Circuit-Elements - Engineering Electrical Circuits - Lecture Slides, Slides of Electrical Circuit Analysis

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Circuit-Elements,

KCL & KVL,

Ohm’s Law

Circuit Elements

• Passive Elements
  • R, C, L

 Active, Independent Sources

• (a) ≡ V-source
• (b) ≡ Battery
  • Basically a V-Source with a small series resistance
• (c) ≡ I-Source

Dependent Source Exercises

• Determine Power Supplied by Sources

40 [ V ]

P = ( 10 × 4 [ V ])(− 2 [ A ])=− 80 [ W ] P =( − 10 [ V ])( 4 × 4 [ A ]) =− 160 [ W ]

A

B A

B

 Take VOLTAGE Polarity as Reference: P = VAB∙IAB

 Take CURRENT Direction as Reference : P = VAB∙IAB

16 [ A ]

Power Example

• Determine Power Absorbed Or Supplied By

Each Element

( )( ) [ ]

( )( ) [ ]

( )( ) [ ]

P (^ V )(^ A )^ [ W^ ]

P A A W

P V A W

P V A W

P V A W

DS 36 4 144

1 4 2 8

28 2 56

24 2 48

( 12 )( 4 ) 48 [ ]

36

3

2

1

= − = −

=− Ω× =−

= =

= =

= =

 Note That

• Power-Supplied = Power-Absorbed
  • In both Cases = 152W

Node, Loops, Branches

• NODE: Point Where Two,

Or More, Elements Are

Joined (e.g., Big Node 1)

 LOOP: A Closed Path

That Never Goes Twice

Over A Node (e.g., The Blue Line)

• The red path is NOT a loop (2x on Node 1)

 BRANCH: a Component Connected

Between Two Nodes (e.g., R 4 Branch)

Charge Conservation at Nodes

• A Node Connects Several Components But It

DOES NOT HOLD Any Charge

• By The Conservation of Charge Principle We

Have K irchoff’s C urrent L aw:

TOTAL CURRENT

FLOWING INTO THE NODE

MUST BE EQUAL TO THE

TOTAL CURRENT OUT OF

THE NODE

NODE

KCL Algebra

• Two Equivalent KCL Statements
  • Algebraic Sum Of Currents (Flowing) OUT Of A Node Is ZERO
  • Algebraic Sum Of Currents Flowing INTO to A Node Is ZERO
• Example: Use Sign

Convention ( )

( ) ( ) ( ) ( ) ( ) (^0)

i t i t i t i t i t

INto Nodei t

KCL Problem Solving

• KCL Can Be Used To

Find A Missing Current

• ∑(Currents INto Node-a) = 0

5 A

3 A

IX =? a

b

c

d I (^) X + 5 A + ( − 3 A ) = 0 or IX = − 2 A Charges FlowingWhich Way are in Branch a-b?

b a

c

d

2A e

-3A (^) 4A Ibe =?

• I (^) ab = 2A
• I (^) cb = −3A
• I (^) bd = 4A
• I (^) be =?
  • Nodes = a,b,c,e,d
  • Branches = a-b, c-b, d-b, e-b − I (^) be + 2 A + ( − 3 A ) − 4 A = 0 or Ibe =− 5 A

 Notation Practice

KCL Alternate Sign Convention

• KCL Works Equally Well When Currents OUT

Are Defined as Positive

• Write the +OUT KCL 1 2 3 4 5
• Note That Node-5 Eqn is Redundant ; It Is The SUM of The Other 4

Example

• Find Currents
  • Use +OUT

1 2 3 4

• KCL Depends Only On The Interconnection.  The Type Of Component Is Irrelevant  KCL Depends Only On The Topology Of The Circuit

KCL Convention: In = Out

• An Equivalent Algebraic Statement of Charge

Conservation

∑ Currents INTO Node =^ ∑CurrentsOUT of Node

I 1 (^) + 50 mA = (^0) I (^) T = 10 mA + 40 mA + 20 mA

Find I 1 Find IT

Examples: In = Out

I mA

I mA mA

6

10 4 1

1

= −

I (^) 1 = I 2 + 3 mA 12 mA = I 1 + 4 mA

Find I 1 Find I 1 and I 2 10 mA = I 1 + 4 mA

I I mA mA mA mA

I mA mA mA 3 8 3 5

12 4 8 2 1

1 = − = − =

= − =

KCL & Direction Summary Demo

A

B

C

D E

F

G

I (^) DE = 10 A I A EG =^4

I EF 5 A I x

Ix = OnBD currentflowsfrom__to __ IEF = OnEF currentflowsfrom__to __

3 A

I (^) X + ( − 5 A )+( 3 A )+ 10 A = 0

-8A B D

I (^) EF + 4 A − 10 A = 0

6A E F

 For I (^) x use ΣI (^) out = 0  Note Directions for I (^) DE and I (^) EF and I (^) EG

 For I (^) EF use ΣI (^) out = 0

Energy Conservation

• One Of The Fundamental Conservation Laws

In Electrical Engineering is K irchoff’s V oltage

L aw:

THE CONSERVATION OF

ENERGY PRINCIPLE:

“ENERGY CANNOT BE

CREATED NOR DESTROYED”