Lecture 4

Notes in Voltages Sources , Current Sources, and Star - Delta transformation

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Example 1

Example 2Allowed

Not Allowed

Example 3

Example 4

Example 5Allowed Not Allowed

Current Sources in Series

Series and Parallel SourcesVoltage sources in series can be combined into

a single voltage source:

Current sources in parallel can be combined into a single current source:

Ia + Ib + Ic

Va+Vb+Vc

Va

Vb

Vc

Ia Ib

Ic

Independent SourcesIndependent voltage

source

maintains the prescribed voltage across its terminals regardless of the current drawn from it

Independent current source

maintains the prescribed current through its terminals regardless of the voltage across those terminals

“Controlled” or “Dependent” Sources

• A voltage or current source whose value “depends” on the value of voltage or current elsewhere in the circuit

• Use a diamond-shaped symbol

Dependent Voltage Sources

+–

6Vx

Voltage-Controlled Voltage Source (VCVS)

6000Ix

Current-Controlled Voltage Source (CCVS)

+–

Dependent Current Sources

0.006Vx

Voltage-Controlled Current Source (VCCS)

6Ix

Current-Controlled Current Source (CCCS)

Practical Dependent SourcesOperational amplifiersTransistors

Bipolar Junction Transistors (BJTs)Metal-Oxide-Semiconductor Field Effect

Transistors (MOSFETs)Voltage and current regulatorsOther devices include:

Photodetectors, LEDs, and lasersPiezoelectric devicesThermocouples, thermovoltaic sources

Star - Delta Transformation:

a

bc

a

bc

R a

R bR c

R 1 R 2

R 3

(a ) w ye c o n fig u ra tio n (b ) d e lta c o n fig u ra tio n

a

accbba

c

accbba

b

accbba

R

RRRRRRR

R

RRRRRRR

R

RRRRRRR

3

2

1

321

31

321

32

321

21

RRR

RRR

RRR

RRR

RRR

RRR

c

b

a

Q: Find the resistance between the points E and F ?

Solution

•Ans. : 5.6 Ω

Home WorkQ 1 : Find Rab and I

?

13

100 V

50

10

i a

b Figure 2.54

Q2 : Use -to-Y transformation to find the voltages v1 and v2 ?

1 10

24 V

15

+V1-

+V2-

Q 3 :Find the total resistance in the circuit below?