RT = 3Ù

RT = Ea / ITRT = 60V / 20A

RT = 3Ω

OR

64

DC CALCULATIONS



DC CALCULATIONSFind: RT, IT, IR1, IR2, IR3, PT, PR1, PR2, PR3

Given:Ea=100VR1=10kÙR2=15kÙR3=12kÙ

100V

21

21T RR

RRR

+=

15k10k15kx10kR T

+=

25k

150kR T =

Re = 6kÙ

12k6k

12kx6kR T

+=

18k72kR T =

RT = 4kÙ

65

DC CALCULATIONS




RT = 4kÙ

IT = 25mA

Voltage is common

IT = Ea / RT IT = 100V / 4kÙ IT = 25mA

IR1

= ER1

/ R1

IR1

= 100V / 10kÙ IR1

= 10mA

IR2 = ER2 / R2 IR2 = 100V / 15kÙ IR2 = 6.67mA

IR3 = ER3 / R3 IR3 = 100V / 12kÙ IR3 = 8.33mA

IT = IR1 + IR2 + IR3

IT = 10mA + 6.67mA + 8.33mA IT = 25mA

Given:Ea=100VR1=10kÙ

R2=15kÙR3=12kÙ

RT = 4kÙ100V

66

DC CALCULATIONS




P = I x E

PT = IT x Ea

PT = PR1+ PR2+ PR3

PR1 = IR1 x ER1

PR2 = IR2 x ER2

PR3

= IR3

x ER3

PT = 25mA x 100V PT = 2.5W

PR1 = 10mA x 100V PR1 = 1000mW

PR2 = 6.67mA x 100V PR2 = 667mWPR3 = 8.33mA x 100V PR3 = 833mW

PT

= 1000mW + 667mW + 833mW

PT = 2500mW or 2.5W

RT = 4kÙ

IT = 25mAIR1 = 10mA

IR2 = 6.67mA

IR3 = 8.33mA

PT = 2.5WPR1 = 1000mW

PR2 = 667mW

PR3 = 833mW

Given:Ea=100VR1=10kÙ

R2=15kÙR3=12kÙ

100V

67

DC CALCULATIONS



DC CALCULATIONS

Given:R1=90kÙR2=45kÙ

R3=30kÙIR1=2mA

Find: Ea

ER#

= IR#

x R#ER1 = 2mA x 90kÙ ER1 = 180V

Ea = ER1= ER2= ER3=…Ea = 180V

2mA

68

DC CALCULATIONS




Ea =ER1 =

ER2 =

ER3 =

RT =R1 =

R2 =

R3 =

IT =

IR1 =

IR2 =

IR3 =PT =

PR1 =

PR2 =

PR3 =

ANSWERS:

Ea =ER1 =

ER2 =

ER3 =

RT =R1 =

R2 =

R3 =

IT =

IR1 =

IR2 =

IR3 =PT =

PR1 =

PR2 =

PR3 =

69

DC CALCULATIONS




Ea =ER1 =

ER2 =

ER3 =

RT =R1 =

R2 =

R3

=

IT =

IR1 =

IR2 =

IR3 =PT =

PR1 =

PR2 =

PR3 =

ANSWERS:

Ea =ER1 =

ER2 =

ER3 =

RT =R1 =

R2 =

R3

=

IT =

IR1 =

IR2 =

IR3 =PT =

PR1 =

PR2 =

PR3 =

70

DC CALCULATIONS



Polarity of Voltage DropsDC CALCULATIONS

-

+++

+

---

Polarity of components is referenced to negative side of the battery.

ER1 ER2 ER3

71

DC CALCULATIONS



Current Divider

DC CALCULATIONS

A A A

TP 1 TP 2 TP 3

72

DC CALCULATIONS




DC CALCULATIONS

Voltage sources must be of equal value

Provides increase in current capacity

73

TRANSITION



TRANSITION

That was easy - Let’s kick itup a notch !

Series-ParallelCircuits

74

DC CALCULATIONS



Series-Parallel Circuit Calculations:

• Identification of a Series-parallel

circuit

• Calculate Equivalent Resistance ofParallel Components (R

e)

• Calculate RT

• Calculate IT

• Calculate Individual Branch Currents

• Calculate ERS

• Subtract ERS from Ea to obtain ERe

DC CALCULATIONS

75

DC CALCULATIONS



Series-Parallel Circuit Review

DC CALCULATIONS

Voltage:

Series portion:

Parallel portion:

Current:

Series portion:

Parallel portion:

Let’s do a quick simplification of this circuit.

