Kirchhoff's Current Law (KCL)
Kirchhoff's current law: the sum of currents entering a node equals the sum leaving.
Essential for circuit analysis and node equations.
The Formula
Kirchhoff's current law states that the total current flowing into any junction (node) in a circuit equals the total current flowing out.
This is based on the conservation of electric charge — charge cannot build up at a node.
Equivalently: the algebraic sum of all currents at a node is zero.
Variables
| Symbol | Meaning |
|---|---|
| ΣI_in | Sum of all currents entering the node (Amperes, A) |
| ΣI_out | Sum of all currents leaving the node (Amperes, A) |
Example 1
Three wires meet at a junction. Wire A carries 5 A into the junction, wire B carries 3 A into the junction. What current flows through wire C?
ΣI_in = ΣI_out
I_A + I_B = I_C
5 A + 3 A = I_C
I_C = 8 A (flowing out of the junction)
Example 2
At a circuit node, 10 A flows in from the source. Three branches leave: I₁ = 4 A, I₂ = 3.5 A. Find I₃.
ΣI_in = ΣI_out
10 = I₁ + I₂ + I₃
10 = 4 + 3.5 + I₃
I₃ = 10 - 7.5
I₃ = 2.5 A
When to Use It
Use Kirchhoff's current law when you need to:
- Find unknown currents at junctions in complex circuits
- Verify that your circuit analysis is correct
- Set up node equations for systematic circuit solving
- Analyse parallel branches where current divides
KCL works for both DC and AC circuits.
In AC circuits, currents are represented as phasors (complex numbers) to account for phase differences.