Electric Circuits (Networks) Study Notes for GATE Electronics and Communication Exams

By Kajal Vats|Updated : August 17th, 2021

Best Books to Prepare and Study Notes for Electrical Circuits (Networks) for GATE Exam 2021: In this article, we will provide you with a list of books for GATE & ESE Preparation. These books are based on popularity and standard, they are easy to understand and covers all required topics for these exams.

Table of Content

Best Books you can refer to for the preparation of GATE 2021

Circuit Theory:- Analysis & Synthesis by Abhijit Chakrabarti, Edition:- 6

Highlights of the book:

  • Easy to understand
  • Best book for GATE and ESE preparation
  • All Concepts are covered from basic level
  • Worked examples are available in every chapter
  • learn the concepts easily with the help of theory and examples

Fundamentals of Electric Circuits by Charles K. Alexander, Matthew N. O. Sadiku

networks-2

  • This book is easier to understand than other books. It has balanced theory, work, practice, and extended examples. It is also a good to book to prepare for GATE, ESE, and other exams. It covers all topics required for these exams.

Network Analysis by Van Valkenburg

networks-3

  • This book provides comprehensive coverage of the topics, such as Thevenin's and Norton's theorems, the Nyquist criterion, the Routh Hurwitz criterion, the Gauss elimination method, and Fourier transforms. The exercises containing problems are provided at the end of every chapter. This book is easy to understand the concepts and also covers all important topics required for exams.

Basic Concepts of Electrical Circuits

  • Kirchhoff’s Voltage Law ( KVL): The sum of voltages around a closed-loop circuit is equal to zero.
  • Kirchhoff's Voltage Law (KVL) is Kirchhoff's second law that deals with the conservation of energy around a closed circuit path. This voltage law states that for a closed-loop series path the algebraic sum of all the voltages around any closed loop in a circuit is equal to zero.

  • Kirchhoff’s Current Law ( KCL): The algebraic sum of electrical current that merge in a common node of a circuit is zero.
  • Kirchhoff's Current Law (KCL) is Kirchhoff's first law that deals with the conservation of charge entering and leaving a junction. This idea by Kirchhoff is commonly known as the Conservation of Charge, as the current is conserved around the junction with no loss of current.

                                               ∑ IIN = ∑IOUT

  • NODAL ANALYSIS
    • The procedure for analysing a circuit with the node method is based on the following steps:
    • Clearly, label all circuit parameters and distinguish the unknown parameters from the known ones.
    • Identify all nodes of the circuit after that Select a node as the reference node also called the ground and assign to it a potential of 0 Volts. All other voltages in the circuit are measured with respect to the reference node.
    • Label the voltages at all other nodes & Assign and label polarities.
    • Apply KCL to each node and express the branch currents in terms of the node voltages.
    • Solve the resulting simultaneous equations for the node voltages.
    • Now that the node voltages are known, the branch currents may be obtained from Ohm’s law.

Example: Find out the nodal voltage at each node & current in each loop by using the Nodal method?

                 

Solution: First of all we have labelled all elements and identified all relevant nodes in the circuit.     

 

There are a few general guidelines that we need to remember as we make the selection of the reference node.

  1. A useful reference node is one that has the largest number of elements connected to it.
  2. A useful reference node is one that is connected to the maximum number of voltage sources.

     For the next step, we assign current flow and polarities

 For node n1 voltage of the voltage source is known so     

v1=Vs      ……………………………(1)

 & KCL at node n2 associated with voltage v2 gives:             

 i1=i2+i3     ….………………………… (2)

 

The currents i1, i2, i3 are expressed in terms of the voltages v1, v2, v3 as follows 

                      …………………….. (3)                                 

From the relation (1) (2) & (3) we get….

                                …………………………  (4)

                                                                                                                        

 Rewrite the above expression as a linear function of the unknown voltages v2 and v3 gives.

               ………………………. (5)

                                                                                                                            

KCL at node n3 associated with voltage v3 gives:

       or      .....................……. (6)

 Now we can write equations (5) & (6) in matrix form for the node voltage v2 and v3.

