Mc GrawHill Education Kulshreshtha D C Basic Electrical

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@ Mc. Graw-Hill Education Kulshreshtha, D. C. Mc. Graw-Hill Education © 2010 Basic Electrical

Thought of The DAY Whatever THE MIND OF MAN can CONCIEVE and BELIEVE, it can ACHIEVE. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 3

Topics to be Discussed n n n n Electric Circuit, The Resistance Parameter, The Capacitance Parameter, The Inductance Parameter, Energy Sources-Classification Ideal Voltage Source. Ideal Current Source. Tuesday, September 21, 2021 n n n Series and Parallel Combinations. Practical Voltage Source. Practical Current Source Transformation. Kirchhoff’s Laws. Ch. 3 Network Analysis- Part I Next 4

Electric Circuit n It is a closed path, composed of active and passive elements. n Active Element : It supplies energy to the circuit. Passive Element : It receives energy and then 1) either converts it to heat, as in a Resistance (R). 2) or stores it in (a) Electric Field, as in a Capacitor (C). (b) Magnetic Field, as in an Inductor (L). n Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 5

Energy Sources n Classification Independent Source Voltage Source DC Source Ideal Source Tuesday, September 21, 2021 Or Or Dependent Source Current Source AC Source Practical Source Ch. 3 Network Analysis- Part I Next 6

Independent Ideal Voltage Source Load Note that the source determines the voltage, but the current is determined by the load. The source has zero internal resistance. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 7

n n The voltage source is said to be idle if the output terminals are open such that i = 0. When turned off (killed or made inactive), so that v = 0, it is equivalent to a short circuit. Reference Marks : One terminal is marked plus and the other minus. (Oversimplification; one mark can be omitted. ) When actual polarity is opposite to the reference marks, the voltage is a negative number. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 8

Independent Ideal Current Source Load Note that the source determines the current, but the voltage is determined by the load. The Source has infinite internal resistance (Ri). Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 9

n n The current source is said to be idle if the output terminals are shorted together, such that v = 0. When turned off (killed or made inactive), so that i = 0, it is equivalent to an open circuit. Reference Marks : An arrow is put. When actual direction of current is opposite to the reference (arrow) direction, the current is a negative number. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 10

Do you observe duality ? The roles for the current and voltage are interchanged in the two sources. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 11

Practical Voltage Source It is represented by an ideal voltage source in series with an internal resistance (RSV). Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 12

Practical Current Source It is modelled as an ideal current source in parallel with an internal resistance (RSI). Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 13

Source Transformation A practical current source can be converted into its equivalent practical voltage source, and vice versa. n This conversion is valid only for the external load connected across the terminals of the source. n Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 14

Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 15

Equivalence between Voltage Source and Current Source n Two sources would be equivalent if they produce identical values of VL and IL, when they are connected across the same load. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 16

Series and Parallel n. Combinations What would be the net emf of the combination if two ideal voltage sources of 2 V and 4 V are connected in series so as to aid each other? Click n Ans. 6 V n What would be the net emf of the combination if two ideal voltage sources of 4 V and 4 V are connected in parallel ? 4 V or 8 V ? Click n Ans. Obviously, it should be 4 V Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 17

n n n What would be the net emf of the combination if two ideal voltage sources of 2 V and 4 V are connected in parallel ? 2 V or 4 V or 3 V ? Click The question seems to be quite tricky! Click Ans. The question is wrong. The question contradicts itself. Ideal Voltage Sources in parallel are permissible only when each has the same terminal voltage at every instant of time. What is its dual ? Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 18

Ideal Voltage Sources Connected in Series Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 19

Ideal Current Sources Connected in Parallel Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 20

Practical Current Sources Connected in Series Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 21

Practical Voltage Sources Connected in Parallel Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 22

Example 1 : Reduce the network shown in figure to its simplest possible form by using source transformation. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 23

Solution Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 24

Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 25

Example 2 n In the given figure, (a) If RL = 80 Ω, find current i. L. (b) Transform the practical current source into a practical voltage source and find i. L if RL = 80 Ω again. (c) Find the power drawn from the ideal source in each case. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 26

Solution : Click Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 27

Benchmark Example 3 n Take the benchmark example of the circuit given in figure. Using source transformation, determine the voltage v across 3 -Ω resistor. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 28

Solution : Transforming the 4 -A current source into a voltage source, Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 29

Combining the two voltage sources, Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 30

Again transforming the voltage source into current source, Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 31

Combining the two current sources we get Fig. (e). Transforming this current source into voltage source (Fig. f ) Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 32

Combining the two resistances, we get Fig. (g). Finally, using voltage divider, we get Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 33

Kirchhoff’s Laws n (1) KCL : Algebraic sum of currents meeting at a junction of conductors in a circuit is zero. q It is simply a restatement of the principle of conservation of charge. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 34

n (2) KVL : The algebraic sum of voltages around a closed circuit or a loop is zero. q It is simply a restatement of the principle of conservation of energy. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 35

Polarity of Voltages Note that polarity of the voltage (emf) across a battery does not depend upon the assumed direction of current. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 36

Applying KVL 1. 2. 3. 4. Select a closed loop. Mark the voltage polarity (+ and -) across each element in the closed loop. Go round the selected loop, and add up all the voltages with + or – signs. Any one of the following two rules can be followed : Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 37

(i) Rule 1 : While travelling, if you meet a voltage rise, write the voltage with positive sign ; if you meet a voltage drop, write the voltage with negative sign. (ii) Rule 2 : While travelling, write the voltage with positive sign if + is encountered first; write the voltage with negative sign if – is encountered first. We shall be following Rule 1, as it has a strong analogy with the physical height (altitude) of a place. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 38

Example 5 : Use KVL to find v. R 2 and vx. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 39

For finding v. R 2, we write KVL eqn. going around loop abgha clockwise : If you choose to go around the loop anticlockwise, you get Click Giving the same result. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 40

There are two ways to determine vx 1) We can consider this voltage as the voltage across the gap from d to f. Writing KVL (habcdfgh) : Click 2) Knowing v. R 2 , apply a short-cut (bcdfgb) : Click Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 41

Important Note about KVL The assumed direction of current through a resistor and the polarity of voltage across it are always in conformity. n The end into which the current enters is marked positive. n Passive-element sign convention. n Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 42

Example 6 : Find the current supplied by the 60 -V source in the network. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 43

Solution : n n We need not find the currents I 1, I 2 and I 3. Instead, we reduce the network. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 44

Example 7 : Determine the value of current I. 2– 3–I– 4=0 Tuesday, September 21, 2021 or I = -5 A Ch. 3 Network Analysis- Part I Next 45

Example 8 Using KCL and KVL, determine the currents ix and iy in the network shown. Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 46

Solution : Using KCL, the currents in other branches are marked as shown. Writing KVL equations for the loops 1, 2 and 3, Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Next 47

Writing the above equations in matrix form, Using Calculator, we solve for Ix and Iy, Tuesday, September 21, 2021 Ch. 3 Network Analysis- Part I Click Next 48

Review n n n n Electric Circuit, The Resistance Parameter, The Capacitance Parameter, The Inductance Parameter, Energy Sources-Classification Ideal Voltage Source. Ideal Current Source. Tuesday, September 21, 2021 n n n Series and Parallel Combinations. Practical Voltage Source. Practical Current Source Transformation. Dependent Sources. Kirchhoff’s Laws. Ch. 3 Network Analysis- Part I Next 49