76

DC CALCULATIONS



Identification of a Series-Parallel Circuit

C C CU O S

32

32e1 RR

RRR

+=

Re2 = R1 + Re1

1 voltage source and 1 resistance

=Simplified Series-parallel circuit

Ea Ea

Ea

Re1

Re1

Re2 = RT

77

DC CALCULATIONS



Series-Parallel Calculations: Equivalent Resistance

43

43e

RR

RRR

+

=

43

e

R1R1

1R

+

=

OR

Re = 307.69Ù Re = 307.69Ù

78

DC CALCULATIONS




43

43e RR RRR

+=

43

e

R1

R1

1R

+=

OR Re = 307.69Ù

Re = 307.69Ù

Parallel Portion

79

DC CALCULATIONS




65

65e2

RR

RRR

+

=

65

e2

R1

R1

1R

+

=

OR

2

321

e1

R1

R1

R1

1R

++

=

N

RR N

e2 =

OR

80

DC CALCULATIONS




Parallel Portions

65

65e2 RR

RRR +=

65

e2

R1

R1

1R+

=

ORRe1 = 40Ù

Re2 = 60Ù321

e1

R1

R1

R1

1R

++

=

Re2 = 60Ù

N

RR N

e2 =

OR

Re2 = 60Ù

1

81

DC CALCULATIONS



Series-Parallel Calculations: Total Resistance (RT)

Parallel Portions

Re1 = 40Ù

321

e1

R1

R1

R1 1R

++=

N

RR N

e2 =

Re2 = 60Ù

1Basic Formula:

RT = RS + Re

RS = R4 = 60Ù

Calculate Re

RS Re1 Re2

RT = 60Ù + 40Ù + 60Ù RT = 160ÙCalculate RT

82

DC CALCULATIONS



Series-Parallel Calculations: Total Current (IT)

Parallel Portions

Re1

= 40Ù

Re2 = 60Ù

1

Basic Formula:

IT = Ea / RT

Calculate Re

RT = 160Ù

IT = 80V / 160Ù

IT = 500mA

Calculate RT

Calculate IT

83

DC CALCULATIONS



Series-Parallel Calculations: Branch Currents (IB#)

Parallel Portions

1

Before we can calculate branch currents we need to calculate the voltagedrops of the series resistances (RS) and the parallel resistances (Re).

84

DC CALCULATIONS



Series-Parallel Calculations: Series Voltage Drop (ERS)

Parallel Portions

Re1 = 40Ù

Re2 = 60Ù

1

Basic Formula:

ERS = IT x RS

Calculate Re

RT = 160Ù

IT = 500mA

Calculate RT

Calculate IT

Calculate ERS

ERS = 500mA x 60ÙERS = 30V

85

DC CALCULATIONS



Series-Parallel Calculations: Parallel Voltage Drops (ERe)

Parallel Portions

Re1 = 40Ù

Re2 = 60Ù

1Basic Formula:ERe = IT x Re

ERe = Ea – ERS

Calculate Re

RT = 160Ù

IT = 500mA

Calculate RT

Calculate IT

Calculate ERS

ERS = 30VCalculate ERe1 & ERe2

ERe1 = 500mA x 40Ù ERe1 = 20V

ERe2 = 500mA x 60Ù ERe2 = 30V

Now we can go backand calculate thebranch currents.

86

DC CALCULATIONS



Series-Parallel Calculations: Branch Currents (IB#)

Parallel Portions

Re1 = 40Ù

Re2 = 60Ù

1

Basic Formula:

IB# = ERe / R#

What we know.

RT = 160Ù

IT = 500mA

ERS = 30V

ERe1 = 20V

ERe2 = 30V

IB of Re1IB1 = 20V / 200Ù IB1 = 100mA

IB2 & IB3 = 20V / 100Ù IB2 & IB3 = 200mA

IB of Re2

IB5 & IB6 = 30V / 120ÙIB5 & IB6 = 250mA

87

DC CALCULATIONS



Series-Parallel Circuit: Voltage Loops

Looking at the voltage loops of a circuit can help determine if your calculations are correct.

