Kirchhoff's Current Law (KCL)
Learning Objectives
- Understand Kirchhoff's Current Law and its physical basis
- Apply KCL to solve for unknown currents at circuit nodes
- Master sign conventions for current direction
- Analyze complex circuits with multiple junctions
Statement of KCL
Kirchhoff's Current Law states that the algebraic sum of all currents entering and leaving any node (junction) in an electrical circuit is zero at any instant.
Σ I_in = Σ I_out
or equivalently
Σ I = 0 (with proper signs)
⚠️ Key Point
Current cannot accumulate at a node. Whatever current enters must leave!
KCL Visualization
At this node: I₁ + I₂ = I₃ + I₄
Sign Convention
| Convention | Current Direction | Sign |
|---|---|---|
| Entering Node | → | + Positive |
| Leaving Node | → | − Negative |
| Assume Direction | Calculate | Check sign |
💡 Pro Tip
Always assume a direction first. If your answer is negative, the actual current flows opposite to your assumption!
Example Problem
Find I₃ and I₄
Given: I₁ = 5A (entering), I₂ = 3A (entering), I₃ = ? (leaving)
Show Solution
// Apply KCL at the node
Σ I_in = Σ I_out
I₁ + I₂ = I₃ + I₄
5A + 3A = I₃ + I₄
8A = I₃ + I₄
// Need another equation - often from another node!
// In real circuits, KCL applies to ALL nodes
// Example: If we know I₃ = 2A
I₄ = 8A - I₃ = 8A - 2A = 6AAnswer: I₃ + I₄ = 8A (they must sum to 8A)
Summary
- KCL: Σ currents entering = Σ currents leaving
- Conservation: Charge cannot accumulate at a node
- Sign Convention: Entering = positive, Leaving = negative
- Assumption: Negative answer means opposite direction