chapter 02-1.ppt

8/14/2019 Chapter 02-1.ppt

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Chapter 2

Resistive Circuits

Chapter 2

Resistive Circuits

1. Solve circuits (i.e., find currents and

voltages of interest) by combining

resistances in series and parallel.

2. Apply the voltage-division and current-

division

principles.3. Solve circuits by the node-voltage

technique.

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Chapter 2

Resistive Circuits

4. Solve circuits by the mesh-current technique.

5. Find Thévenin and Norton equivalents.

6. Apply the superposition principle.

7. Draw the circuit diagram and state the principl

of operation for the Wheatstone bridge.

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Chapter 2

Resistive Circuits

8/14/2019 Chapter 02-1.ppt


Chapter 2

Resistive Circuits

Circuit Analysis using

Series/Parallel Equivalents1. Begin by locating a combination of

resistances that are in series or parallel.

Often the place to start is farthest from thesource.

2. Redraw the circuit with the equivalentresistance for the combination found instep 1.

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Chapter 2Resistive Circuits

3. Repeat steps 1 and 2 until the circuit isreduced as far as possible. Often (but notalways) we end up with a single source anda single resistance.

4. Solve for the currents and voltages in thefinal equivalent circuit.

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8/14/2019 Chapter 02-1.ppt



Voltage Division

total

321

111 v

R R R

Ri Rv

total

321

222 v

R R R

Ri Rv

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8/14/2019 Chapter 02-1.ppt



Application of the Voltage-

Division Principle

V5.1

156000200010001000

1000

total

4321

11

v

R R R R

Rv

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8/14/2019 Chapter 02-1.ppt



Current Division

total

21

2

1

1 i R R

R

R

vi

total

21

1

2

2 i R R

R

R

vi

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8/14/2019 Chapter 02-1.ppt



Application of the Current-

Division Principle

206030

6030

32

32

eq R R

R R R

A10152010

20

eq1

eq

1

si

R R

Ri

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8/14/2019 Chapter 02-1.ppt



Although they are very

important concepts,series/parallel equivalents and

the current/voltage divisionprinciples are not sufficient to

solve all circuits.

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Node Voltage Analysis

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8/14/2019 Chapter 02-1.ppt



Writing KCL Equations in

Terms of the Node Voltagesfor Figure 2.16

s

vv 1

03

32

4

2

2

12

R

vv

R

v

R

vv

03

23

5

3

1

13

R

vv

R

v

R

vv

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8/14/2019 Chapter 02-1.ppt



0

2

21

1

1

si

R

vv

R

v

04

32

3

2

2

12

R

vv

R

v

R

vv

si

R

vv

R

v

4

23

5

3

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8/14/2019 Chapter 02-1.ppt



Circuits with Voltage

Sources

We obtain dependent

equations if we use all of thenodes in a network to write

KCL equations.

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0

1515

3

2

4

2

1

1

2

1

R

v

R

v

R

v

R

v

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8/14/2019 Chapter 02-1.ppt



010 21 vv

13

32

2

31

1

1

R

vv

R

vv

R

v

0

4

3

3

23

2

13

R

v

R

vv

R

vv

14

3

1

1

R

v

R

v

8/14/2019 Chapter 02-1.ppt



Node-Voltage Analysis with

a Dependent Source

First, we write KCL equationsat each node, including the

current of the controlled

source just as if it were anordinary current source.

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8/14/2019 Chapter 02-1.ppt



x s ii

R

vv2

1

21

03

32

2

2

1

12

R

vv

R

v

R

vv

02

4

3

3

23

xi

R

v

R

vv

8/14/2019 Chapter 02-1.ppt



Next, we find an expression for the

controlling variable i x in terms of the

node voltages.

3

23

R

vvi x

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Substitution yields

3

23

1

21 2 R

vvi

R

vv s

03

32

2

2

1

12

R

vv

R

v

R

vv

023

23

4

3

3

23

R

vv

R

v

R

vv

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8/14/2019 Chapter 02-1.ppt



Node-Voltage Analysis

1. Select a reference node and

assign variables for the unknown

node voltages. If the reference

node is chosen at one end of an

independent voltage source, one

node voltage is known at the

start, and fewer need to be

computed.

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2. Write network equations. First, use

KCL to write current equations for

nodesand supernodes. Write as many current

equations as you can without using all

ofthe nodes. Then if you do not have

enough equations because of voltage

sources

connected between nodes, use KVL to

write additional equations.

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3. If the circuit contains dependent

sources, find expressions for the

controlling variables in terms of the

node voltages. Substitute into the

network equations, and obtain

equations having only the node

voltages as unknowns.

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4. Put the equations into standard formand solve for the node voltages.

5. Use the values found for the nodevoltages to calculate any other

currents or voltages of interest.

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8/14/2019 Chapter 02-1.ppt



Mesh Current Analysis

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Choosing the Mesh

Currents When several mesh currents flow throughone element, we consider the current in

that element to be the algebraic sum of

the mesh currents.

