Kirchhoff's First Law

Dhristi JEE 2022-24

Kirchhoff’s First Law Equation

Are you someone who is finding it difficult to solve circuit problems in Physics? If yes, then maybe this is because of your understanding of Kirchhoff's law. To help you with this problem, Vedantu has brought for you an article dedicated to Kirchhoff's First Law. The entire topic has been covered holistically for you. First, let’s start by understanding Kirchhoff’s rules.

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 behavior 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 the 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 their 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: 

\[i_{1}(t) + i_{2}(t) - i_{3}(t) = 0\], 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 becomes 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 Analysing 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.


This concludes the topic of Kirchhoff's First Law. This law comes in very handy in solving circuits at various places. It is one of the many fundamental concepts in Physics. A thorough understanding of this along with Kirchhoff’s second law will make you an expert in solving circuit problems. It will also help you score excellent marks in various entrance exams such as JEE Mains, AIIMS, JIPMER, NEET, etc. 

Other Resources by Vedantu for Physics

Vedantu understands what a nightmare Physics can be for students. To take away this tension from you, Vedantu has brought to you an entire website dedicated to Physics. Here the various topics of Physics have been covered in great detail by Vedantu’s subject matter experts. You can access various topics of Physics on the official website of Vedantu and also on its mobile application.

These will help you in scoring excellent marks in the upcoming board exams as well as in the various national-level entrance exams. They ensure you secure a seat in the college that you desire. 

FAQs on Kirchhoff's First Law

1. What are the applications and limitations of Kirchhoff’s laws?

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 e.m.f 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?

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 meeting 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.

3. What is Kirchhoff’s second law?

Kirchhoff’s second law is also known as Kirchhoff’s voltage law. It is very widely used to solve circuits. In simple words, this law states that the summation of all voltage in a close loop in a circuit must be equal or zero. This is a simple application of the law of conservation of energy and charge conservation. You can read about Kirchhoff's Second Law in great detail on Vedantu’s website for free. Both Kirchhoff's first and second laws are widely used to solve considerations. 

4. What problems can be expected based on Kirchhoff's First Law?

In the Physics exam every year you can expect at least 2 questions based on Kirchhoff’s laws. Both these problems will require you to know Kirchhoff’s first law in detail. You can expect problems based on circuits for 2 or 3 marks. Also, theoretical problems based on the same can be expected. Also in entrance exams more complicated circuit-based problems are used, a proper understanding of this law can make your journey simpler. Thus it is recommended not to skip this topic and get a thorough understanding of it as it is used in high standards as well. 

5. What are the advantages of Kirchhoff's First Law?

Knowing Kirchhoff's First Law offers various advantages.

Some of these are as follows:

  • It makes calculations involving unknown voltage and current easier. 

  • One may come across circuits that are highly complex. In order to solve the problem, the knowledge of Kirchhoff's First Law becomes inevitable. Thus it makes complex circuits manageable.

  • It helps electrical engineers to solve advanced-level circuits that have direct applications in various electrical plants.

There are many other advantages of Kirchhoff's First Law. The above three are the most important ones.