ENGR-43_Lec-02-2b_KVL.ppt 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce...

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Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engineering 43

Chp 2.2Chp 2.2Kirchoff’s Kirchoff’s VoltageVoltage

LawLaw



Energy ConservationEnergy Conservation One Of The Fundamental Conservation

Laws In Electrical Engineering

THE CONSERVATION OF THE CONSERVATION OF ENERGY PRINCIPLE:ENERGY PRINCIPLE:

““ENERGY CANNOT BE ENERGY CANNOT BE CREATED NOR CREATED NOR DESTROYED”DESTROYED”



Kirchoff’s Voltage Law (KVL)Kirchoff’s Voltage Law (KVL) KVL Is A Conservation Of Energy

Principle• A Positive Charge Gains Energy As It

Moves To A Point With Higher Voltage And Releases Energy If It Moves To A Point With Lower Voltage

AV

BBV)( AB VVqW

q

abVa b

q

abqVW LOSES

cdVc d

q

cdqVW GAINS



"Gedanken" Experiment "Gedanken" Experiment If The Charge Comes

Back To The SameInitial Point, Then TheNet Energy Gain MustBe Zero (ConservativeNetwork)• Otherwise, With Repeated Loops The Charge

Could End Up With Infinite Energy, Or Supply An Infinite Amount Of Energy. Mathematically

AV

BBV

q

CV

ABV

BCV

CAV

0)( CABCAB VVVq



Kirchoff’s Voltage LawKirchoff’s Voltage Law

THE ALGEBRAIC SUM OF THE ALGEBRAIC SUM OF VOLTAGEVOLTAGE

DROPSDROPS AROUND ANY CLOSED AROUND ANY CLOSED LOOP MUST BE ZEROLOOP MUST BE ZERO

A B V

A B )( V

Note That a Voltage RISE is Equivalent to a NEGATIVE DROP



ExamplesExamples

0321 RRRs VVVV

VVR 181

VVR 122

VVR 203

Find VR3 Given• VR1 = 18V

• VR2 = 12V

A

Start & End @ A



KVL Problem SolvingKVL Problem Solving KVL Is Useful To Determine Voltages

• Find A Loop Including The Unknown Voltage– The Loop Does NOT Have To Be Physical

Example: VR1, VR3

Are KnownVR2, is UNknownDetermine Vbe

beV

0][3031

VVVV RbeR

Using the “Virtual”Loop Shown



Linear DependenceLinear Dependence Background: For KCL We Saw That Not All

Possible KCL Equations Are Independent• The Same Situation Arises When Using KVL

• The Third Equation Is The Sum Of The Other Two



Dependence QuantifiedDependence Quantified For a Given Circuit Define

• N Number of Nodes• B Number of Braches

Then• N-1 No. of Linearly Independent KCL Eqns• B-(N-1) No. of Linearly Independent KVL

Eqns– Example: For Previous Circuit We Have

N = 6, B = 7. Hence There Are Only Two Independent KVL Equations



Choose Loop WiselyChoose Loop Wisely Find Vae, Vec

• Try to Find TheSimplest Loop– Make Use of

Virtual Loops

1

2

3

12

3



Dependent SourcesDependent Sources Dependent

Sources are JustAnother VoltageDrop

1

2

1 2



ExamplesExamples

VVVVV

ac

ac

10064

VVVVV

bd

bd

6042

1

2

1

2

VVVVVV

ad

ad

2606812

VVVVVV

eb

eb

1001264

1 2

1

2



More ExamplesMore Examples Find Vbd

• First Find VR1

VVVV

VVVV

RRbd

RRR

1110

1010112

12

111

V V

Remember: ALWAYS Use The Passive Sign Convention With Resistors



Virtual Loop ExampleVirtual Loop Example Find

• Vx, Vab

• Power Dissipatedin the 2 kΩ Resistor

Need To Find A Closed Path With Only One Unknown Potential

VVVVVV

VVVV

X

X

X

404124

0412

VVVVVVV

VVV

ab

Xab

abX

844

0

2

2

1 2

1

2

mWkV

RVP k

k 824 22

22



Combo Example Combo Example Find Find VV11

NO LoopsWith Only1 Unknown• But This

is a SERIESCircuit– The Current thru the 10k & 5k Resistors is the SAME

→ V Across 5k is HALF that Across The 10k

+-

+-

k10 k5

xV

V25 4

xV

1V- Vx/2 +

][20

042

][25

VV

VVVV

X

XXX

][54

024

1

1

VVV

VVV

X

XX

1 2

1

2



WhiteBoard WorkWhiteBoard Work Let’s Work Problem

This Nice Little Problem

3 0 k

1 2 V2 V x

1 0 k

+

V x_

Find Vx & P30kΩ

ENGR-43_Lec-02-2b_KVL.ppt 1 Bruce Mayer, PE Engineering-43: Engineering Circuit Analysis Bruce...

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