Voltage drops of L1 and L3 = Voltage source (Ea)

ER2 + ER1 = Ea ER3 + ER1 = Ea 20V+30V = 50V

Voltage drop of L2 = Voltage source (R2)ER2 = ER3 20V = 20V

Circuit 1 Circuit 2

Voltage drops of L1 and L2 ? Voltage source (Ea)

ER6+ER4+ER3+ER2? Ea 4V+2V+3V+2V ? 10

ER6+ER5+ER1 ‚ Ea 4V+5V+2V ‚ 10

88

DC CALCULATIONS



Series-Parallel Circuit: Unknown Current Values

Looking at the current loops of a circuit can help determine unknown current values.IR2 = ?

IR2 = IT – IB2

IR2 = 750mA – 150mA

IR2 = 600mA

B1 B2

89

DC CALCULATIONS



Series-Parallel Circuit: Simplify & Find E, I, R, & P

90

DC CALCULATIONS




Ea Ea

Ea

Re1

Re1

Re2 = RT

?Ù

?Ù

Re1 =

RT =

91

DC CALCULATIONS



Re = 40KÙ

RT = 50kÙ

IT =

ERS =

ERe =

IR2 =

IR3 =

PT =


Ea

Ea Re1

+

-

+

++

+

+

-

--

-

-

- +

?A

?A

?A

?A?A

?V

?V ?V

?V

?P

?P

?P ?P

?V

92

DC CALCULATIONS




Re =

RT =

IT =

ER4 =

ER5 =

ERe =

IR1 =

IR2 & IR3 =

ER2 =

ER3 =

PT =

93

DC CALCULATIONS



Finding Unknown Values:

Find:IT =

Re =

ERe

=

IR3 =

IR2 =

R2 =

Givens:

Ea = 10V

ERS = 6V

R1 = 6kÙR3 = 8kÙ

94

DC CALCULATIONS



Finding Unknown Values:

Find:

ER1 =IR2 =

ER2 =

R2 =

IR3 =ERe =

R4 =

Re =Ea =

Givens:IT = 25mA

IR4 = 10mA

R1 = 200Ù

R3 = 1.5kÙPR2 = 625mW

95

DC CALCULATIONS



Series-Parallel Circuit: Do your own

For some brain teasers click here.

96

DC CALCULATIONS



Remember, series circuits makeUnloaded Voltage Dividers

97

DC CALCULATIONS



Voltage Dividers: Unloaded

Ground as a reference

98

DC CALCULATIONS



Voltage Dividers: Unloaded

Ground as a reference

30V

A

B

15V

10V

5V

C

D

15 Ù

10 Ù

5 Ù

A=GND

B=

C=

D=

A=

B=GND

C=D=

A=

B=

C=GND

D=

A=

B=

C=D=GND

99

DC CALCULATIONS



Series-parallel circuits can be usedto make Loaded Voltage Dividers

100

DC CALCULATIONS



Loaded Voltage Dividers

R130K

R230K

R315K

120VS1

Y

Unloaded

(S1 open)

RT =IT =

ER1 =

ER2 =ER3 =

Y =

Loaded

(S1 closed)

Re =RT =

IT =

ER1 =ER2 =

ER3 =

Y =

101

DC CALCULATIONS



Series-parallel circuit:Loaded Voltage Dividers

102

DC CALCULATIONS



Objective 5a

Given formulas, calculate values for aresistive DC circuits IAW the PCchecklist.

Appraisal

Assignments

103

PARAMETER CHANGES



Objective 5b

Given formulas, calculateparameter changes on a resistiveDC circuits IAW the PCchecklist. Meas: PC

104

PARAMETER CHANGES



Series Circuit

Increase Applied Voltage:

↔↑=↑

1

1

R

E I R

T

When resistance remains constant,current follows the change in voltage.

↔↑=↑

T

T

R

Ea I

?

105

PARAMETER CHANGES



Series Circuit

Decrease Applied Voltage:


↔

↓=↓

1

1

R

E I RT

↔

↓=↓

T

T

R

Ea I

?

106

PARAMETER CHANGES



Series Circuit

Add Resistance:

Voltage follows opposition

RT = R1+R2

Ea = ER1 +ER2

IT = RT

↑

↔=↓

T

T

R

Ea I

107

PARAMETER CHANGES



Series Circuit

Increase Resistance:


RT = R1+R2

IT RT

Ea = ER1 +ER2

↑

↔

=↓T

T

R

Ea

I

↓∴↑↑ T R

I E R22

↑

↑=↓

2

2

R

E I

R

T

↓∴↓↔ 11 RT E I R

↔

↓=↓

1

1

R

E I

R

T

?

