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Kirchhoff's First Law

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Kirchhoff’s First Law Equation

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The fundamentals of Network Theory comprise Kirchhoff’s rules. These are the laws that are taught at the very beginning when someone starts studying Circuit Theory and its application. The first law of Kirchhoff quantifies the value and states the nature of current flowing through a circuit. It studies how the current is flowing through the mesh. On the other hand, the second law of Kirchhoff studies and quantifies the behaviour of voltage across a loop or circuit. It measures how the voltage is varying across the terminals in a circuit. Gustav Kirchhoff, a renowned German physicist was the first one to describe Kirchhoff’s rules for us back in 1845. 

Kirchhoff’s First Law Overview

Various names have been given for Kirchhoff’s first law such as Kirchhoff nodal rule, Kirchhoff’s junction rule, Kirchhoff’s point rule, KCL, or Kirchhoff’s current law. It is a direct application of the electric charge conservation principle. The law simply states that the sum of the currents flowing out of the junction is equal in value with the sum of currents flowing out of that junction. The junction can be any node present inside the circuit. KCL means that the total current flowing into the node and out of the node are always equal. 

Based on the outflow and inflow of electric current, analysis of all nodes in a circuit was carried out. Directions of current were presumed beforehand and current directions at any node were based on the presumption. The original direction of current in the circuit will be reflected in the outcome of the analysis. But it will only be possible if from node to node all the directions of current are consistent. Mathematically, Kirchhoff's first law states that the summation of all currents entering or leaving a note in a circuit having n number of branches is equal to zero. One might also have a good idea regarding Lenz’s law, ohm's law, and Wheatstone bridge concepts to learn about Kirchhoff’s laws.

Using KCL to Solve Circuits

To practically demonstrate the laws, we need to consider a few real-life examples and understand about its significance. To find the unknown parameters, it is extremely essential to understand the laws conceptually first. Firstly, let us consider a network or branches having presumed directions of current. The next one needs to determine a particular sign convention for the currents entering or leaving the node. For example, let us consider the currents entering the node to be positive while the current leaving the node should be negative. This convention should be considered throughout the problem. Considering this convention, if we apply Kirchhoff’s junction rule, then we will get the following equation: 

i1(t) + i2(t) – i3(t) = 0. Here we have considered the current i1 and i2 to enter the node and i3 is the current leaving the node. In totality, the current entering the node is equivalent to the current leaving the node. In many problems, an unknown current is given which is either entering or leaving a node with all the other current values given. One needs to find the unknown value. Here one can easily apply Kirchhoff’s current law to find out the value by framing the equation just like before.

Advantages of Kirchhoff’s Law

There are various advantages of using Kirchhoff’s laws due to which they form a major part of the basics regarding the circuit theory section. Firstly, unknown voltage and current calculation become far easier. There are plenty of complex circuits which are closed in a structure where circuit analysis is usually a bit tricky. But with Kirchhoff’s law first law the analysis and calculation of these complex circuits become manageable and easy. There are plenty of other advantages but these are the most important ones.

Solved Examples

  1. What are the Basic Laws for Analyzing Electrical Circuits?

  1. Faraday’s Law

  2. Newton’s Law

  3. Einstein’s Law

  4. Kirchhoff’s Law

Answer: Option d.

     2. What is the Basic Principle on Which KCL is based?

  1. At a node, no charge accumulation can take place.

  2. At a node, charge accumulation is very much possible.

  3. Charge accumulation may or may not be possible at any nodes.

  4. A node can easily store energy.

Answer: Option a. 

     3. To Which of these is Kirchhoff’s Current Rule Applicable?

  1. Electronic Devices

  2. Circuit loops and meshes

  3. Electrical Devices

  4. Junction and nodes

Answer: Option d.

FAQ (Frequently Asked Questions)

1. What are the Applications and Limitations of Kirchhoff’s Laws?

Answer: The Kirchhoff’s laws have plenty of applications but it also has many limitations and disadvantages. To start with, many complex circuits require detailed analysis. Kirchhoff’s laws help to simplify these circuits and calculate unknown currents and voltages more effectively. These laws can be used in the analysis of any electrical circuit practically. But there are pros and cons to everything. Similarly, Kirchhoff’s law also has various limitations and disadvantages. The major drawback of Kirchhoff’s law is that it assumes that the closed-loop has no magnetic field in it which is fluctuating. Induction of emf or any electric fields is possible in the circuit. This will eventually cause the current and voltage rule to fail. High-frequency circuits are also affected by KCL. Another issue is, only if the entire electric charge is constant inside the circuit, then KCL is valid and applicable.

2. What is Kirchhoff’s First Law?

Answer: The most probable question for any circuit theory beginner is ‘state Kirchhoff’s first law’. Kirchhoff’s first law which is also known as Kirchhoff’s current rule clearly states that zero amount of charge is lost within a node. Hence, the amount of charge entering the node or current incoming is equivalent in value to the amount of charge exiting the same node or current outgoing. When many branches of conductors meet at a particular node, then the total sum of charge or current around the node is zero. Generally, a sign convention is maintained throughout a circuit analysis. The current entering a particular node is considered as positive while the one leaving is considered as negative.