1. Chp 2.2 Kirchoff’s Current Law
Engineering 43
Chp 2.2 Kirchoff’s Current Law
Bruce Mayer, PE
RegisteredElectrical & Mechanical Engineer

2. “CHARGE CANNOT BE CREATED NOR DESTROYED”
Charge Conservation
One Of The Fundamental Conservation Principles In Electrical Engineering:
“CHARGE CANNOT BE CREATED NOR DESTROYED”

3. 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., R4 Branch)

4. Charge Conservation at Nodes
A Node Connects Several Components But It DOES NOT HOLD Any Charge
By The Conservation of Charge Principle We Have Kirchoff’s Current Law:
NODE
TOTAL CURRENT FLOWING INTO THE NODE MUST BE EQUAL TO THE TOTAL CURRENT OUT OF THE NODE

5. Kirchoff’s Current Law (KCL)
Practical Restatement of KCL
Sum Of Currents Flowing Into A Node Is Equal To Sum Of Currents Flowing Out Of The Node
Usual KCL Sign Convention
POSITIVE Direction → INTO Node
+5A
NEGATIVE Direction → OUT of Node
-5A

6. KCL Algebra Two Equivalent KCL Statements Example: Use Sign Convention
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

7. Supernodes
A Generalized Node is any part of a circuit where there is No Accumulation of Charge
Suggests We Can Make SUPERNODES By Aggregating Nodes
Good for when we are not interested in All CURRENTS => in this case do find i4

8. Supernodes cont.
INTERPRETATION: Sum Of Currents Entering Nodes 2&3 is Zero
VISUALIZATION: We Can Enclose Nodes 2&3 Inside A Surface That Is Viewed As A GENERALIZED Node (Or SUPERnode)
Supernode is Indicated as the GREEN Surface on the Diagram; Write KCL Directly
Same as Previous

9. Which Way are Charges Flowing in Branch a-b?
KCL Problem Solving b
KCL Can Be Used To Find A Missing Current
(Currents INto Node-a) = 0 ? = X I A 5 c a A 3 d
Which Way are Charges Flowing in Branch a-b?
Notation Practice
Iab = 2A
Icb = −3A
Ibd = 4A
Ibe = ?
Nodes = a,b,c,e,d
Branches = a-b, c-b, d-b, e-b b a c d e 2A -3 A 4A I be
= ?
Ibe = -5A

10. UnTangling
A node is a point of connection of two or more circuit elements, and Region of Constant Potential
It may be stretched-out or compressed or Twisted or Turned for visual purposes…But it is still a node
Equivalent Circuits

11. KCL Alternate Sign Convention
KCL Works Equally Well When Currents OUT Are Defined as Positive
Write the +OUT KCL 1 2 3
The 5eqns are NOT linearly independent 4 5
Note That Node-5 Eqn is Redundant; It Is The SUM of The Other 4

12. Example Find Currents Use +OUT 1 2 3 4
TOPOLOGY => geometric form that is Invariant under bending, stretching, or twisting – in circuit case it the nature of the interconnections only, the form of the branches do NOT affect KCL
KCL Depends Only On The Interconnection.
The Type Of Component Is Irrelevant
KCL Depends Only On The Topology Of The Circuit

13. Example Find Currents Use +OUT 1 2 3 4
The Presence of the Dependent Source Does NOT Affect KCL
KCL Depends Only On The Topology
Again, Node-4 Eqn is (Linearly) Dependent on the Other 3

14. Example  Supernode
Supernodes Can Eliminate Redundancies and Speed Analysis
Shaded Region = Supernode, S
Use +OUT
 of Currents Leaving Node-S = 0 S
The Current i5 Becomes Internal To The Node And It Is Not Needed!!!

15. KCL Convention: In = Out
An Equivalent Algebraic Statement of Charge Conservation

16. Examples: In = Out

17. Find Ix

18. Find Unknown Currents The Plan Mark All Known Currents
Find Nodes Where All But One Current is Known
Given
I1 = 2 mA
I2 = 3 mA (2I2 = 6 mA)
I3 = 6 mA 3 1 1 2 3 2

19.  Find Ix At Node 2 At Node 1 Verification at Nodes b & c 2 b 1
I1 is Opposite the Assumed Direction
At Node 1 c
Verification at Nodes b & c 

20. KCL & Direction Summary Demo
For Ix use ΣIout = 0
Note Directions for IDE and IEF and IEG
For IEF use ΣIout = 0
-8A B D 6A E F

21. WhiteBoard Work
Let’s Work This Problem
Find