108

Series Circuit

PARAMETER CHANGES



Series Circuit

Increase Resistance: 8

8

Voltage follows opposition 8↑↔

=↓T

T

R

Ea I

RT = R1+R2 8Ù

IT 0A RT 8ÙEa = ER1 0V +ER2 Ea

109

PARAMETER CHANGES



Series Circuit

Decrease Resistance:


RT = R1+R2

IT RT

Ea = ER1 +ER2

↑∴↓↓ T R

I E R22 ↓

↓=↑

2

2

R

E I

R

T

↑∴↑↔ 11 RT E I R

↔

↑=↑

1

1

R

E I

R

T

↓

↔

=↑T

T

R

Ea

I

?

110

Series Circuit

PARAMETER CHANGES



Series Circuit

Decrease Resistance: 0Ù

0ÙVoltage follows opposition

RT = R1+R2 0Ù

IT RT = 5ÙEa = ER1

↑∴↓↓ T R

I E R22 ↓

↓=↑

2

2

R

E I

R

T

↑∴↑↔ 11 RT E I R

↔

↑=↑

1

1

R

E I

R

T

↓

↔

=↑T

T

R

Ea

I

111

PARAMETER CHANGES



Where R decr

All others

Resistance

Where R incr

All others

Resistance

Source Voltage

Total CurrentTotal ResistanceVoltage DropsEa

Series Circuit Summary

112

P ll l Ci i

PARAMETER CHANGES



Parallel Circuit


↔↑=↑

2

2

2

R

E I

R

R


↔↑=↑

T

T

R

Ea I

↔↑=↑

1

1

1

R

E I

R

R

?

113

P ll l Ci it

PARAMETER CHANGES



Parallel Circuit


↔

↓=↓

2

2

2

R

E I

R

R


↔

↓=↓

T

T

R

Ea I

↔

↓=↓

1

1

1

R

E I

R

R

?

114

P ll l Ci it

PARAMETER CHANGES



Parallel Circuit

Adding Branch Resistance:

↓

↔=↑

T

T

R

Ea I

321

T

R

1

R

1

R

11

R++

=

21

T

R1

R1

1R

+

=

RT ITIR1

IR2

↔

↔=↔

1

1

1

R

E I

R

R

↔↔=↔

2

2

2

R

E I

R

R

Increase in IT is due to added branch

Any increase in IT goes to added branch

115

P ll l Ci it

PARAMETER CHANGES



Parallel Circuit

Increase Branch Resistance:

?

321

T

R

1

R

1

R

11

R++

=

↔

↔=↔

1

11

R

E I R R

↔

↔=↔

2

2

2

R

E I

R

R

RT ITIR1

IR2

IR3

↑

↔=↓

T

T

R

Ea I

↑

↔=↓

3

3

3

R

E I

R

R

Decrease in IT is due to increase in R3

Any decrease in IT is from R3 branch

116

Parallel Circuit

PARAMETER CHANGES



Parallel Circuit

Increase Branch Resistance: 8

8Ù

321

T

R1

R1

R1

1R

++

=

21

T

R1

R1

1R

+

=

RT ITIR1

IR2

IR3 0A

↔

↔=↔

1

11

R

E I R R

↔

↔=↔

2

2

2

R

E I

R

R

↑

↔=↓

T

T

R

Ea I

↑

↔=↓

3

3

3

R

E I

R

R

Decrease in IT is due to increase in R3

Any decrease in IT is from R3 branch

117

Parallel Circuit

PARAMETER CHANGES



Parallel Circuit

Decrease Branch Resistance:

?

321

T

R

1

R

1

R

11

R++

=

↔

↔=↔

1

11

R

E I R R

↔

↔=↔

2

2

2

R

E I

R

R

RT ITIR1

IR2

IR3

Increase in IT is due to decreased in R3

Any increase in IT is from R3 branch

↓

↔=↑

T

T

R

Ea I

↓↔=↑

3

3

3

R

E I

R

R

118

Parallel Circuit

PARAMETER CHANGES



Parallel Circuit

Decrease Branch Resistance: 0Ù

321

T

R

1

R

1

R

11

R++

=

Increase in IT is due to decreased in R3

Any increase in IT is from R3 branch

Voltage decrease due to max. current

RT ITIR1 0A

IR2 0A

IR3 Max.

