Kirchhoff's Current Law (KCL)

ΣI = I₁ + I₂ + I₃ + ... = 0

Quick answer

This calculator solves ΣI = I₁ + I₂ + I₃ + ... = 0 for ΣI. With Branch Currents 2 A, 4.4 A, 9.4 A, the result is 15.8.

Calculator

Result
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Formula

ΣI = I₁ + I₂ + I₃ + ... = 0

Description

Kirchhoff's Current Law states that the algebraic sum of all currents entering and leaving any node (junction) in a circuit must equal zero. This is a consequence of conservation of charge: charge cannot accumulate at a node. Currents flowing into the node are conventionally positive and currents flowing out are negative (or vice versa, as long as the convention is consistent). KCL is the basis of nodal analysis, the most widely used systematic method for solving circuit equations, and is essential for understanding current distribution in parallel networks.

Variables

  • I₁, I₂, I₃... — Currents at the node (A), with sign convention: positive for currents entering, negative for currents leaving

Practical Notes

Enter currents entering the node as positive and currents leaving as negative. The sum should be zero for a valid node. KCL applies to any closed boundary, not just single nodes — it can be applied to a supernode enclosing multiple components. In AC circuits, KCL applies to the phasor currents including both magnitude and phase.

Symbols and units

Symbol Meaning Default unit Accepted units
values Branch Currents A pA, nA, µA, mA, A, kA

Step by step

  1. 1. What you know: Branch Currents 2 A, 4.4 A, 9.4 A
  2. 2. The relation: ΣI = I₁ + I₂ + I₃ + ... = 0
  3. 3. Substitute: values = 2 A, 4.4 A, 9.4 A
  4. 4. Result: ΣI = 15.8

Totals for common combinations

Components Values Total
2 2 A + 2 A 4 A
2 2 A + 4.4 A 6.4 A
2 2 A + 20 A 22 A
3 2 A + 2 A + 2 A 6 A
3 2 A + 4.4 A + 9.4 A 15.8 A
4 2 A + 2 A + 2 A + 2 A 8 A
4 2 A + 4.4 A + 9.4 A + 20 A 35.8 A
5 2 A + 2 A + 2 A + 2 A + 2 A 10 A

Worked examples

Minimum range

Given: Branch Currents 2 A, 4.4 A, 9.4 A

Result: ΣI = 15.8

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Frequently asked questions

How do you calculate Kirchhoff's Current Law (KCL)?

Use ΣI = I₁ + I₂ + I₃ + ... = 0. With Branch Currents 2 A, 4.4 A, 9.4 A, ΣI works out to 15.8.

What is the formula for Kirchhoff's Current Law (KCL)?

The formula is ΣI = I₁ + I₂ + I₃ + ... = 0. Kirchhoff's Current Law states that the algebraic sum of all currents entering and leaving any node (junction) in a circuit must equal zero.

Related Concepts

All Basic Electronics formulas →
Ohm's Law Electrical Power Voltage Divider Current Divider Thévenin Equivalent Norton Equivalent Temperature Coefficient of Resistance Kirchhoff's Current Law (KCL)

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