Kirchhoff’s Current Law (KCL)

1. Definition

Kirchhoff’s first law, or Kirchhoff’s junction rule, states that, for any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node.

1.1. Visualization

KCL

  • The current entering any junction is equal to the current leaving that junction : [i2 + i3 = i1 + i4]
  • The sum of currents entering and leaving a junction, with currents entering counted as positive and leaving as negative, always equals zero.

1.2. In Formula Form

Formula of KCL

or Equivalently : Sum of currents in = Sum of currents out

Where:

  • I = Current is measured in amperes (A).
  • n = the total number of branches with currents flowing towards or away from the node.

1.3. Example

If 4A and 2A flow into a junction, and one branch has 3A flowing out, the other branch must have: I out = 4+2−3 =3A

So the total is zero:

4A + 2A - 3A -3A = 0A

2. Usage

  • Calculating unknown currents in a circuit.
  • Analyzing complex networks of resistors, capacitors, or other components.
  • Circuit troubleshooting to detect wiring or component faults.
  • Ensuring correct current distribution in power systems.

3. Limitations

  • KCL assumes steady state conditions (currents are constant over time), for rapidly changing fields, displacement currents must be considered.

  • Assumes ideal conductors with no charge storage at junctions.

  • In very high-frequency AC circuits, stray capacitance or inductance can cause small deviations.

4. Video Explanation

video coming soon