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ECE 1311

Chapter 2 Basic Laws

1

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Outlines

2

Ohms law

Nodes, branches and loops

Kirchoffs laws

Series resistors and voltage division

Parallel resistors and current division

Wye-Delta transformations

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Ohms Law

4

Gives a relationship between current andvoltage within a circuit element.

The voltage across a resistor is directlyproportional to the current flowing throughthe resistor.

Therefore:

R is called resistor and measured in Ohms( ).Has the ability to resist the flow of electriccurrent.

iv

iv

Ror iRv

iRv

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Resistor

5

Its value varies from 0 to infinity.Two extreme values: 0 and infinity

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Short circuit Open circuit

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Conductance and Power ( p )

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Conductance:The ability of an element to conduct electric current.Measured in Siemens (S) or mhos.Reciprocal of resistance.

Power:

RG 1

watts Rv

v Rv

watts RiiRiiv p2

2

)(

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Example 1

8

Determine voltage ( v ), conductance ( G ) and power ( p)from the circuit shown.

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Example 2

9

Calculate current i from the circuit shown when theswitch is in position 1.Find the current when the switch is in position 2.

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Nodes, Branches and Loops

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Branch:Represents a single element (i.e. voltage, resistor, etc.)

Node:The point of connection between two or more branches.

Loop:Any closed path in a circuit.

Note:Two or more elements are in SERIES if they exclusively share a singlenode and consequently carry the same current .Two or more elements are in PARALLEL if they are connected tothe same two nodes and consequently have the same voltage.

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Example 3

11

Determine how many branches and nodes in the circuitshown below.Identify which elements are in series and which are inparallel.

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Example 4

12

Determine how many branches and nodes in the circuitshown below.Identify which elements are in series and which are inparallel.

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30 V

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Example 5

14

Write an equation for each circuit shown below.

(a) (b)

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Kirchoffs Voltage Law (KVL)

16

Applied to a loop in a circuit.

KVL states that the algebraic sum of all voltages around a closedpath (or loop) is zero.

Or:

.

0 dropsvoltagerisesvoltage

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Example 7

17

Determine v 1, v 2 and v 3 in the circuit below.

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Example 8

18

Determine V 0 in the circuit below.

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Series Resistors

20

Same current flowing through series resistors.

Therefore, for N resistors in series:.

21

21

2121

21

2211

)(

0

:

R R Rwhere

Rv

R Rv

i

iR R Rivvv

vvv

KVL

iRvand iRv

eq

eq

eq

N eq R R R R ......21

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Voltage Division

21

Previously:

Therefore:

eq Rv

R Rv

i

iRvand iRv

21

2211

2122

2111 R R

v Rvand

R Rv

Rv

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Parallel Resistors

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Common voltage across parallel resistors.

Therefore, for N resistors in parallel:

.

21

21

21

21

2121

2211

111

11

R R R R

Rthus R R R

Rv

R Rvi

Rv

Rv

iii

Ri Riv

eqeq

eq

N eq R R R R

1......

111

21

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Current Division

23

Previously:

Therefore:

eqiRv

Ri Riv 2211

21

12

21

21

R R

iRiand

R R

iRi

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Conductance

24

Series conductance:

Parallel conductance: N eq GGGG ......21

N eq GGGG1

......111

21

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Example 10

25

Calculate v 1 , v 2 , i 1 and i 2 in the circuit below.

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Example 11

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Calculate i 1 through i 4.

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Example 12

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Determine v and i .

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Example 14

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Determine Rab.

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Example 15

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Determine v x and power absorbed by the 12

resistor.

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Wye-Delta Transformations

31

How to simplify the circuit given below?

The resistors are neither in series nor parallel.

Use wye-delta transformations to simplify.

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Two Forms of Same Network

32

Y network T network

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Two Forms of Same Network

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network network

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Wye-Delta Transformations

35

cba

ba

cba

ca

cba

cb

R R R R R

R

R R R R R

R

R R R

R R R

3

2

1

3

133221

2

133221

1

133221

R

R R R R R R R

R

R R R R R R R

R

R R R R R R R

c

b

a

Delta to Y Y to Delta

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Example 17

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Determine Rab

.

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Example 18

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Determine I0.