   Or     …………………………… (7)

 In defining the set of simultaneous equations, we want to end up with a simple and consistent form. The simple rules to follow and check are

  • Place all sources (current and voltage) on the right-hand side of the equation, as inhomogeneous drive terms.                                                                                                                
  • The terms comprising each element on the diagonal of the matrix must have the same sign.
  • If you arrange so that all diagonal elements are positive, then the off-diagonal elements are negative and the matrix is symmetric: Aij =Aji. If the matrix does not have this property there is a mistake somewhere.

Once we put the equations in matrix form and perform the checks detailed above the solutions

then there is a solution if the   unknown voltage VK is given by:

                          …………………………………  (8)

So for our example the voltages v2 and v3 are given by:

                   ………………………………… (9)

              ………………………………. (10)                                                                     

Nodal Analysis with Floating Voltage Sources. (THE SUPERNODE)

If a voltage source V2 is not connected to the reference node it is called a floating voltage source and special care must be taken when performing the analysis of the circuit.  In the circuit of given figure below the voltage source V2 is not connected to the reference node and thus it is a floating voltage source. Here v2 is the node voltage while V2 is the source voltage between node n2 & n3.

Circuit with a Supernode

The part of the circuit enclosed by the dotted ellipse is called a supernode. Kirchhoff’s current law may be applied to a supernode in the same way that it is applied to any other regular node. This is not surprising considering that KCL describes charge conservation which holds in the case of the supernode as it does in the case of a regular node.

 

 In our example application of KCL at the supernode gives                                

 i1= i2+ i3                           ………………………….  (11)

               

In term of the node voltages Equation (11) becomes:                       

             …………………………… (12)

 

The relationship between node voltages v1 and v2 is the constraint that is needed in order to completely define the problem. The constraint is provided by the voltage source V2.

   V2 = v3 - v2                        ……………………………………(13)

   From equation (12) & (13),

         and        ........................……..(14)             

 Example- Nodal Analysis with supernode.

 Determine the node voltages v1, v2, and v3 of the circuit in the Figure below?

                  

Solution: We have applied the first five steps of the nodal method and now we are ready to apply KCL to the designated nodes. In this example, the current source Is constraints the current i3 such that i3.

 KCL at node n2 gives,

            i1 = i2+I                            …………….. (1)

                           

 And with the application of Ohm’s law             

                       ……………… (2)                                                                    

 Where we have used v1 = Vs at node n1.

The current source provides a constraint for the voltage v3 at node n3.

          V3 = ISR3                               ……………………….   (3)

 Now combining the equation (2) & (3).

                       .......………………..  (4)

 

MESH ANALYSIS

A mesh is defined as a loop that does not contain any other loops The procedure for obtaining the solution is similar to that followed in the Node method and the various steps are given below. 

  1. Clearly, label all circuit parameters and distinguish the unknown parameters from the known ones.
  2. Identify all meshes of the circuit & assign mesh currents and label polarities.
  3. Apply KVL to each mesh and express the voltages in terms of the mesh currents.
  4. Solve the resulting simultaneous equations for the mesh currents.
  5. Now that the mesh currents are known, the voltages may be obtained from Ohm’s law.

Example - Find out the mesh current i1 & i2 for mesh 1 & mesh 2?

                                   

 

Solution: Our circuit example has three loops but only two meshes as shown, the meshes of interest are mesh1 and mesh2.

In the next step, we will assign mesh currents, define current direction and voltage polarities.  The direction of the mesh currents I1 and I2 is defined in the clockwise direction as shown in the next figure.

The branch of the circuit containing resistor R2 is shared by the two meshes and thus the branch current (the current flowing through R2) is the difference between the two mesh currents.

              

Considering mesh1. For clarity we have separated mesh1 from the circuit in doing this, care must be taken to carry all the information of the shared branches. Here we indicate the direction of mesh current I2 on the shared branch.

