Introduction to Kirchoff's Law & Network Analysis

The following paper was presented at CEOCOR – Brussels, Belgium – 19th – 22nd May 2014.

The paper was authored by Ken Lax, and presented by Ken at the conference.

DISCLAIMER: All information, references to Standards and / or criteria correct at time of paper.


Kirchhoff’s Laws are the foundation for many network analysis techniques. 

Cathodic Protection systems are essentially d.c. electrical networks and the distribution of current follows these laws.

Most CP applications will not require any knowledge of these laws but sooner or later every CP practitioner will need to apply and understand them.

By the end of this presentation you will be able to apply Kirchhoff’s Laws and resolve the simultaneous equations using matrix algebra.

An understanding of Kirchhoff’s Laws, and the ability to apply them, will enable you to understand:

  • I-V equivalent circuits (source transformations)
  • Superposition applications
  • Mesh networks
  • LaPlace transformations (not covered in this presentation)
  • Node Voltage Analysis (NVA)
  • Thevenin and Norton Theorems (not covered in this presentation)

We will only be considering d.c. circuits in this introduction.


  • Circuit definitions (branch, junction, node)
  • Definition of Kirchhoff’s Current Law (KCL)
  • Definition of Kirchhoff’s Voltage Law (KVL)
  • Some warm-up exercises with Ohms Law
  • Simple rules for applying KCL and KVL to produce independent simultaneous equations
  • KCL and KVL exercises with increasing complexity
  • Simple way to solve simultaneous equations using Excel
  • Solving simultaneous equations using augmented or inverted matrix operations



Kirchoff's Current Law (KCL) and Kirchoff's Voltage Law (KVL) will add to the existing knowledge of CP engineers and designers and help to explain some of those mysterious situations that cannot be explained just by Ohms Law.


Passive sign convention:  Current enters a passive device at its POSITIVE terminal.

Current:  Measurement of the electric charge passing through a given point within a certain amount of time.  Units are Coulombs per second (amperes).

Voltage:  measures the amount of energy required to move a given amount of charge as it passes through a circuit.  Units are Joules per Coulomb (Volts).

Junction:  Any place where two or more wires come together.

Branch:  Anything that connects two junctions

Node:  A point in the circuit


Also known as the JUNCTION rule.  Conservation laws tell us that electrons must behave in a certain way when connecting devices to make a circuit.   The electron behaviour governs the voltage and current around the loops and at the nodes.  So Kirchhoff’s Laws apply whatever devices are used in the circuit since it is a law of conservation of charge (KCL) or energy (KVL).

The sum of the currents entering any junction must equal the sum of the currents leaving that junction.



Also known as the LOOP rule. 

The sum of the potential differences across all elements around any loop must be zero.