Electrical Engineering Fundamentals_V. Del Toro.pdf

Scilab Textbook Companion for Electrical Engineering Fundamentals by V. Del Toro1 Created by Aditi Pohekar Electrical Engineering Electrical Engineering IIT Bombay College Teacher Madhu N. Belur Cross-Checked by Mukul R. Kulkarni May 19, 2016

1 Funded

by a grant from the National Mission on Education through ICT, http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilab codes written in it can be downloaded from the ”Textbook Companion Project” section at the website http://scilab.in

Book Description Title: Electrical Engineering Fundamentals Author: V. Del Toro Publisher: Prentice - Hall International Edition: 2 Year: 2009 ISBN: 9780132475525

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Scilab numbering policy used in this document and the relation to the above book. Exa Example (Solved example) Eqn Equation (Particular equation of the above book) AP Appendix to Example(Scilab Code that is an Appednix to a particular Example of the above book) For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 means a scilab code whose theory is explained in Section 2.3 of the book.

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Contents List of Scilab Codes

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1 The Fundamental laws of Electrical Engineering

5

2 The circuit elements

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3 Elementary network theory

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4 Circuit differential equations Forms and Solutions

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5 Circuit dynamics and forced responses

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6 The laplace transform method of finding circuit solutions

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7 Sinusoidal steady state response of circuits

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9 Semiconductor electronic devices

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11 Binary logic Theory and Implimentation

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12 Simplifying logical functions

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15 Magnetic circuit computations

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16 Transformers

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18 The three phase Induction motor

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19 Computations of Synchronous Motor Performance

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3

20 DC machines

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23 Principles of Automatic Control

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24 Dynamic behaviour of Control systems

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List of Scilab Codes Exa 1.1 force between two like charges in free space . . . . . . Exa 2.1.a Determine the current flow and voltage drop across the resistor . . . . . . . . . . . . . . . . . . . . . . . . . . Exa 2.1.b Determine the current flow and voltage drop across each resistor . . . . . . . . . . . . . . . . . . . . . . . . . . Exa 2.1.c Repeat parts A and B with the voltage source replaced by a current source of 1A . . . . . . . . . . . . . . . . Exa 2.2 From the given list of resistors choose a suitable resistor which can carry a current of 300mA . . . . . . . . . . Exa 2.3 Find the resistance of the round copper conductor having the given specifications . . . . . . . . . . . . . . . Exa 2.4 Find the resistance of the round copper conductor having the given specifications . . . . . . . . . . . . . . . Exa 2.5 Find the time variation of the voltage drop appearing across the inductor terminals . . . . . . . . . . . . . . Exa 2.6 Find the time variation of the capacitor voltage . . . . Exa 2.7 Find A actual value of the voltage gain of the opamp circuit B ideal value of the voltage gain C percent error Exa 2.8 Design a non inverting opamp circuit of voltage gain 4 Exa 2.9 Find the input resistance of an inverting opamp circuit with voltage gain of 4 . . . . . . . . . . . . . . . . . . Exa 3.1 for the given circuit calculate the current flowing from the voltage source . . . . . . . . . . . . . . . . . . . . Exa 3.2 Calculate the potential difference across terminals bc . Exa 3.3 Determine the equivalent series circuit . . . . . . . . . Exa 3.4 Value of E for which power dissipation in R5 is 15W R5 is 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 6 6 7 7 8 8 9 10 11 11 12 13 13 14 14

