Kirchhoff's Current Law (KCL)

Previous Topics Covered

• Resistors and Capacitors
• Ohm's Law
• Series Resistors
• Kirchhoff's Laws

Introducing Kirchhoff's Current Law (KCL)

• Basic Concept: Current entering a node is equal to current leaving the node.
• Node (Junction): Point where components connect.

Basic Example with Series Resistors

• Current through resistors:
  • Charge does not collect anywhere.
  • Current entering a resistor equals current leaving.
  • Labeling Currents:
    • i1: Current entering first resistor.
    • i2: Current leaving = i1.
  • Conservation of Charge: i1 = i2.

Adding Another Resistor to the Node

• Complex Node Configuration:
  • Additional Resistor: Current i3 through another branch.
  • New Current Equation: i1 = i2 + i3
  • General Rule: Sum of currents entering = Sum of currents leaving.

Mathematical Expression of KCL

• Summation Notation: Σ i in = Σ i out

Generalizing KCL

Example with Multiple Wires

• Node with Multiple Wires:
  • Several currents entering the node.
  • Current Definition Arrows: Orient all currents towards the node.
• Example Calculation:
  • Currents: 1A, 1A, 1A, and i.
  • Equation: 1 + 1 + 1 + i = 0 → i = -3A
  • Interpretation: -3A flowing in = 3A flowing out.

Alternative Representation

• Defining Current Directions: All arrows pointing out of the node.
  • Result: Sum of currents pointing out equals zero.

Applying KCL in Circuit Analysis

• Defining Currents: Can be defined either way (flowing in or out).
• Conclusion: Choice of representation can vary; all adhere to KCL principles.

Practical Applications

• Use in Circuit Analysis: Will be frequently used in analyzing and solving circuit problems.