Dept of Electrical & Electronics

ELE 1001: BASIC ELECTRICAL TECHNOLOGY

LECTURE 02

RESISTANCE &STAR-DELTA TRANSFORMATION

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We will learn here…

Fundamentals of Resistor

Star & Delta connections

Star-Delta & Delta-Star Transformations

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Resistors Resistance

Property which opposes the flow of current

R = V/I Unit – Ohms () Power P = VI = V2/R = I2R

Conductance Reciprocal of resistance Symbol: G Unit: siemens (S)

R

V

I

+ -

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Resistivity & Temperature Coefficient

For a homogeneous material:

where, ρ= resistivity, l= length & a= cross-sectional area of the material

where, α0 = Temp coefficient of resistivity at 0°CR0 = Resistance at 0°C

Positive temp coefficient: Aluminum, Copper, Gold, TungstenNegative temp coefficient: Carbon, Germanium (pure), Silicon (pure)

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Resistive Circuits

Resistors in parallel:

Resistors in series:

R1

R2

R3

+ +

+ +

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Current Division in Parallel Circuits

R1

R2

V

I I 2I 1

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Voltage Division in Series Circuits

R 1

R 2

V

+ V1 -

- V2 +

I

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Star & Delta Connections

A

BC

Rab

Rbc

Rca

BC

Ra

RbRc

A

Star Connection

Delta Connection

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Star-Delta Transformation

BC

Ra

RbRc

AA

BC

Rab

Rbc

Rca

Delta to Star Transformation:

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Star-Delta Transformation contd…Star to Delta Transformation:

BC

Ra

RbRc

A A

BC

Rab

Rbc

Rca

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Example 1

For the circuit shown, determine the power supplied to the resistive network using star- delta transformation.

G

2 0

5

1 0 0

1 7 .5

4 0

1 0 1 2 V

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• Convert 20 Ω, 40 Ω & 100 Ω delta-connected resistors into star

• OR• Convert 100 Ω, 17.5 Ω & 5 Ω delta-

connected resistors into star

Hint for Example 1…

Ans: Psupplied

= 4.8 W

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Example 2

Find the power dissipated in 10Ω resistor using star-delta transformation.

Ans: P10Ω = 2.72 W

1 5

1 0

2 0 5

4

6 3 0

2 0

1 2 V

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Example 3

Find the equivalent resistance between A & B using star-delta transformation.

1 0

9 .3 7 5 7 .5

2 5 1 5

3

5 .5

6 .2 5 5

2 5

1 5

A B

Ans: RAB

= 15 Ω

Dept of Electrical & Electronics

Summary

We started with Resistance and its properties

Then discussedResistive circuits Current Division in Parallel CircuitVoltage Division in Series CircuitStar-Delta Transformation

Concluded withApplication of star-delta & source

transformation concepts.