Exa 3.8 Exa 3.12

Exa 3.13 Exa 4.3 Exa 5.2 Exa 6.1 Exa 7.1 Exa 7.2 Exa Exa Exa Exa Exa

7.3 7.4 7.5 7.6 7.7

Exa 7.8 Exa 7.9 Exa 7.10 Exa 7.11 Exa 9.2 Exa 9.3 Exa 11.1 Exa 11.2

Find current flowing through all the branches of the circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . Find A current flowing through Rl B valye of Rl for which the power transfer is maximum and the maximum power . . . . . . . . . . . . . . . . . . . . . . . . . . . Find the current flowing through R2 by using Nortons current source equivalent circuit . . . . . . . . . . . . Determine the operational driving point impedances appearing at terminals ad and dg . . . . . . . . . . . . . Find the expression for the current flowing through the circuit and the total energy dissipated in the resistor . Find the laplace transform of the given pulse . . . . . Find the average value of the given periodic function . Determine the power factor and average power delivered to the circuit . . . . . . . . . . . . . . . . . . . . . . . Find the expression for the sum of i1 and i2 . . . . . . Find the effective value of the resultant current . . . . Find the time expression for the resultant current . . . Find the value of the given expression . . . . . . . . . Find A value of steady state current and the relative phase angle C magnitude and phase of voltage drops appearing across each element D average power E power factor . . . . . . . . . . . . . . . . . . . . . . . . . . . Find the equivalent impedance appearing between points a and c . . . . . . . . . . . . . . . . . . . . . . . . . . Find the current which flows through branch Z3 . . . Find the current in the Z3 branchby using the Nodal method . . . . . . . . . . . . . . . . . . . . . . . . . . Find the current flowing through Z3 by using Thevinins theoram . . . . . . . . . . . . . . . . . . . . . . . . . . Find the values of self bais source resistance and drain load resistance at Q point . . . . . . . . . . . . . . . . Find A midband frequency current gain of the first stage B bandwidth of the first stage amplifier . . . . . . . . Determine th decimal equivalents of the binary numbers A 101 B 11011 . . . . . . . . . . . . . . . . . . . . . . Determine the decimal equivalent of A octal number 432 B hexadecimal number C4F . . . . . . . . . . . . . . . 6

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17 18 19 20 22 23 23 24 24 25 26

26 28 28 29 30 31 31 34 34

Exa 11.3 Exa 15.1 Exa 15.3 Exa 15.5 Exa 16.1

Exa 16.2 Exa 16.3 Exa 18.1 Exa 19.1 Exa 20.2 Exa 20.3 Exa 20.4 Exa 23.1 Exa 24.2

Find the binary and octal equivalents of 247 . . . . . . Find A magneto motive force B current C relative permiability and reluctance of each material . . . . . . . Find the mmf produced by the coil . . . . . . . . . . . B Find the magnetic force exerted on the plunger . . . Find A equivalent resistance and reactance referred to both the sides B voltage drops across these in Volts and in per cent of the rated winding voltage C Repeat B for the low voltage side D equivalent leakage impedances referred to both the sides . . . . . . . . . . . . . . . . Compute the 6 parameters of the equivalent circuit referred to the high and low sides . . . . . . . . . . . . . For the transformer compute A efficiency B voltage regulation . . . . . . . . . . . . . . . . . . . . . . . . . . Find A input line current and power factor B developed electromagnetic torque C horse power output D efficiency Find A induced excitation voltage per phase B line current C power factor . . . . . . . . . . . . . . . . . . . Caculate A electromagnetic torque B flux per pole C rotational losses D efficiency E shaft laod . . . . . . . Determine the new operating speed . . . . . . . . . . . find A motor speed B required pulse frequency C repeat part A and B for the given ON time to cycle time ratio Determine the new transfer gain and feedback factor . find A dynamic response of the system B position lag error C change in amplifier gain D damping ratio and maximum percent overshoot E output gain factor for maximum overshoot equal to 25percent . . . . . . . .

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35 37 38 40

41 43 45 47 50 52 53 54 56

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Chapter 1 The Fundamental laws of Electrical Engineering

Scilab code Exa 1.1 force between two like charges in free space 1 2 3 4 5 6 7 8

E0 = 1/(36* %pi *10^9) ; // p e r m i t i v i t y i n f r e e s p a c e k = 4* %pi * E0 ; q1 = 1; // c h a r g e on t h e f i r s t p a r t i c l e i n c o u l o m b s q2 = 1; // c h a r g e on t h e s e c o n d p a r t i c l e i n c o u l o m b s d = 1; // d i s t a n c e b e t w e e n t h e p a r t i c l e s i n m e t e r F = ( q1 * q2 ) /( k * d ^2) ; // f o r c e b e t w e e n t h e two p a r t i c l e s i n newtons disp (F , ” f o r c e i n f r e e s p a c e b e t w e e n t h e two p a r t i c l e s i s i n Newtons i s : ” )

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Chapter 2 The circuit elements

