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?
Faraday’s Law
Newton’s Law
Einstein’s Law
Kirchhoff’s Law
Answer: Option D.
2. What is the Basic Principle on Which KCL is based?
At a node, no charge accumulation can take place.
At a node, charge accumulation is very much possible.
Charge accumulation may or may not be possible at any nodes.
A node can easily store energy.
Answer: Option A.
3. To Which of these is Kirchhoff’s Current Rule Applicable?
Electronic Devices
Circuit loops and meshes
Electrical Devices
Junction and nodes
Answer: Option D.
Conclusion
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 is Kirchhoff's First Law?
Kirchhoff's First Law, also known as Kirchhoff's Current Law (KCL) or the Junction Rule, states that the algebraic sum of all electric currents meeting at any junction in an electrical circuit is zero. In simpler terms, the total current entering a junction must be equal to the total current leaving that same junction. This law applies to any node in a circuit.
2. What fundamental principle is Kirchhoff's First Law based on, and what does it imply?
Kirchhoff's First Law is based on the fundamental law of conservation of electric charge. This principle implies that charge cannot be created or destroyed, nor can it accumulate at a junction in a circuit. Therefore, the rate at which charge flows into a junction must be precisely equal to the rate at which it flows out, ensuring a steady flow of current.
3. How is Kirchhoff's First Law expressed mathematically?
Mathematically, Kirchhoff's First Law is expressed as ΣI = 0, where 'ΣI' represents the algebraic sum of all currents at a junction. To apply this, a sign convention is used:
- Currents entering the junction are considered positive (+).
- Currents leaving the junction are considered negative (-).
4. How do you apply the sign convention for Kirchhoff's First Law in a circuit diagram?
To apply the sign convention correctly in a circuit analysis as per the CBSE curriculum for 2025-26, follow these steps:
- First, identify a junction (a point where three or more conductors meet).
- Next, assign a direction to the current in each branch connected to the junction. This can be an assumption if the direction is unknown.
- Then, apply the convention: treat all currents flowing towards the junction as positive and all currents flowing away from the junction as negative.
- Finally, write the equation by summing these currents and setting the total to zero. If the solution for an unknown current yields a negative value, it simply means the actual current flows in the opposite direction to your initial assumption.
5. What is the main difference between Kirchhoff's First Law (KCL) and Second Law (KVL)?
The main differences between Kirchhoff's two laws are:
- Focus: The First Law (KCL) deals with current at a junction, while the Second Law (KVL) deals with voltage in a closed loop.
- Conservation Principle: KCL is based on the conservation of charge, whereas KVL is based on the conservation of energy.
- Application: KCL is applied to analyse nodes or junctions in a circuit, while KVL is applied to analyse closed loops or meshes.
6. What are some practical applications of Kirchhoff's First Law?
The primary application of Kirchhoff's First Law is in the analysis of complex electrical circuits where Ohm's law alone is insufficient. It is fundamental for:
- Calculating unknown currents in various branches of a circuit.
- Serving as the basis for Nodal Analysis, a powerful technique to determine the voltage at different nodes in a circuit.
- Analysing parallel circuits to understand how current divides among different paths.
7. Are there any limitations to Kirchhoff's First Law? When might it not apply?
Yes, while Kirchhoff's First Law is widely applicable, it has limitations. The law assumes that signals and currents propagate instantaneously, which is a valid approximation for DC and low-frequency AC circuits. However, this assumption breaks down in high-frequency AC circuits. In such cases, electromagnetic wave effects become significant, and the distributed capacitance in the circuit can cause charge to accumulate, meaning the net current at a junction may not be zero at all instants.