Ea = 0V

0Ù

↓

↓=↑

T

T

R

Ea I

↔

↓=↓

1

11

R

E I R R

↔

↓=↓

2

2

2

R

E I

R

R

↓↓=↑

3

3

3

R

E I

R

R

119

PARAMETER CHANGESParallel Circuit Summary



Effected

Others

Effected

Others

Branch

Effected

OthersBranch or

Removed

OthersRemove a Branch

Added

OthersAdd a Branch

Source Voltage

Total CurrentBranch CurrentTotal ResistanceEa

Parallel Circuit Summary

+

-

0Ù 0Ù Max. Max.0A

0V

8Ùor 0A

120

Series Parallel Circuit

PARAMETER CHANGES



Series-Parallel Circuit


↔

↑=↑

S

RS

T

R

E I


↔

↑=↑

T

T

R

Ea I

?

↔

↑=↑

e R

E I

Re

Re

121


PARAMETER CHANGES






↔

↓=↓

S

RS

T

R

E I

↔

↓=↓

T

T

R

Ea I

↔

↓=↓

e R

E I

Re

Re

?

122


PARAMETER CHANGES




Add Series Resistance:

Voltage follows opposition (R4)

↑

↔=↓

T

T R

Ea I

R4

?

RT = R1+R4+Re

Ea = ER1+ER4+ERe

ITER1

ERe

↔

↓=↓

1

1

R

E I

R

T

↔

↓=↓

e

T

R

E I

Re

Changes effect entire circuit

123


PARAMETER CHANGES




Add Parallel Resistance:

R1

R2 R3

Ea

2Ù

10Ù 15Ù60V

R4

?

RT = R1+Re

ITER1

ERe

↓

↔=↑

T

T

R

Ea I

↔

↑=↑

1

1

R

E I

R

T

↓↓=↑

e

T

R E I Re



124


PARAMETER CHANGES




Increase Series Resistance:


RT = R1 +Re

ITER1

ERe

↑

↔=↓

T

T

R

Ea I

?

↑

↑=↓

1

1

R

E I

R

T

↔↓=↓

e

T

R

E I ReChanges effect entire circuit

125


PARAMETER CHANGES




Increase Parallel Resistance:


RT = R1+Re

ITER1

ERe

↑

↔=↓

T

T

R

Ea I

↑

↑=↓e

T

R

E I

Re

↔

↓=↓

1

1

R

E I

R

T ?


126


PARAMETER CHANGES



Increase Series Resistance: 8


↑

↔=↓

T

T

R

Ea I

RT = R1 +Re

RT 8Ù

IT 0AER1 = Ea

ERe = 0V

↔

↓=↓

e

T

R

E I

Re

↑

↑=↓

1

1

R

E I

R

T

Changes effect entire circuit8Ù

127

Series-Parallel CircuitPARAMETER CHANGES



Increase Parallel Resistance: 8

↑

↔=↓

T

T

R

Ea I RT = R1+Re

ITER1

ERe↔

↓=↓

1

1

R

E I

R

T

↑

↑=↓

e

T

R

E I

Re


8Ù

128


PARAMETER CHANGES




Decrease Series Resistance:


RT = R1 +Re

ITER1

ERe

↓

↔=↑

T

T

R

Ea I

?

↓

↓=↑

1

1

R

E I

R

T

↔

↑=↑

e

T

R

E I

Re


129


PARAMETER CHANGES




Decrease Parallel Resistance:


RT = R1+Re

ITER1

ERe

↓

↓=↑

e

T

R

E I

Re

↔

↑=↑

1

1

R

E I

R

T

↓

↔=↑

T

T

R

Ea I

?