Scilab code Exa 2.1.a Determine the current flow and voltage drop across the resistor 1 V = 1; // v o l t a g e s u p p l y 2 R = 10; // r e s i s t a n c e i n ohms 3 I = V / R // c u r r e n t f l o w i n g t h r o u g h R 4 disp ( ” a ) ” ) 5 disp (V , ” v o l t a g e a c r o s s t h e r e s i s t o r ( i n v o l t s )=” ) 6 disp (I , ” c u r r e n t f l o w i n g t h r o u g h t h e r e s i s t o r ( i n

amps ) =” )

Scilab code Exa 2.1.b Determine the current flow and voltage drop across each resistor 1 2 3 4 5 6

V = 1; // v o l t a g e s u p p l y R1 = 10; // f i r s t r e s i s t a n c e i n ohms R2 = 5; // r e s i s t a n c e o f t h e s e c o n d r e s i s t o r Vr1 = V * ( R1 /( R1 + R2 ) ) ; // v o l t a g e a c r o s s R1 Vr2 = V - Vr1 ; // v o l t a g e a c r o s s R2 Ir = Vr1 / R1 ; // c u r r e n t f l o w i n g t h r o u g h R 9

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disp ( Vr1 , ” v o l t a g e a c r o s s t h e f i r s t r e s i s t o r ( i n v o l t s )=” ) 9 disp ( Vr2 , ” v o l t a g e a c r o s s t h e s e c o n d r e s i s t o r ( i n v o l t s )=” ) 10 disp ( Ir , ” c u r r e n t f l o w i n g t h r o u g h t h e r e s i s t o r ( i n amps ) =” )

Scilab code Exa 2.1.c Repeat parts A and B with the voltage source replaced by a current source of 1A 1 // c − a 2 R1 = 10; // f i r s t r e s i s t a n c e i n ohms 3 I = 1; // c u r r e n t s o u r c e 4 V = I * R1 ; // v o l t a g e a c r o s s R 5 disp ( ” c − a ) ” ) 6 disp (V , ” v o l t a g e a c r o s s t h e r e s i s t o r ( i n v o l t s )=” ) 7 disp (I , ” c u r r e n t f l o w i n g t h r o u g h t h e r e s i s t o r ( i n

amps ) =” ) 8 9 // c − b 10 Vr1 = I * R1 ; // v o l t a g e a c r o s s R1 11 Vr2 = I * R2 ; // v o l t a g e a c r o s s R2 12 disp ( ” c − b ) ” ) 13 disp ( Vr , ” v o l t a g e a c r o s s t h e r e s i s t o r ( i n v o l t s )=” ) 14 disp (I , ” c u r r e n t f l o w i n g t h r o u g h t h e r e s i s t o r ( i n

amps ) =” )

Scilab code Exa 2.2 From the given list of resistors choose a suitable resistor which can carry a current of 300mA 1 R = 100; // r e s i s t a n c e i n ohms 2 I = 0.3; // c u r r e n t i n amps

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3 P = I ^2 * R ; // power 4 // power s p e c i f i c a t i o n o f t h e

resistors

available in

the stock 5 Pa = 5; 6 Pb = 7.5; 7 Pc = 10; 8 9 10 11 12 13 14 15 16 17

if Pa > P then disp ( ”we s h o u l d s e l e c t end if Pb > P then disp ( ”we s h o u l d s e l e c t end if Pc > P then disp ( ”we s h o u l d s e l e c t end

r e s i s t o r a”)

r e s i s t o r b”)

r e s i s t o r c ”)

Scilab code Exa 2.3 Find the resistance of the round copper conductor having the given specifications 1 L = 1; // l e n g t h o f t h e c o p p e r w i r e i n m e t e r s 2 A = 1 * 10^ -4; // c r o s s s e c t i o n a l a r e a o f t h e w i r e

i n meter square 3 rho = 1.724 * 10^ -8; // r e s i s t i v i t y o f c o p p e r i n ohm meter 4 R = rho * L / A ; // r e s i s t a n c e o f t h e w i r e i n ohm 5 6

disp (R , ” r e s i s t a n c e o f t h e w i r e ( i n ohms )=” )

Scilab code Exa 2.4 Find the resistance of the round copper conductor having the given specifications 1

