Kirchhoff's Laws Study Notes for SSC JE & Other AE JE Exams

By Vishnu Pratap Singh|Updated : May 24th, 2022

Kirchhoff's Laws is one of the important topics in Circuit Theory. Apart from being essential for the subject, it also contains a good weightage in AE JE Exams.

Complete coverage of the Electrical Engineering AE JE Exam syllabus is an important aspect of any competitive examination, but before that, basic subjects and their concept must be covered thoroughly. For your convenience, we are providing you with the study notes on Kirchhoff's Laws for SSC JE, RRB JE, and other state-wise AE & JE exams.

Table of Content

Kirchhoff's Law

Kirchhoff’s current law (KCL):

KCL states that the algebraic sum of the currents entering a node or meeting at a point is zero.

→ It is based on law of conservation of charge.


               Figure 1

⇒I1 + I2 + (– I3) + I4 + (– I5) = 0

Incoming current consider as Positive

Outgoing current consider as Negative.

Kirchhoff’s voltage law(KVL):

It states that algebraic sum of all the voltages in a closed loop is zero.

It is based on the law of conservation of energy.


                 Figure 2

– Vs + IR1 + IR2 = O

Rise in potential = negative, Fall in potential = positive (or) vice-versa.

Mesh Analysis

Mesh is a loop which cannot contain any inner loop.

It is applicable only for the planner network and a planner network is that can be drawn in a plane with no branches crossing are another.

Mesh analysis

                           Figure 3

Loops → L1, L2, L3

Mesh → L1, L2


  • Identify the total number of meshes.
  • A sign the mesh current
  • Develop KVL equation for each mesh.
  • Solve equation to find the loop current.

Note: Number of equations required to solve the circuit with the help of mesh analysis are:



b = number of branches

N = number of nodes

Nodal Analysis


  • identify total number of nodes in the circuit.
  • Assign the voltage at each node and one of the nodes is taken as the reference node and the potential of reference node is equal to the ground potential.
  • Develop KCL equation for each non – reference node.
  • By solving KCL equation, find the node voltages.

 The total number of equations required to solve the network by using nodal analysis are:


Way of writing equation at a node:

Nodal Analysis

                                                Figure 4

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  • You can download the Kirchhoff's Laws Study Notes PDF prepared by experts at BYJU’S Exam Prep.

  • Kirchhoff's Laws Notes are important for SSC JE, RRB JE, and other state wise AE & JE exams.

  • The topic Introduction of Kirchhoff's Laws carries 1 to 4 marks weightage.

  • KCL and KVL are applicable to lumped network and not applicable for distributed network, also Kirchhoff's Laws are not valid for very high frequencies.

  • Kirchhoff's current law is also called as Kirchhoff's first law according to this law sum of all incoming and outgoing current at any node is equal to zero.

    KCL based on the law of conservation of charge.

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