We know that professionals in the World of Electrical must increasingly train themselves, look for more knowledge and know-how to analyze the various types of electrical circuits, using different methods, this is an important point! Thinking about helping professionals, students, and lovers of electricity to better understand the methods and concepts for the analysis of electrical circuits, we made this article explaining in detail one of Kirchhoff’s laws, specifically Kirchhoff’s first law.

Kirchhoff’s Laws were created and developed by the German physicist Gustav Robert Kirchhoff, hence the name Kirchhoff’s laws. Kirchhoff’s laws are generally used in more complex electrical circuits, such as circuits with more than one source and resistors, whether in series or in parallel. We have that Kirchhoff’s laws have fundamental concepts for the analysis of electrical circuits, from the simplest circuits to the most complex circuits.

To understand Kirchhoff’s laws it is important to define what “nodes” are in electrical circuits, which are basically points where three or more conductors are interconnected, that is, where the current will separate at a certain point in the circuit. We find “knots” in the most diverse types of circuits, for example, in parallel circuits or in parallel series circuits, but not in series circuits.

It is also important to understand what meshes are in electrical circuits, which are defined as closed paths of electrical conductors, which, unlike the “knot”, we have in all circuits, as it is a closed path for the circulation of electrical current. Disregarding the association of resistors, the image below shows a parallel series circuit that has three loops, respectively indicated.

## Kirchhoff First Law – Definitions

The first law of Kirchhoff, also known as the law of “knots” or Kirchhoff’s law for currents (LKC), states that the sum of the currents that enter a “node” is equal to the sum of the currents that leave this same “node” ”, As a consequence of the conservation of the electric charge, where the algebraic sum of the charges existing in a closed system remains constant.

As an example, in the figure below we represent a section of a circuit covered by currents i1, i2, i3 and i4, which facilitates the understanding of this concept.

The arrows indicated in the image above determine the direction of the electric current, that is, they determine whether the currents are entering or leaving the “node”. Thus, applying the first law of Kirchhoff we have currents I1 and I2 entering the “node”, while currents I3 and I4 are leaving this same “node”. Therefore, the sum of currents I1 and I2 is equal to the sum of currents I3 and I4.

For Kirchhoff’s first law we can also state that the sum of the currents in a “node” is equal to zero, that is, it does not accumulate a charge.

Before performing the analysis in this way, it is necessary to define a signal convention, that is, the currents that are entering a “node” must be considered positive, while the currents that leave this same “node” must be considered negative, as we can see in the image below.

## Kirchhoff’s First Law – Application

Now that we know the concept of Kirchhoff’s first law, let’s apply it to a certain circuit, to find the value of all currents contained in the electrical circuit in the image below:

The circuit below is relatively simple, containing a single “node”, which we will call “Node A”. Thus, when we analyze the currents that enter and leave this same “node”, we see that there is only one current entering (i1), which is also the total current of this circuit and we also observe that two currents are leaving this same “node”, or that is, currents i2 and i3.

In this example above, we have defined the value of current i1 and also the value of current i3, so we need to find the value of current i2, which we can easily define, just by applying the kirchhoff law to the currents, without the need to apply others methods, such as ohm laws or current divider.

Applying the law of “we” we have that the current i1 is equal to the sum of the currents i2 and i3, therefore we have that the current i2 is equal to the difference between the currents i1 and i3. Substituting the values in the expression we have that i2 is equal to 0.34 minus 0.17 A. Thus we have that the current i2 is equal to 0.17 A.

To make sure it is right, we can also apply the other definition given for the first kirchhoff law, that the sum of the currents i1, i2 and i3 must be equal to zero.

Applying the kirchhoff law to the currents, we have 0.34 A plus -0.17 plus -0.17 must be equal to zero, remembering that currents i2 and i3 are negative because they are coming out of the node, as highlighted above . When performing the calculations we have that the sum of the currents in this node is equal to zero, as shown in the image below.

To make it even easier to understand what the first kirchhoff law is and how to apply it, we have made available a video from the World of Electrical explaining step by step and with all the details about the kirchhoff law for currents.

## Kirchhoff’s first law – Final considerations

All concepts referring to the first Kirchhoff law are valid for any electrical circuits that contain electrical “node (s)”, therefore, when dimensioning or determining the electrical current at specific points in the electrical circuit and the information is not the same there is certainly something wrong with the circuit analysis.

We finish one more article, if you have any questions, feel free to read other articles related to the topic and leave in the comments your question (s) or curiosities that we will answer.