// 1 i n c h e s = 0 . 0 2 5 4 m e t e r s 11

2 // 1 f o o t = 0 . 3 0 4 8 m e t e r s 3 d = 0.1*0.0254; // d i a m e t e r o f t h e w i r e i n m e t e r s 4 L = 10*0.3048; // l e n g t h o f t h e w i r e i n m e t e r s 5 rho = 1.724*10^ -8; // r e s i s t i v i t y o f t h e w i r e i n ohm

−m e t e r 6 A = %pi *( d /2) ^2; // c r o s s s e c t i o n a l a r e a o f t h e w i r e 7 R = rho * L / A ; // r e s i s t a n c e o f t h e w i r e i n ohm 8 disp (R , ” r e s i s t a n c e o f t h e w i r e ( i n ohm )=” )

Scilab code Exa 2.5 Find the time variation of the voltage drop appearing across the inductor terminals 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

L = 0.1; // i n d u c t a n c e o f t h e c o i l i n h e n r y t1 = [0:0.001:0.1]; t2 = [0.101:0.001:0.3]; t3 = [0.301:0.001:0.6]; t4 = [0.601:0.001:0.7]; t5 = [0.701:0.001:0.9] // c u r r e n t v a r i a t i o n a s a f u n c t i o n o f t i m e i1 = 100* t1 ; i2 = ( -50* t2 ) + 15; i3 = -100* sin ( %pi *( t3 -0.3) /0.3) ; i4 = (100* t4 ) - 60; i5 = ( -50* t5 ) + 45; t = [ t1 , t2 , t3 , t4 , t5 ]; i = [ i1 , i2 , i3 , i4 , i5 ]; plot (t , i ) dt = 0.001; di = diff ( i ) ; V = L * di / dt ; // v o l t a g e d r o p a p p e a r i n g a c r o s s t h e inductor terminals 12

21 Tv = [0:0.001:0.899]; 22 plot ( Tv , V , ” g r e e n ” )

Scilab code Exa 2.6 Find the time variation of the capacitor voltage 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

C = 0.01; // c a p a c i t a n c e o f t h e c a p a c i t o r i n F a r a d s t1 = [0:0.001:0.1]; t2 = [0.101:0.001:0.3]; t3 = [0.301:0.001:0.6]; t4 = [0.601:0.001:0.7]; t5 = [0.701:0.001:0.9] // c u r r e n t v a r i a t i o n a s a f u n c t i o n o f t i m e i1 = 100* t1 ; i2 = ( -50* t2 ) + 15; i3 = -100* sin ( %pi *( t3 -0.3) /0.3) ; i4 = (100* t4 ) - 60; i5 = ( -50* t5 ) + 45; t = [ t1 , t2 , t3 , t4 , t5 ]; i = [ i1 , i2 , i3 , i4 , i5 ]; plot (t , i ) // v o l t a g e a c r o s s t h e c a p a c i t o r a s a f u n c t i o n o f time V1 = (1/ C ) * integrate ( ’ 1 00 ∗ t ’ , ’ t ’ ,0 , t1 ) ; V2 = (1/ C ) * integrate ( ’ ( −50∗ t ) +15 ’ , ’ t ’ ,0.101 , t2 ) ; V3 = (1/ C ) * integrate ( ’ −100∗ s i n ( %pi ∗ ( t − 0 . 3 ) / 0 . 3 ) ’ , ’ t ’ ,0.301 , t3 ) ; V4 = (1/ C ) * integrate ( ’ ( 1 0 0 ∗ t ) − 60 ’ , ’ t ’ ,0.601 , t4 ) ; V5 = (1/ C ) * integrate ( ’ ( −50∗ t ) + 45 ’ , ’ t ’ ,0.701 , t5 ) ; V = [ V1 , V2 , V3 , V4 , V5 ]; plot (t , V , ” g r e e n ” ) 13

Scilab code Exa 2.7 Find A actual value of the voltage gain of the opamp circuit B ideal value of the voltage gain C percent error // a Ri = 1; Rf = 39; A = 10^5; // open l o o p g a i n o f t h e op−amp G = A /(1 + ( A * Ri /( Ri + Rf ) ) ) ; // a c t u a l v o l t a g e g a i n o f the c i r c u i t 6 disp ( ” a ” ) 7 disp (G , ” a c t u a l v o l t a g e o f t h e c i r c u i t =” ) 1 2 3 4 5

