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EE6201 Circuit Theory Regulation 2013 Lecture Notes

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  • 5/28/2018 EE6201 Circuit Theory Regulation 2013 Lecture Notes

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    EE6201 - Circuit Theory - Regulation 2013 - Lecture NotesbyVidyarthiplus Team - www.Vidyarthiplus.com

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    KIRCHHOFFS LAWS

    Kirchhoffs laws are basic analytical tools in order to obtain the solutions

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    Solution of Electric Circuit Based on Mesh (Loop) Current Method

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    Solution of Electric Circuit Based on Node Voltage Method

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    SUPERPOSITION THEOREM

    INTRODUCTION

    Statement of superposition theorem

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    Limitations of superposition Theorem

    B

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    omThe procedure for applying Thevenins theorem

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    Maximum Power Transfer Theorem

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    Proof of Thevenin Theorem

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    load. Just as with Thevenin's Theorem, the qualification of linear is identical to that found in the

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    connect our original load resistance of 2 , we can analyze the Norton circuit as a

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    Nortons Theorem

    In some ways Norton's Theoremcan be thought of as the opposite to "Thevenins Theorem", in that Thevenin

    reduces his circuit down to a single resistance in series with a single voltage. Norton on the other hand reduces his

    circuit down to a single resistance in parallel with a constant current source. Nortons Theoremstates that "Any linearcircuit containing several energy sources and resistances can be replaced by a single Constant Current generator in

    parallel with a Single Resistor". As far as the load resistance, RLis concerned this single resistance, RSis the value

    of the resistance looking back into the network with all the current sources open circuited and ISis the short circuit

    current at the output terminals as shown below.

    Nortons equivalent circuit.

    The value of this "constant current" is one which would flow if the two output terminals where shorted together while

    the source resistance would be measured looking back into the terminals, (the same as Thevenin).

    For example, consider our now familiar circuit from the previous section.

    To find the Nortons equivalent of the above circuit we firstly have to remove the centre 40load resistor and short

    out the terminals Aand Bto give us the following circuit.

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    arth ip luscomWhen the terminals Aand Bare shorted together the two resistors are connected in parallel across their tworespective voltage sources and the currents flowing through each resistor as well as the total short circuit current can

    now be calculated as:

    with A-B Shorted Out

    If we short-out the two voltage sources and open circuit terminals Aand B, the two resistors are now effectively

    connected together in parallel. The value of the internal resistor Rsis found by calculating the total resistance at the

    terminals Aand Bgiving us the following circuit.

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    Find the Equivalent Resistance (Rs)

    Having found both the short circuit current, Isand equivalent internal resistance, Rsthis then gives us the following

    Nortons equivalent circuit.

    Nortons equivalent circuit.

    Ok, so far so good, but we now have to solve with the original 40load resistor connected across terminals Aand B

    as shown below.

    Again, the two resistors are connected in parallel across the terminals Aand Bwhich gives us a total resistance of:

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    The voltage across the terminals Aand Bwith the load resistor connected is given as:

    Then the current flowing in the 40load resistor can be found as:

    which again, is the same value of 0.286 amps, we found using Kirchoffscircuit law in the previous tutorials.

    Nortons Theorem Summary

    The basic procedure for solving a circuit using Nortons Theoremis as follows:

    1.Remove the load resistor RLor component concerned.

    2.Find RSby shorting all voltage sources or by open circuiting all the current sources. 3.Find ISby placing a shorting link on the output terminals Aand B.

    4.Find the current flowing through the load resistor RL.

    In a circuit, power supplied to the load is at its maximum when the load resistance is equal to the source resistance.

    In the next tutorial we will look at Maximum Power Transfer. The application of the maximum power transfer

    theorem can be applied to either simple and complicated linear circuits having a variable load and is used to find the

    load resistance that leads to transfer of maximum power to the load.

    Example-L.8.5 For the circuit shown in fig.8.10(a), find the current through resistor ( branch) using

    Nortons theorem & hence calculate the voltage across the current source (). 21LRR==abIcgV

    Solution:

    Step-1: Remove the resistor through which the current is to be found and short the terminals a andb (see fig.8.10(b)).

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    Step-2: Any method can be adopted to compute the current flowing through the a-b branch. Here, we

    apply mesh current method.Loop-13R

    4(I

    1I

    2) = 0, where I

    2= - 2A

    R4I1= 3 + R

    4I2= 32 2 = - 1I

    1= - 0.5A

    Loop-3

    133323333- RI-R(I-I)=0- 3I-4(I+2)=0- 7I-8=08 I=-=7

    N138-7+1I=(I-I)=-0.5+=7149A14=(current is flowing from a to b)Step-3: To compute R

    N, all sources are replaced with their internal resistances. The equivalent

    resistance between a and b terminals is same as the value of Thevenins resistance of the circuit

    shown in fig.8.3(d).

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    Step-4: Replace the original circuit with an equivalent Nortons circuit as shown in fig.8.10(d).

    NLNNLR1.555I=I=0.643=0.39A (a to b)R+R1.555+1

    In order to calculate the voltage across the current source the following procedures are adopted.

    Redraw the original circuit indicating the current direction in the load.

    bgbgcbcg V=3-10.39=2.61volt2.61 I==1.305A2 I=1.305-0.39=0.915A ('c' to 'b')

    V=21.305+4.915=6.26volt ('c' is higher potential than 'g')

    L.8.8 Test Your Understanding [Marks: 60]T.1 When a complicated dc circuit is replaced by a Thevenin equivalent circuit, it consists of one ----

    --- in series with one --------- . [2]

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    T.2 When a complicated dc circuit is replaced by a Norton equivalent circuit, it consists of ------ in --

    --- with one -------. [2]

    T.3 The dual of a voltage source is a -----------. [1]

    T.4 When a Thevenin theorem is applied to a network containing a current source; the current source

    is eliminated by --------- it. [1]

    T.5 When applying Nortons theorem, the Norton current is determined with the output terminals ----

    ----------, but the Norton resistance is found with the output terminals ---------.and subsequently all

    the independent sources are replaced -----------. [3]

    T.6 For a complicated circuit, the Thevenin resistance is found by the ratio of -------- voltage and -----

    ------- current. [2]

    T.7 A network delivers maximum power to the load when its -------- is equal to the -------- of circuit

    at the output terminals. [2]

    T.8 The maximum power transfer condition is meaningful in ------------ and --------- systems. [2]

    T.9 Under maximum power transfer conditions, the efficiency of the system is only --------- %. [1]

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    In this lesson, we shall study two winding ideal transformer, its properties and workingprinciple under no load condition as well as under load condition. Induced voltages in primary and

    secondary are obtained, clearly identifying the factors on which they depend upon. The ratio between

    the primary and secondary voltages are shown to depend on ratio of turns of the two windings. At the

    end, how to draw phasor diagram under no load and load conditions, are explained. Importance of

    studying such a transformer will be highlighted. At the end, several objective type and numerical

    problems have been given for solving.

    Key Words: Magnetising current, HV & LV windings, no load phasor diagram, reflected current,

    equivalent circuit

    23.2 Introduction

    Transformers are one of the most important components of any power system. It basically

    changes the level of voltages from one value to the other at constant frequency. Being a static

    machine the efficiency of a transformer could be as high as 99%.

    Big generating stations are located at hundreds or more km away from the load center (where the

    power will be actually consumed). Long transmission lines carry the power to the load centre from

    the generating stations. Generator is a rotating machines and the level of voltage at which it generates

    power is limited to several kilo volts only

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