Chp 2.2 Kirchoff’s Current Law Engineering 43 Chp 2.2 Kirchoff’s Current Law Bruce Mayer, PE RegisteredElectrical & Mechanical Engineer BMayer@ChabotCollege.edu

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

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)

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

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

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

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

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

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

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

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

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

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

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!!!

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

Examples: In = Out

Find Ix

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

 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 

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

WhiteBoard Work Let’s Work This Problem Find