8 9 // b 10 G1 = 1 + ( Rf / Ri ) ; // v o l t a g e g a i n o f t h e

circuit

w i t h i n f i n i t e open l o o p g a i n 11 disp ( ” b” ) 12 disp ( G1 , ” f o r i d e a l c a s e t h e v o l t a g e g a i n =” ) 13 14 // c 15 er = (( G1 - G ) / G ) *100; // p e r c e n t e r r o r 16 disp ( ” c ” ) 17 disp ( er , ” p e r c e n t e r r o r o f t h e i d e a l v a l u e compared

t o t h e a c t u a l v a l u e=” )

Scilab code Exa 2.8 Design a non inverting opamp circuit of voltage gain 4 1 G = 4; // v o l t a g e g a i n o f t h e c i r c u i t 2 r = G -1; // r a t i o o f t h e r e s i s t a n c e s

i n v e r t i n g op−amp c i r c u i t 3 disp (r , ” Rf / Ri =” ) 14

i n t h e non−

4 5

// R e s u l t : //A s u i t a b l e c h o i c e f o r R1 i s 10K, Hence Rf = 30K

Scilab code Exa 2.9 Find the input resistance of an inverting opamp circuit with voltage gain of 4 1 G = 4; 2 r = G ; // r a t i o 3 4 5 6

of the r e s i s t a n c e s in the i n v e r t i n g op−amp c i r c u i t disp (r , ” Rf / Ri ” ) // R e s u l t ; //A s u i t a b l e c h o i c e f o r Rf=30K and R1=7.5K // t h e r e f o r e i n p u t r e s i s t a n c e R1 = 7 . 5K

This code can be downloaded from the website wwww.scilab.in

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Chapter 3 Elementary network theory

Scilab code Exa 3.1 for the given circuit calculate the current flowing from the voltage source V = 100; // v o l a t a g e s u p p l y i n v o l t s Rs = 40; // r e s i s t a n c e i n s e r i e s i n ohms // p a r a l l e l r e s i s t a n c e s i n ohms Rp1 = 33.33; Rp2 = 50; Rp3 = 20; Rpinv = (1/ Rp1 ) +(1/ Rp2 ) +(1/ Rp3 ) ; // r e c i p r o c a l o f equivalent r e s i s t a n c e in parallel 8 Req = Rs + (1/ Rpinv ) ; 9 I = V / Req ; // c u r r e n t f l o w i n g from t h e v o l t a g e s o u r c e i n amps 10 disp (I , ” c u r r e n t f l o w i n g from t h e v o l t a g e s o u r c e ( i n amps ) = ” ) 1 2 3 4 5 6 7

Scilab code Exa 3.2 Calculate the potential difference across terminals bc 1 V = 100; // v o l a t a g e s u p p l y i n

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volts

Rs = 40; // r e s i s t a n c e i n s e r i e s i n ohms // p a r a l l e l r e s i s t a n c e s i n ohms Rp1 = 33.33; Rp2 = 50; Rp3 = 20; Rpinv = (1/ Rp1 ) +(1/ Rp2 ) +(1/ Rp3 ) ; // r e c i p r o c a l o f equivalent r e s i s t a n c e in parallel 8 Rp = 1/ Rpinv ; // e q u i v a l e n t e s i s t a n c e i n p a r a l l e l 9 Vbc = V *( Rp /( Rs + Rp ) ) ; // p o t e n t i a l d i f f e r e n c e a c r o s s bc 10 disp ( Vbc , ” p o t e n t i a l d i f f e r e n c e a c r o s s bc = ” ) 2 3 4 5 6 7

Scilab code Exa 3.3 Determine the equivalent series circuit 1 2 3 4 5 6 7 8 9 10 11 12

// R1 R2 R3 R4 R5

r e s i s t a n c e s i n ohms = 25; = 300; = 80; = 30; = 60;

Rcd = R5 * R4 /( R5 + R4 ) ; Rbd1 = Rcd + R3 ; Rbd = Rbd1 * R2 /( Rbd1 + R2 ) ; Req = Rbd + R1 ; // e q u i v a l e n t r e s i s t a n c e disp ( Req , ” e q u i v a l e n t r e s i s t a n c e = ” )

