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Circuit Theory I – ECE 201 Simple Resistive Circuits

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Simple Resistive Circuits DC Sources Series Parallel

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Resistors in Series Carry the same current

1 node in common n Nothing else is connected to this node.

KCL on node c Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

i2 i1 0 i2 i1

Single loop circuit

KVL abcdefghija

R1 i s

is vs

R 2 is ........

R 9 is

vs

vs R1

R 2 .......

i s ( R1

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

R9

R 2 .......

R9 )

0

(1)

is

vs R eq

vs

is R eq

R eq

R1

R 2 .......

R9

For k resistors in series, the equivalent resistance is k

R eq

Ri i 1

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

R1

R 2 .......

R9

Resistors in Parallel

Gi

1 Ri

R1 / / R 2 / / R 3 // R 4 Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

i

KCL at (a), s

i1

i2

i3

i4

i1

Vs ,i R1 2

Vs ,i R2 3

Vs ,i R3 4

Vs R4

i1 VsG1 , i2 V sG 2, i 3 V sG 3, i 4 V sG 4 is Vs ( G1 G2 G3 G4 ) Geq

G1 G2 G3 G4

is VsGeq 1 R eq Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

1 R1

1 R2

1 R3

1 R4

2 Resistors in Parallel ( Special Case )

1 Req

1 R1

R eq

( R1 )( R 2 ) ( R1 R 2 )

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

1 R2

( R1 R 2 ) ( R1 )( R 2 ) Product Sum

Equivalent Resistance Series n Equivalent resistance is increased k

Req

Ri i 1

Parallel n Equivalent resistance is decreased

1 R eq

k

i1

1 Ri

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Network Reduction DE 3.1

Ladder Network series parallel reduction 6 + 10 = 16 Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

64 //16 Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

(64)(16) 64 16

12.8

12.8 + 7.2 = 20

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

30// 20

(30)(20) 20 30

12

Req [30//(7.2 [64//(6 10)])] Req 12 v i R eq (5)(12) 60V P5A

(5)*(60)

300W

64 2.4A i10 3* 64 16 P10 (2.4)2 *10 57.6W Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Special Cases

R1 R eq R eq

R2 R1 2

10//10

(10)(10) 10 10

5

R eq is always less than either R1 or R2

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Special Cases Short Circuit (R 2 = 0)

R eq

( R1 )(0) R1 0

0

No current flows through R1

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Current Divider (Parallel Circuit)

is vs

i1 i2 i1R1 i2 R2 is Req

vs is

R1 R2 R1 R2

i1

R2 is R1 R2

i2

R1 is R1 R2

Current chooses the path of LEAST RESISTANCE Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Voltage Divider (Series Circuit)

KVL abca i R1

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

i R2 - vs

0

i

Vs R1 R2

Vo

iR2

Vo

R2 R1 R2 Vs

R2

0

Vo

R2

Vo

Vo is always Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

0 (short circuit) Vs (open circuit) Vs

Loading Effect

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Req

R2 // RL

Req

R2 R 1 2 RL

R2 RL R2 RL

V

R o

R

1

e q e q

R

2

R R

1

V

o

R

V

R

2

1 Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

V

L

R 1

s

2

R R

2 L

s

W ith Load: Vo

Vs

R2 R2 ) R2 R 1 (1 RL

W i t h o u t L oa d : Vo if R L

R

V s R 2R 1 2 ? R 2 , t h e n V o ( Load )

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

V o ( N o Load )

Tolerance The deviation from the mean value

Tolerance = +/- 10%

Nominal:

Vo 100 100K 80V 100 K 25K

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Sensitivity to Tolerance Tolerance : +10%

Vo1

100(100 10)K (100 10) K 25K

81.5V

Tolerance : -10%

Vo2

100(100 10) K (100 10)K 25K

78.3V

Voltage varies from 78.3V to 81.5V

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Voltage Divider Example Problem similar to DE 3.2

(a)No Load: Vo 120 50 K 30 K 50 K

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

75V

With Load

(b)R L :450K Vo

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

120

50 K 30 K (1 50K ) 50k 450K

72V

( c ) i 120 4m A 30 k P30 k

(4x10 3 )2 (30x103 ) 0.48W

Accidental short circuit

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

i50K( NOLOAD) i50K( LOAD)

75 1.5mA 3 50 10 72 1.44mA 50 K 3 2

3

P50K (NOLOAD) (1.5 10 ) (50 10 ) 0.1125W P50K (LOAD) (1.44 10 3 )2 (50 10 3 ) 0.10368W Maximum Power(Pmax ) 0.1125W Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Wye Delta Connections Wye (Star) connection

Delta Connection

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Y - Transform - Y Transform Rab

Rc //( Rb Ra ) R1 R2

Rab

Rc ( Rb Ra ) Ra Rb Rc

R1 R2

Rbc

Ra ( Rb Rc ) Ra Rb Rc

R3 R2

Rca

Rb ( Rc Ra ) Ra Rb Rc

R1 R3

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Y-

Transform Ra Rb Rc

R1 R 2

R 2 R3 R1

R3 R1

R1 R 2

R 2 R3 R2

R3 R1

R1 R 2

R 2 R 3 R 3R 1 R3

- Y Transform R1

R b Rc Ra Rb R c

R2

Rc Ra Ra Rb R c

R3

Ra Rb Ra Rb Rc

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Example similar to Problem 3.56 (page 104)

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Convert the abc delta to wye : R1

(28) (48) (28 48 124)

6.72

R2

(28) (124) (28 48 124)

17.36

R3

(124) (48) (28 48 124)

29.76

R eq 3.28 6.72 [(17.36 12.64) //(29.76 30.24)] 15 R eq 10 (30 // 60) 15 R eq 10 20 15 45

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

ig = 540 / 45 = 12 A

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

i2 ( 303060 )12 4A

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

KVL left loop bdcb, (12.64)8 4(30.24) v 0 v 19.84V 19.84 v 124 124 KCL at b, i1 io 8

io

i1

0.16 8

i1 7.84 A Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

0.16 A

Example similar to Problem 3.12 page 91

Find vo , vg 60 // 120 40 i35

(25)(50) 10 A 125

vo (10)(40) 400V vo 35 i35 750V vg 8(25) 750V vg 950V Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

Example similar to Problem 3.10 page 91

i2 k

(4.5)(7.5) 5 7.5

2.7 m A

v3 k (2.7m)(3k ) 8.1V i1.5 k 4.5 2.7 1.8 mA v6 k (6) (1.8) 10.8V vo 8.1 10.8

Dr. Vishnu K. Lakdawala Dept. of ECE – OLD DOMINION UNIVERSITY ECE 201 : Lecture Notes 3 – SIMPLE RESISTIVE CIRCUITS

2.7V...