Introductory Electrical Engineering With Math Explained in Accessible Language

19Kirchhoff’s Laws: Circuit Analysis

19.1 Introduction

In this chapter, we will examine the Kirchhoff’s laws, created by the German physicist Gustav Robert Kirchhoff (1824–1887) and how these laws can be used to find unknowns in electric circuits.

19.2 Kirchhoff's Laws

To use the Kirchhoff’s laws, it is necessary to understand two concepts: nodes and meshes.

19.2.1 Nodes or Junctions

It is a point where two or more wires connect.

Figure 19.1 shows a circuit with two nodes, A and B, where all components connect.

Figure 19.1 Two nodes, A and B.

In electronic diagrams, nodes are identified by a dot or small circle drawn where two or more lines connect. This indicates that the lines are electrically connected.

19.2.2 Mesh

It is any closed path in which current circulates.

Figure 19.2 shows dashed lines that represent the three meshes possible for the circuit: M1, M2, and M3.

Figure 19.2 Three meshes, M1, M2, and M3.

19.2.3 Kirchhoff's First Law

Kirchhoff's first law, also known as the Kirchhoff’s current law (KCL), postulates that at any junction in a circuit, the sum of the currents arriving at the junction is equal to the sum of the currents leaving the same junction.

KIRCHHOFF'S FIRST LAW (KCL)

• I_in are the currents entering the node.
• I_out are the currents ...