130

Series-Parallel CircuitÙ

PARAMETER CHANGES



Decrease Series Resistance: 0Ù


RT = R1 +Re

RT = Re

IT

ER1 = 0V

ERe

= Ea

↓

↓=↑

1

1

R

E I

R

T

↔

↑=↑

e

T

R

E I

Re

↓

↔=↑

T

T

R

Ea I

0ÙChanges effect entire circuit

131

Series-Parallel CircuitÙ

PARAMETER CHANGES



Decrease Parallel Resistance: 0Ù


↓

↓=↑

e

T

R

E I

Re

↔

↑=↑

1

1

R

E I

R

T

↓

↔=↑

T

T

R

Ea I

RT = R1 +Re

RT = R1

IT

ER1 = Ea

ERe = 0V

0Ù


132

PARAMETER CHANGESSeries-Parallel Summary



Branch Ù

Series Ù

Branch Ù

Series Ù

Add a Branch

Added

Others

Add Seriesresistance

Source VoltageIReIRS (IT)Re

RS

RT

EReERSEa

8Ù

8Ù

0Ù

0Ù

+

+

0A 0A0V

0AEffected

Others

0V

0V

0Ù IRS = IRe

IT

0ÙERS = Ea RT = RS IRe = IRS

133

Voltage Dividers: Unloaded D

PARAMETER CHANGES



g

Same as series circuit.

_____V

A

B

_____V

_____V

_____V

C

D

_____Ù

_____Ù

_____Ù

A=GND

B=

C=

D=

A=

B=GND

C=D=

A=

B=

C=GND

D=

A=

B=

C=D=GND

134


PARAMETER CHANGES




R1 ___Ù

R2 ___Ù

R3 ___Ù

____VS1

Y

Unloaded

(S1 open)

RT =IT =

ER1 =

ER2 =ER3 =

Y =

Loaded

(S1 closed)

Re =RT =

IT =

ER1 =ER2 =

ER3 =

Y =

Same as series and series-parallel circuits.

135

PARAMETER CHANGES



If you need morepractice, click here

and try these!

136

PARAMETER CHANGES



Objective 5b

Given formulas, calculateparameter changes on a resistive

DC circuits IAW the PCchecklist. Meas: PC

Appraisal

137

35.APPRAISAL30 k



RT ______IT ______

ER1 ______ER2 ______

ER3 ______

PT ______40 k

10 k

160 VDC

138

36.APPRAISAL20 k



RT ______IT ______

ER1 ______ER2 ______

ER3 ______

PT ______20 k

10 k

200 VDC

139

APPRAISAL37.

R



R1 R2 R3Ea

60 kÙ 40 kÙ 24 kÙ

48 VDC

RT

______

IT ______

IR1 ______

IR2 ______

IR3 ______

PT ______

140

APPRAISAL38.R



R1 R2 R3Ea

12 kÙ 20 kÙ 30 kÙ

60 VDC

RT

______

IT ______

IR1 ______

IR2 ______

IR3 ______

PT ______

141

APPRAISALR1

39.



R2 R3Ea

24 kÙ

60 kÙ 40 kÙ

240 VDC

RT ______

IT ______

IR1 ______

IR3 ______

ER1 ______

PT ______

Re ______

ER2

______

ER3 ______

IR2 ______

142

APPRAISALR1

40.



R2 R3Ea

8 kÙ

30 kÙ 20 kÙ

60 VDC

RT ______

IT ______

IR1 ______

IR3 ______

ER1 ______

PT ______

Re ______

ER2

______

ER3 ______

IR2 ______

143

Let’sCheck



Checkouranswers

144

35.APPRAISAL30 k



RT ______IT ______

ER1 ______ER2 ______

ER3 ______

PT ______40 k

10 k

160 VDC

80 k

2 mA

60 VDC

20 VDC

80 VDC

320 mW

145

36.APPRAISAL20 k



RT ______IT ______

ER1 ______ER2 ______

ER3 ______

PT ______20 k

10 k

200 VDC

IT ______50 k

80 VDC

40 VDC

80 VDC

800 mW

4 mA

146

APPRAISAL37.