Sometimes it is said that the mesh

currents are defined by “soaping thewindow panes.”

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8/14/2019 Chapter 02-1.ppt



Writing Equations to Solve

for Mesh Currents

If a network contains only resistances

and independent voltage sources, wecan write

the required equations by following each

current around its mesh and applying

KVL.

U i thi tt f h 1 f Fi

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Using this pattern for mesh 1 of Figure

2.32a, we have

For mesh 2, we obtain

024123 Bvi Rii R

For mesh 3, we have

031132 Bvi Rii R

021312 A s

vii Rii R

In Figure 2 32b

8/14/2019 Chapter 02-1.ppt



In Figure 2.32b

021441211 Avii Rii Ri R

032612425 ii Rii Ri R

043823637 ii Rii Ri R

034814243 ii Rii Ri R

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8/14/2019 Chapter 02-1.ppt



M h C i Ci i

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Mesh Currents in Circuits

Containing Current Sources

A common mistake made by beginning

students is to assume that the voltages

across current sources are zero. InFigure 2.35, we have:

A21 i

0105)(10 212 iii

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Combine meshes 1 and 2 into a supermesh In other

8/14/2019 Chapter 02-1.ppt



Combine meshes 1 and 2 into a supermesh. In other

words, we write a KVL equation around the periphery of

meshes 1 and 2 combined.

01042 32311 iiiii

Mesh 3:

0243 13233 iiiii

512 ii

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8/14/2019 Chapter 02-1.ppt



026420 221 iii

124

iiv x

22iv x

M h C t A l i

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Mesh-Current Analysis

1. If necessary, redraw the network

without crossing conductors or elements.

Then define the mesh currents flowing

around each of the open areas defined

by the network. For consistency, we

usually select a clockwise direction foreach of the mesh currents, but this is not

a requirement.

2 Write network equations stopping after

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2. Write network equations, stopping after

the number of equations is equal to the

number of mesh currents. First, use KVLto write voltage equations for meshes that

do not contain current sources. Next, if

any current sources are present, writeexpressions for their currents in terms of

the mesh currents. Finally, if a current

source is common to two meshes, write aKVL equation for the supermesh.

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3. If the circuit contains dependent

sources, find expressions for the

controlling

variables in terms of the mesh currents.

Substitute into the network equations,

and obtain equations having only the

mesh currents as unknowns.

4 Put the equations into standard form

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4. Put the equations into standard form.

Solve for the mesh currents by use of

determinants or other means.

5. Use the values found for the mesh

currents to calculate any other currentsor voltages of interest.

8/14/2019 Chapter 02-1.ppt



Thévenin Equivalent

Circuits

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8/14/2019 Chapter 02-1.ppt



Thévenin Equivalent

Circuits ocvV

t

sc

oc

i

v R

t

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8/14/2019 Chapter 02-1.ppt



Finding the Thévenin

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g

Resistance Directly

When zeroing a voltage source, it becomes ashort circuit. When zeroing a current source,

it becomes an open circuit.

We can find the Thévenin resistance by

zeroing the sources in the original network

and then computing the resistance between

the terminals.

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8/14/2019 Chapter 02-1.ppt



Step-by-step

8/14/2019 Chapter 02-1.ppt



Thévenin/Norton-

Equivalent-Circuit Analysis 1. Perform two of these:

a. Determine the open-circuit voltage V t = v oc.

b. Determine the short-circuit current I n =i sc.

c. Zero the sources and find the Thévenin

resistance R t looking back into theterminals.

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2. Use the equation V t = R t I n to compute

the remaining value.

3. The Thévenin equivalent consists of a

voltage source V t in series with R t .

4. The Norton equivalent consists of a

current source I n in parallel with R t .

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8/14/2019 Chapter 02-1.ppt


Chapter 2

Resistive Circuits

Source Transformations

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Chapter 2

Resistive Circuits

8/14/2019 Chapter 02-1.ppt


Chapter 2

Resistive Circuits

Maximum Power Transfer

The load resistance that absorbs the

maximum power from a two-terminal

circuit is equal to the Théveninresistance.

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Chapter 2

Resistive Circuits

8/14/2019 Chapter 02-1.ppt


Chapter 2

Resistive Circuits

SUPERPOSITION

8/14/2019 Chapter 02-1.ppt


Chapter 2

Resistive Circuits

SUPERPOSITION

PRINCIPLE

The superposition principle states

that the total response is the sum of

the responses to each of theindependent sources acting

individually. In equation form, this is

nT r r r r 21

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Chapter 2

Resistive Circuits

8/14/2019 Chapter 02-1.ppt


8/14/2019 Chapter 02-1.ppt


Chapter 2

Resistive Circuits

8/14/2019 Chapter 02-1.ppt


Chapter 2

Resistive Circuits

WHEATSTONE BRIDGE

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The Wheatstone bridge is used by mechanical

and civil engineers to measure the resistancesof strain gauges in experimental stress studies

of machines and buildings.

3

1

2 R

R

R R

x

chapter 02-1.ppt

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