Kirchhoff’s Laws are fundamental in the analysis of electrical and electronic circuits. They describe the behavior of linear circuits accurately, and work well with approximations in other types of systems as well, making them extremely useful (“Electrical Principles”, 2013). Further, they are more popular and widely used than Maxwell’s equations, from which they can be derived. This is because Maxwell’s equations are very complex and involve brute Mathematics to solve even simple circuits, while the Kirchhoff’s laws are relatively much easier to use in most cases.
There are two laws which were given by Kirchhoff:
1) Kirchhoff’s Current law (KCL)
2) Kirchhoff’s Current law (KCL)
This paper deals with KCl: what it means; its applications; examples; and limitations.
KCL: Kirchhoff’s current law states that the algebraic sum of currents at any node (junction) must be zero (“Kirchhoff’s laws”, 2013). It is important to understand the term node: it means the meeting point of one or more branches of an electrical circuit, as shown in Figure 1, where the point A is a node.
Figure 1: A is the node
It is also important to note that while calculating the algebraic sum, a sign convention must be followed based on direction. For instance, if all currents entering a junction are considered positive, then all currents leaving a junction are negative. The other way around can also be used, but it is essential to be consistent and follow only one throughout a particular analysis.
Uses: The main use of KCL is in the derivation of currents in series and parallel circuits. Using KCL, a generalized rule has been deduced, which has made analysis very simple. The following explains the same with examples:
a) Series: When a circuit or part of a circuit is connected in series as shown in Figure 2, it can be seen that all junctions have only two branches. In other words, in a limiting case, al points can be considered as a junction, where the current entering on one side must necessarily leave from the other, according to KCL. This gives an important result: The current through elements in a series network are equal.
Figure 2: A series network: all currents are same according to KCL
b) In a parallel circuit, as shown in Figure 3, the current drawn from the source must equal the sum of currents drawn by each device, according to KCL.
Figure 3: Parallel circuit: I = I1 + I2
Other uses: Ohm’s law can be derived and verified by the Kirchhoff’s laws. Further, a very important circuit analyzing technique called the nodal analysis is also a consequence of KCL. Using the nodal analysis, complex circuits including star and delta networks can be simplified (“Kirchhoff’s current and”, 2013). Finally, the concept of KCL is also used in many analogous non-electrical situations. For example, in traffic flow analysis, the flow is designed as a linear model and the algebraic sum of flows (currents) at any intersection (node) is considered as zero.
Limitations: Though Kirchhoff’s laws provide the most useful tools to analyze circuits, it is essential to understand where they can be applied, and where they cannot. Most importantly, KCL and KVL do not work well for complex non-linear systems. Also they only work with an approximation in cases of transient circuits. In other words, the main assumption that the elements are lumped masses needs to be satisfied for KVL and KCL to work well.
References
Electrical Principles. (2013). Retrieved October 11, 2013, from
http://www.ni.com/white-paper/14449/en/
Kirchhoff’s laws. (2013). Retrieved October 12, 2013, from http://denethor.wlu.ca/pc200/lectures/kirchbeam.pdf
Kirchhoff’s Current and Voltage Laws. (2013). Retrieved October 7, 2013, from http://hades.mech.northwestern.edu/index.php/Kirchhoff's_Current_and_Voltage_Laws
