Kirchhoff's Current Law (KCL)

KCL states that the total current entering any node in a circuit equals the total current leaving it. This follows directly from conservation of charge — current can't pile up at a junction, it has to go somewhere. It sounds obvious when you say it plainly, but it's the formal rule that lets you write equations for complex circuits and solve for unknown currents.

The Law

Sum of currents into a node = Sum of currents out of a node

∑I_in = ∑I_out

Or equivalently (taking entering currents as positive, leaving as negative):
∑I = 0

Simple Example

         I1 = 5A
         ↓
    ─────●─────→ I3 = ?
         ↑
         I2 = 3A

KCL: I1 + I2 = I3
     5A + 3A = 8A

I3 = 8A

More Branches

         I1 = 10A
         ↓
    ─────●─────→ I3 = 4A
    ↑         ↓
    I4         I2

KCL: I1 = I2 + I3 + I4

If I2 = 3A and I3 = 4A:
I4 = I1 - I2 - I3 = 10 - 3 - 4 = 3A

Using KCL to Analyse Circuits

KCL is used at each node in nodal analysis — a systematic method for finding voltages throughout a circuit. The process:

1. Pick a reference node (ground)
2. Assign a voltage variable to every other node
3. At each node, write a KCL equation: currents leaving = 0 (where each current is expressed using Ohm's Law as (V_node - V_adjacent) / R)
4. Solve the system of equations

Example — single node V1, with V_supply = 12V and GND = 0V:

        12V
         |
        [R1=4Ω]
         |
    ─────●─────[R3=6Ω]─── 0V
         |
        [R2=3Ω]
         |
         0V

KCL at V1 (currents leaving the node):
(V1 - 12) / 4 + V1 / 3 + V1 / 6 = 0

Multiply through by 12:
3(V1 - 12) + 4(V1) + 2(V1) = 0
3V1 - 36 + 4V1 + 2V1 = 0
9V1 = 36
V1 = 4V

KCL and Parallel Components

KCL directly explains why parallel resistors add current — each branch draws its own current from the same node, and the total current from the supply is their sum. If you have three parallel branches drawing 1A, 2A, and 3A respectively, KCL says the supply must deliver 6A to that node.