Scilab code Exa 3.4 Value of E for which power dissipation in R5 is 15W R5 is 15 1 // r e s i s t a n c e s 2 R1 = 25; 3 R2 = 300;

i n ohms

17

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

R3 = 80; R4 = 30; R5 = 60; P5 = 15; // power d i s s i p a t e d i n R5 ( i n w a t t ) I5 = sqrt ( P5 / R5 ) ; // c u r r e n t f l o w i n g t h r o u g h R5 V5 = R5 * I5 ; // v o l t a g e a c r o s s R5 Vcd = V5 ; // v o l t a g e a c r o s s cd I4 = Vcd / R4 ; // c u r r e n t f l o w i n g t h r o u g h R4 Icd = I5 + I4 ; // c u r r e n t f l o w i n g t h r o u g h cd Vbd = ( Icd * R3 ) + Vcd ; // v o l t a g e a c r o s s bd Ibd = ( Vbd / R2 ) + Icd ; // c u r r e n t t h r o u g h bd V1 = R1 * Ibd ; // v o l t a g e a c r o s s R1 E = V1 + Vbd ; disp (E , ”E = ” ) // R e s u l t : V a l u e o f E f o r which power d i s s i p a t i o n i n R i s 15W = 200V

This code can be downloaded from the website wwww.scilab.in This

code can be downloaded from the website wwww.scilab.in This code can be

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downloaded from the website wwww.scilab.in

Scilab code Exa 3.8 Find current flowing through all the branches of the circuit 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

// mesh e q u a t i o n s : // 60∗ I 1 − 20∗ I 2 = 20 // −20∗ I 1 + 80∗ I 2 = −65 R = [60 -20; -20 80]; E = [120; -65]; I = inv ( R ) * E ; I1 = I (1 ,:) ; // c u r r e n t f l o w i n g i n f i r s t mesh I2 = I (2 ,:) ; // c u r r e n t f l o w i n g i n s e c o n d mesh Ibd = I1 - I2 ; // c u r r e n t f l o w i n g t h r o u g h b r a n c h bd Iab = I1 ; // c u r r e n t f l o w i n g t h r o u g h b r a n c h ab Icb = - I2 ; // c u r r e n t f l o w i n g t h r o u g h b r a n c h cb disp ( Ibd , ” c u r r e n t f l o w i n g t h r o u g h b r a n c h bd = ” ) disp ( Iab , ” c u r r e n t f l o w i n g t h r o u g h b r a n c h ab = ” ) disp ( Icb , ” c u r r e n t f l o w i n g t h r o u g h b r a n c h cb = ” )

This code can be downloaded from the website wwww.scilab.in This

code can be downloaded from the website wwww.scilab.in This code can be

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downloaded from the website wwww.scilab.in

Scilab code Exa 3.12 Find A current flowing through Rl B valye of Rl for which the power transfer is maximum and the maximum power 1 2 3 4 5 6 7 8

// a // c i r c u i t p a r a m e t e r s E1 = 120; R1 = 40; R2 = 20; R3 = 60;

Voc = E1 * R2 /( R2 + R1 ) ; // open c i r c u i t v o l t a g e appearing at terminal 1 9 Ri = R3 + ( R1 * R2 /( R1 + R2 ) ) ; // e q u i v a l e n t r e s i s t a n c e looking into the n e t w o r k from t e r m i n a l p a i r 01

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

function I = Il ( Rl ) I = Voc /( Ri + Rl ) // c u r r e n t t h r o u g h Rl endfunction Il1 = Il (10) ; // Rl = 10 ohm Il2 = Il (50) ; // Rl = 50 ohm Il3 = Il (200) ; // Rl = 200 ohm disp ( ” a ” ) disp ( Il1 , ” I l ( Rl = 10ohm ) = ” ) disp ( Il2 , ” I l ( Rl = 50ohm ) = ” ) disp ( Il3 , ” I l ( Rl = 200ohm ) = ” ) // b // f o r maximum power Rl = Ri Rl = Ri ; Plmax = ( Voc /(2* Ri ) ) ^2 * Ri ; //maximum power t o Rl disp ( ” b” ) 20

29

disp ( Plmax , ”maximum power t o Rl ( i n Watt ) = ” )

Scilab code Exa 3.13 Find the current flowing through R2 by using Nortons current source equivalent circuit 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

