RESISTIVE CIRCUITS LEARN TO ANALYZE THE SIMPLEST CIRCUITS THE VOLTAGE DIVIDER THE CURRENT DIVIDER SERIES/PARALLEL RESISTOR COMBINATIONS - A TECHNIQUE TO.

RESISTIVE CIRCUITS

• LEARN TO ANALYZE THE SIMPLEST CIRCUITS• THE VOLTAGE DIVIDER• THE CURRENT DIVIDER

• SERIES/PARALLEL RESISTOR COMBINATIONS - A TECHNIQUE TO REDUCE THE COMPLEXITY OF SOME CIRCUITS

• WYE - DELTA TRANSFORMATION - A TECHNIQUE TO REDUCE COMMON RESISTOR CONNECTIONS THAT ARE NEITHER SERIES NOR PARALLEL

SERIES PARALLEL RESISTOR COMBINATIONS

UP TO NOW WE HAVE STUDIED CIRCUITS THATCAN BE ANALYZED WITH ONE APPLICATION OFKVL(SINGLE LOOP) OR KCL(SINGLE NODE-PAIR)

WE HAVE ALSO SEEN THAT IN SOME SITUATIONSIT IS ADVANTAGEOUS TO COMBINE RESISTORS TO SIMPLIFY THE ANALYSIS OF A CIRCUIT

NOW WE EXAMINE SOME MORE COMPLEX CIRCUITSWHERE WE CAN SIMPLIFY THE ANALYSIS USINGTHE TECHNIQUE OF COMBINING RESISTORS…

… PLUS THE USE OF OHM’S LAW

SERIES COMBINATIONS

PARALLEL COMBINATION

Np GGGG ...21

FIRST WE PRACTICE COMBINING RESISTORS

6k||3k

(10K,2K)SERIES

SERIESk3

kkk 412||6

k12k3

k5

EXAMPLES COMBINATION SERIES-PARALLEL

k9

kkk 69||18

kkk 1066

RESISTORS ARE IN SERIES IF THEY CARRYEXACTLY THE SAME CURRENT

RESISTORS ARE IN PARALLEL IF THEY ARECONNECTED EXACTLY BETWEEN THE SAME TWONODES

If the drawing gets confusing…Redraw the reduced circuit and start again

EFFECT OF RESISTOR TOLERANCE

10% :TOLERANCE RESISTOR

2.7k : VALUERESISTORNOMINAL

RANGES FOR CURRENT AND POWER?

mAI

mAI

115.47.29.0

10

367.37.21.1

10

max

min

:CURRENT MAXIMUM

:CURRENT MINIMUM

mAI 704.37.2

10

:CURRENTNOMINAL

_

mWP 04.377.2

10 2 :POWERNOMINAL

:POWER MAXIMUM

:)POWER(VI MINIMUM min

mW

mW

15.41

67.33

CIRCUIT WITH SERIES-PARALLEL RESISTOR COMBINATIONS

COMBINING RESISTORS IN SERIES ELIMINATESONE NODE FROM THE CIRCUIT.COMBINING RESISTORS IN PARALLEL ELIMINATESONE LOOP FROM THE CIRCUIT

THE COMBINATION OF COMPONENTS CAN REDUCETHE COMPLEXITY OF A CIRCUIT AND RENDER ITSUITABLE FOR ANALYSIS USING THE BASIC TOOLS DEVELOPED SO FAR.

GENERAL STRATEGY: •REDUCE COMPLEXITY UNTIL THE CIRCUIT BECOMES SIMPLE ENOUGH TO ANALYZE.•USE DATA FROM SIMPLIFIED CIRCUIT TO COMPUTE DESIRED VARIABLES IN ORIGINAL CIRCUIT - HENCE ONE MUST KEEP TRACK OF ANY RELATIONSHIP BETWEEN VARIABLES

FIRST REDUCE IT TO A SINGLE LOOP CIRCUITk12kk 12||4

k6

kk 6||6

k

VI

12

121 )12(

93

3

aV

SECOND: “BACKTRACK” USING KVL, KCL OHM’S

k

VI a

62 :SOHM'0321 III :KCL

3*3 IkVb :SOHM'

3I

…OTHER OPTIONS...

4

34

*4124

12

IkV

II

b

5

345

*3

0

IkV

III

C

:SOHM'

:KCL

kkk 12||2

VVkk

kVO 1)3(

21

1

:DIVIDER VOLTAGE

kkk 211

AAkk

kIO 1)3(

21

1

:DIVIDER CURRENT

LEARNING BY DOING

TIONSTRANSFORMAY

THIS CIRCUIT HAS NO RESISTOR IN SERIES OR PARALLEL

IF INSTEADOF THIS

WE COULDHAVE THIS

THEN THE CIRCUIT WOULDBECOME LIKE THIS ANDBE AMENABLE TO SERIESPARALLEL TRANSFORMATIONS

Y

baab RRR

)(|| 312 RRRRab

321

312 )(

RRR

RRRRR ba

321

213 )(

RRR

RRRRR cb

321

321 )(

RRR

RRRRR ac

SUBTRACT THE FIRST TWO THEN ADDTO THE THIRD TO GET Ra

Y

RRR

RRR

RRR

RRR

RRR

RRR

c

b

a

321

13

321

32

321

21

a

b

b

a

R

RRR

R

R

R

R 13

3

1 c

b

c

b

R

RRR

R

R

R

R 12

1

2

REPLACE IN THE THIRD AND SOLVE FOR R1

Y

R

RRRRRRR

R

RRRRRRR

R

RRRRRRR

a

accbba

c

accbba

b

accbba

3

2

1

Y

LEARNING EXAMPLE: APPLICATION OF WYE-DELTA TRANSFORMATION

SI COMPUTE DELTA CONNECTION

a b

c

a b

c

kkkkkkREQ 10)42(||936

Y

RRR

RRR

RRR

RRR

RRR

RRR

c

b

a

321

13

321

32

321

21

1R

2R

3R kkk

kk

18612

612

mAk

VIS 2.1

10

12

ONE COULD ALSO USE A WYE - DELTA TRANSFORMATION ...