The Jargon

A network is a collection of interconnected components.Network Analysis is the process of finding the voltages across, and the current through, every component in the network. Kirchhoff laws Nodal analysis Mesh analysis Source Transformation voltage division & current division Network Theorems Duality principle Network Topology Two port network Transients

Superposition theorem Thevenins & Norton's Theorem Maximum power transfer theorem Reciprocity Theorem Millimans Theorem Substitution Theorem Tellegens Theorem

Tellegen theorem states that  the summation of instantaneous powers for the n number of branches in an electrical network is zero. Suppose n number of branches in an electrical network have i 1 , i 2 , i 3 , .............i n respective instantaneous currents through them. These currents satisfy Kirchhoff's Current Law . Again, suppose these branches have instantaneous voltages across them are v 1 , v 2 , v 3 , ........... v n respectively. If these voltages across these elements satisfy Kirchhoff Voltage Law then,

It states that in a linear network any passive element can be equivalently substitute by ideal voltage source or ideal current source provided to all other branch currents and voltages doesn't change which can be possible  when the substituted element and original element absorb the same power. Substitution Theorem is the replacement of one element with another equivalent element. In a network, if any element is substituted or replaced by a voltage or current source whose voltage and current across or through that element will remain unchanged as the previous network. Example:

The  Millman's Theorem states that – when a number of voltage sources (V 1 , V 2 , V 3 ……… V n ) are in parallel having internal resistance (R 1 , R 2 , R 3 ………….R n ) respectively, the arrangement can replace by a single equivalent voltage source V in series with an equivalent series resistance R.

reciprocity theorem, in a linear passive network, supply voltage V and output current I are mutually transferable.The ratio of V and I is called the transfer resistance. In simple words, we can state the reciprocity theorem as when the places of voltage and current source in any network are interchanged the amount or magnitude of current and voltage flowing in the circuit remains the same. The various resistances R 1 , R 2 , R 3 is connected in the circuit diagram above with a voltage source (V) and a current source (I). It is clear from the figure above that the voltage source and current sources are interchanged for solving the network with the help of Reciprocity Theorem. The limitation of this theorem is that it is applicable only to single source networks and not in the multi-source network. Steps for Solving a Network Utilizing Reciprocity Theorem Step 1 – Firstly, select the branches between which reciprocity has to be established. Step 2 – The current in the branch is obtain

The Maximum Power Transfer Theorem states that the maximum amount of power will be dissipated by a load resistance if it is equal to the Thevenin or Norton resistance of the network supplying power. The Maximum Power Transfer Theorem does not satisfy the goal of maximum efficiency. Suppose we have a voltage source or battery that's internal resistance is R i and a load resistance R L is connected across this battery.  

Thevenin’s Theorem states that any linear electrical network all the voltage sources and resistances  can be replaced by an equivalent voltage source V th in series connection with an equivalent resistance R th .       Example: If you apply source transformation technique to Thevenin's equivalent circuit then you will obtain Norton's equivalent circuit.

The response in a particular branch when all the sources are acting simultaneously is equal to the algebraic sum of individual responses by considering one source at one time. All the voltage sources are eliminated by short circuit and current sources are eliminated by open circuiting. do not disturb any dependent sources. If there are several sources acting simultaneously in an electrical circuit, then the current through any branch of the circuit is summation of currents which would flow through the branch for each source keeping all other sources dead. Example: Eliminate the voltage source by Short circuiting and find voltage and current across each branch. Finally voltage and current across each branch is given as :

Current is constant in a series circuit and voltage is constant in parallel circuit. Voltage Divider : Voltage division is the result of distributing the input voltage among the components of the divider. A simple example of a voltage divider is two resistors connected in series, with the input voltage applied across the resistor pair and the output voltage emerging from the connection between them. Current Divider : Current division refers to the splitting of current between the branches of the divider.    