R 12 k



R1 R2 R3Ea

60 kÙ 40 kÙ 24 kÙ

48 VDC

RT

______

IT ______

IR1 ______

IR2 ______

IR3 ______

PT ______

12 k

192 mW

4 mA

.8 mA

1.2 mA2 mA

147

APPRAISAL38.R 6 k



R1 R2 R3Ea

12 kÙ 20 kÙ 30 kÙ

60 VDC

RT

______

IT ______

IR1 ______

IR2 ______

IR3 ______

PT ______

6 k

600 mW

10 mA

5 mA

3 mA2 mA

148

APPRAISALR1

39.24 k



R2 R3Ea

24 kÙ

60 kÙ 40 kÙ

240 VDC

RT ______

IT ______

IR1 ______

IR3 ______

ER1 ______

PT ______

Re ______

ER2

______

ER3 ______

IR2 ______

24 k

48 k

5 mA

5 mA120 VDC

120 VDC

120 VDC

2 mA

3 mA1.2 W

149

APPRAISALR1

40.12 k



R2 R3Ea

8 kÙ

30 kÙ 20 kÙ

60 VDC

RT ______

IT ______

IR1 ______

IR3 ______

ER1 ______

PT ______

Re ______

ER2

______

ER3 ______

IR2 ______

12 k

20 k

3 mA

3 mA24 VDC

36 VDC

36 VDC

1.2 mA

1.8 mA180 mW

150

TRANSITION



You have now covered one-half of a

semester of college level electronics.It has not been easy, but it takes a lotof hard work to build a successful

career! Coming up next --Circuit Parameter

Changes

Assignments

151

PARAMETER CHANGES



41. If Ea is increased, IT _____________.

152

PARAMETER CHANGES



42. If R1 is increased, IT _____________.

153

PARAMETER CHANGES



43. If R2

is removed from the circuit and continuity maintained,IT _____________.

154

PARAMETER CHANGES



44. If R3 branch is removed from the circuit, RT ___________.

155

PARAMETER CHANGES



45. If R3 is increased in value, IT ___________.

156

PARAMETER CHANGES



46. If another branch is added to the circuit, IT ___________.

157

PARAMETER CHANGES



47. If Ea is increased, IT _____________.

158

PARAMETER CHANGES



48. If the value of R3 is increased, IT _____________.

159

PARAMETER CHANGES



49. When the voltage divider is loaded, RT _____________.

160

PARAMETER CHANGES



Let’s check your Answers

Appraisal

161

PARAMETER CHANGES



41. If Ea is increased, IT _____________.increases

162

PARAMETER CHANGES



42. If R1 is increased, IT ______________.decreases

163

PARAMETER CHANGES



43. If R2 is removed from the circuit and continuity maintained,IT ___________.increases

164

PARAMETER CHANGES



44. If R3 branch is removed from the circuit, RT ___________.increases

165

PARAMETER CHANGES



45. If R3 is increased in value, IT ___________.decreases

166

PARAMETER CHANGES



46. If another branch is added to the circuit, IT ___________.increases

167

PARAMETER CHANGES



47. If Ea is increased, IT _____________.increases

168

PARAMETER CHANGES



48. If the value of R3 is increased, IT _____________.decreases

169

PARAMETER CHANGES



49. When the voltage divider is loaded, RT_____________.decreases

170

CONCLUSION



Summary:

Series Circuits• Current• Voltage• Resistance• Power•

Voltage Dividers• Parameter Changes

171

CONCLUSION



Summary:

Parallel Circuits• Current• Voltage• Resistance• Power•

Voltage Dividers• Parameter Changes

172

CONCLUSION



Summary:

Series-Parallel Circuits• Current• Voltage• Resistance• Power

• Voltage Dividers• Parameter Changes

173

CONCLUSION



Remotivation:

With the knowledge ofapplicable laws and formulas,

we can better understandcircuit operating parameters.This will prepare us for later

lessons in troubleshooting.

174

CONCLUSION



Assignment:

Complete the workbookassignments for Objectives 5a.

Review Unit 5 text as needed tocomplete the assignment.

Review Unit 5 text on Calculating

parameter changes.

175

CONCLUSION



Assignment:

Complete the workbookassignments for Objectives 5b.

Review Unit 5 text as needed tocomplete the assignment.(Assignments may be deferred

to the end of the day)

176

CONCLUSION



Closure:

This concludes this lesson onDC Calculations

177

Series-Parallel Circuit: Try these on for size.DC CALCULATIONS



To return click here.

178

DC CALCULATIONSSeries-Parallel Circuit: Try these on for size.



What does the ammeter read at each test point?To return click here.

179




Find R3


180




Find Ea


181




Find R3 & Ea

The end. Click here to return.

182

PARAMETER CHANGESSeries Circuit:

R1



R1

R2

R3

Ea

______Ù

______Ù

______Ù

_______V


183

PARAMETER CHANGESParallel Circuit:

R3



R1 R2

R3

R4

Ea

_____V_____Ù _____Ù

_____Ù

_____Ù


184

PARAMETER CHANGESSeries-Parallel Circuit:

R R



Ea

______V

R1

R2

R3

R4

R6

R5

______

______

______

______

______

______

Documents

AET 3a DC Calculations