// c i r c u i t p a r a m e t e r s // v o l t a g e s o u r c e s E1 = 120; E2 = 65; // r e s i s t a n c e s R1 = 40; R2 = 11; R3 = 60; I = ( E1 / R1 ) + ( E2 / R3 ) ; // n o r t o n ’ s c u r r e n t s o u r c e Req = R1 * R3 /( R1 + R3 ) ; // e q u i v a l e n t r e s i s t a n c e I2 = I * Req /( Req + R2 ) ; // c u r r e n t f l o w i n g t h r o u g h R2 disp ( I2 , ” c u r r e n t f l o w i n g t h r o u g h R2 = ” )

This code can be downloaded from the website wwww.scilab.in This code

can be downloaded from the website wwww.scilab.in

21

Chapter 4 Circuit differential equations Forms and Solutions

Scilab code Exa 4.3 Determine the operational driving point impedances appearing at terminals ad and dg 1 // ad 2 Zab = complex (1 , -0.5) ; // i m p e d a n c e a p p e a r i n g

across

t e r m i n a l s ab 3 Zbg = complex (1) ; // i m p e d a n c e a p p e a r i n g

across

t e r m i n a l s bg Zbcd = complex (2+1 ,2) ; // i m p e d a n c e a p p e a r i n g a c r o s s t e r m i n a l s bcd 5 Zad = Zab + ( Zbg * Zbcd /( Zbg + Zbcd ) ) ; // i m p e d a n c e a p p e a r i n g a c r o s s t e r m i n a l s ad 6 disp ( Zad , ” i m p e d a n c e a p p e a r i n g a c r o s s t e r m i n a l s ad = ”)

4

7 8 // dg 9 Zdg = Zbg + ( Zab * Zbcd /( Zab + Zbcd ) ) ; // i m p e d a n c e 10

a p p e a r i n g a c r o s s t e r m a i n a l s dg disp ( Zdg , ” i m p e d a n c e a p p e a r i n g a c r o s s t e r m i n a l s dg = ”)

22

Chapter 5 Circuit dynamics and forced responses

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Scilab code Exa 5.2 Find the expression for the current flowing through the circuit and the total energy dissipated in the resistor 1 C = 10*10^ -6 ; // c a p a c i t a n c e ( i n f a r a d s ) 2 R = 0.2*10^6; // r e s i s t a n c e ( i n ohms ) 3 Vi = 40; // i n i t i a l v o l t a g e o f t h e c a p a c i t o r ( i n 4 5 6 7

volts ) Wc = (1/2) * C * Vi ^2; // e n e r g y s t o r e d i n t h e c a p a c i t o r // c u r r e n t f l o w i n g i n c i r c u i t a s a f u n c t i o n o f t i m e i ( t ) = 2∗10ˆ −4∗ exp (− t / 2 ) // power d i s s i p a t e d i n t h e r e s i s t o r = R∗ i ˆ2 Wr = integrate ( ’R∗4∗10ˆ −8∗ exp (− t ) ’ , ’ t ’ ,0 ,100)

23

disp ( Wc , ” e n e r g y s t o r e d i n t h e c a p a c i t o r ( i n J o u l e s ) = ”) 9 disp ( Wr , ” e n e r g y d i s s i p a t e d i n t h e r e s i s t o r ( i n J o u l e s ) = ”) 8

This code can be downloaded from the website wwww.scilab.in This

code can be downloaded from the website wwww.scilab.in This code can

be downloaded from the website wwww.scilab.in This code can be down-

loaded from the website wwww.scilab.in This code can be downloaded from

the website wwww.scilab.in This code can be downloaded from the website

wwww.scilab.in

24

Chapter 6 The laplace transform method of finding circuit solutions

Scilab code Exa 6.1 Find the laplace transform of the given pulse 1 2 3 4

function F = laplace (s , T1 , T2 ) // p u l s e : // f = u ( t − T1 ) − u ( t − T2 ) F = integrate ( ’ exp (− s ∗ t ) ’ , ’ t ’ ,T1 , T2 ) ; // l a p l a c e transform of the pulse 5 endfunction

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Chapter 7 Sinusoidal steady state response of circuits

Scilab code Exa 7.1 Find the average value of the given periodic function 1 Vm = 2; // a s s u m p t i o n 2 // a v e r a g e v a l u e o f t h e f u n c t i o n 3 // v ( t ) = Vm∗ a l p h a / ( %pi / 3 ) f o r 0