 

Apply KVL to mesh1. Starting at the upper left corner and proceeding in a clockwise direction the sum of voltages across all elements encountered is

                 I1R1+ (I1-I2) R2-VS = 0        ………………………. (1)

Similarly, consideration of mesh2: we have indicated the direction of the mesh current I1 on the shared circuit branch.

 

Apply KVL to mesh2:                                             

 I2 (R3 + R4 ) + (I2-I1) R2 = 0            ...………………………….  (2)

From equation (1) & (2),

 I1(R1+ R2) - I2 R2 = VS                         ………………………………. (3)

 -I1R2 + I2 ( R2+R3+R4) = 0              ………………………………  (4)

  

 In matrix form equations  (3) & (4) becomes,

       ……………………..    (5)

                   

Equation (5) may now be solved for the mesh currents  I1 and I2.

Note: It is evident from Figure next figure below that the branch currents are i1, i2 & i3  are obtained from the mesh currents I1 & I2  such as.

 I1 = i1         i2 = I1 – I2         i3 = I2

MESH ANALYSIS With CURRENT SOURCES:

  1.      If a current source exists only in one mesh.

      (i) The mesh current is defined by the current source.

      (ii) Number of variables is reduced.

    

 

  1. If a current source exists between two meshes.

      (i) The two nodes form a Online Classroom Program mesh.

      (ii) Use one current variable for both meshes. The current difference between these two meshes is known.

      (iii) Apply KVL to the Online Classroom Program mesh.

Example: Find out the unknown mesh current I1?

 

Solution:

Consider the circuit in the figure which contains a current source. The application of the mesh analysis for this circuit does not present any difficulty once we realize that the mesh current of the mesh containing the current source is equal to the current of the current source:

i.e.          I2 = IS ……………………………… (1)

 

In defining the direction of the mesh current, we have used the direction of the current IS. We also note that the branch current I3 = IS.

Applying KVL around mesh1 we obtain

I1R1 + (I1 + IS) R2 = VS     ……………………………(2)

The above equation simply indicates that the presence of the current source in one of the meshes reduces the number of equations in the problem.

The unknown mesh current is:              

                                                                 

PRACTICE PROBLEMS WITH ANSWERS.

 Q-1 Determine the currents in the given circuits with reference to the indicated direction?

 Q-2  Determine the currents in the given circuits with reference to the indicated direction?

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Important Related Links

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Kajal VatsKajal VatsMember since Apr 2020
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Rahul Singh Gusain
Solved book of sadiku plss
vishu pandey

vishu pandeyJul 31, 2019

If anybody has solutions of Sadiku book please mail me
Vishu.d14@gmail.com
Arpita Ash

Arpita AshJul 31, 2019

Sir please post sectional quize. Much needed as we dnt have enough time. Please
mukesh pujari
@Kajal Vats  Madam How shall I start study with study plan announced by greadup team
Rishikesh U

Rishikesh UJul 21, 2020

Any links to the pdf of the books will be helpful... I can't find even one source that's not a clickbait for the pdfs
Rahimul

RahimulSep 22, 2020

Please guide me...
Arpan Jain

Arpan JainApr 11, 2021

Those who want gate related books or videos contact @Player4210 in telegram, I hope u all will be getting what u want
Rahul Soni

Rahul SoniApr 12, 2021

I need some good book for
communication subject
Reetam Bagh

Reetam BaghJul 21, 2021

THANKS for uploading this . is it possivble to upload such content for rest subjects of ee for ese

ESE & GATE EC

Electronic & Comm.GATEGATE ECESEESE ECOther ExamsTest Series
tags :ESE & GATE ECNetworksGATE EC OverviewGATE EC NotificationGATE EC Apply OnlineGATE EC Eligibility CriteriaGATE EC Selection Process

ESE & GATE EC

Electronic & Comm.GATEGATE ECESEESE ECOther ExamsTest Series
tags :ESE & GATE ECNetworksGATE EC OverviewGATE EC NotificationGATE EC Apply OnlineGATE EC Eligibility CriteriaGATE EC Selection Process

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