Source Transformation is a simplification technique which eliminates extra nodes in a network. both the networks are equal in performance point of view but, different in connection point of view. Voltage-to-Current Source Transformation   consider a network has voltage source  Vs  in series with resistance R . then the              network   can be converted in to current source Is  with resistance in parallel with it.      the voltage source Vs can be given as : Vs =Vs / R   Current-to-Voltage Source Transformation  consider a network has current source  Is  in parallel with resistance R . then the     network can be converted in to voltage source Vs  with resistance in series with it.      the voltage source Vs can be given as : Vs =Is *R    

Mesh analysis is based on Kirchhoff Voltage Law.   It uses the mesh currents as the circuit variables. we can use Mesh Analysis to find out the voltage , current or power through a particular element or elements. Procedure for Mesh Analysis: 1. Identify all meshes of the circuit and Assign mesh currents and label polarities. for example above circuit has two meshes. mesh 1 is assigned with current I 1  and mesh 2 is assigned with current I 2 .  2. Apply KVL at each mesh and express the voltages in terms of the mesh currents. In the above circuit by applying Kirchhoff's laws we have Equation No 1 :     10 =  50I 1  + 40I 2 Equation No 2 :     20 =  40I 1  + 60I 2 3. Solve the resulting simultaneous equations for the mesh currents. We now have two “ Simultaneous Equations ” that can be reduced to give us the values     of I 1 and I 2  .

The nodal analysis and the mesh analysis are based on the systematic application of Kirchhoff’s laws . Nodal analysis is a method that provides a general procedure for analyzing circuits using node voltages as the circuit variables. Having ‘n’ nodes there will be ‘n-1’ simultaneous equations to solve. The procedure for analyzing a circuit with the node Analysis: Identify all nodes of the circuit. 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. for example in the below circuit nodes are Va,Vb and Vc with respect to reference       node D.  According to Kirchhoff's current law   we have  I 1  + I 2  = I 3    and  I=V/R from ohm's law.    so we have  I 1  = (V a  - V b )/10 ;   I 2  = (Vc - Vb)/20 ;   I 3  = (Vb)/40 As Va = 10v and Vc = 20v  ,  Vb can be easily found by:  

Kirchhoff's Laws There are some simple relationships between currents and voltages  of different branches of an electrical circuit. These relationships are determined by some basic laws that are known as Kirchhoff laws or more specifically Kirchhoff Current and Voltage laws . These laws are very helpful in determining the equivalent electrical resistance or impedance (in case of AC) of a complex network and the currents flowing in the various branches of the network. These laws are first derived by Guatov Robert Kirchhoff and hence these laws are also referred as Kirchhoff Laws . Kirchhoff's First Law – The Current Law, (KCL) Kirchhoff's  Current Law or KCL, states that the “ total current or charge entering a junction or node is exactly equal to the charge leaving the node “. In other words the algebraic sum of ALL the currents entering and leaving a node must be equal to zero, I (entering)  + I (leaving)  = 0. This idea by Kirchhoff is commonly known as the Conservat

Electrostatics Columb’s law  Electric Flux density & Electric field intensity Magnetic Flux density &Magnetic field intensity Gauss law Energy density Continuity equation Magneto statics Biot- savart law Amperes circuit law Magnetic momentum & magnetic flux Boundary conditions Applications (Hall effect) Lorentz force equation conduction, polarization & magnetization Maxwell equations Faraday law, ampere law, gauss law of electric and magnetic fields Law of conservation of charge & boundary conditions Hertzian dipole

Gauss's law states that the net flux of an electric field through a closed surface is proportional to the enclosed electric charge. One of the four equations of Maxwell's laws of electromagnetism, it was first formulated by Carl Friedrich Gauss in 1835 and relates the electric fields at points on a closed surface (known as a "Gaussian surface") and the net charge enclosed by that surface. The electric flux is defined as the electric field passing through a given area multiplied by the area of the surface in a plane perpendicular to the field. Another statement of Gauss's law is that the net flux of an electric field through a closed surface is equal to the charge enclosed divided by the  permittivity.

Magnetic field strength is one of two ways that the intensity of a magnetic field can be expressed. Technically, a distinction is made between magnetic field strength H, measured in amperes per meter (A/m), and magnetic flux density B, measured in Newton-meters per ampere (Nm/A), also called Tesla (T). Magnetic flux density ( B ) is the quantity of  magnetic flux  ( Φ ) per unit area ( A ), measured at right angles to the magnetic field. The magnetic field can be visualized as magnetic field lines. The field strength corresponds to the density of the field lines. The total number of magnetic field lines penetrating an area is called the magnetic flux Density(D). The unit of the magnetic flux is the tesla meter squared (T · m 2 , also called the weber and symbolized Wb). Magnetic flux density (B) is measured in Newton-meters per ampere (Nm/A), also called Tesla (T).