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Schedule…. Examine Yourselves. 2 Cor. 13: 5 5 Examine yourselves, whether ye be in the faith; prove your own selves. Lecture 12 – Exam 1 Review. Chapters 2 - 3. Exam 1. 20 – 23 February (Tuesday – Friday) Chapters 2 and 3 18 questions 15 multiple choice (answer on bubble sheet!)

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Schedule

Schedule…

Discussion #12 –Exam 1 Review


Examine yourselves

Examine Yourselves

2 Cor. 13: 5

5 Examine yourselves, whether ye be in the faith; prove your own selves.

Discussion #12 –Exam 1 Review


Lecture 12 exam 1 review

Lecture 12 – Exam 1 Review

Chapters 2 - 3

Discussion #12 – Exam 1 Review


Exam 1

Exam 1

  • 20 – 23 February (Tuesday – Friday)

  • Chapters 2 and 3

  • 18 questions

    • 15 multiple choice (answer on bubble sheet!)

      • 1 point each

    • 3 long answer (show your work!)

      • Up to 5 points each

  • Closed book!

    • One 3x5 card allowed

  • Calculators allowed

  • No time limit

  • Study lecture slides and homework

Discussion #12 –Exam 1 Review


Exam 1 review overview

Exam 1 Review…Overview

  • Kirchoff’s current law

  • Kirchoff’s voltage law

  • Passive sign convention

  • Voltage/current dividers (Ohm’s Law)

  • Wheatstone bridge

  • Measuring Devices

  • Node voltage method

  • Mesh current method

  • Principle of superposition

  • Source transformation

  • Thévenin equivalent circuits

  • Norton equivalent circuits

  • Maximum power transfer

  • Dependent Sources

Discussion #12 –Exam 1 Review


Exam 1 review kcl

Exam 1 Review…KCL

  • What is Kirchoff’s current law?

Discussion #12 –Exam 1 Review


Exam 1 review kcl1

Node a

is2

is1

i2

+

R2

_

Vs2

+

_

Vs1

R4

i4

R3

i5

i3

R5

Exam 1 Review…KCL

  • What is Kirchoff’s current law?

    a) What is an expression for the current at Node a?

Discussion #12 –Exam 1 Review


Exam 1 review kcl2

Node a

is2

is1

i2

+

R2

_

Vs2

+

_

Vs1

R4

i4

R3

i5

i3

R5

Exam 1 Review…KCL

  • What is Kirchoff’s current law?

    a) What is an expression for the current at Node a?

Discussion #12 –Exam 1 Review


Exam 1 review kcl3

Node a

is2

is1

i2

+

R2

_

Vs2

+

_

Vs1

R4

i4

R3

i5

i3

R5

Exam 1 Review…KCL

  • What is Kirchoff’s current law?

    a) What is an expression for the current at Node a?

    b) what expressions for the current through R2 are valid?

Discussion #12 –Exam 1 Review


Exam 1 review kcl4

Node a

is2

is1

i2

+

R2

_

Vs2

+

_

Vs1

R4

i4

R3

i5

i3

R5

Exam 1 Review…KCL

  • What is Kirchoff’s current law?

    a) What is an expression for the current at Node a?

    b) what expressions for the current through R2 are valid?

Discussion #12 –Exam 1 Review


Exam 1 review kcl5

Node a

is2

is1

i2

+

R2

_

Vs2

+

_

Vs1

R4

i4

R3

i5

i3

R5

Exam 1 Review…KCL

  • What is Kirchoff’s current law?

    a) What is an expression for the current at Node a?

    b) what expressions for the current through R2 are valid?

Discussion #12 –Exam 1 Review


Exam 1 review kvl

Exam 1 Review…KVL

  • What is Kirchoff’s voltage law?

Discussion #12 –Exam 1 Review


Exam 1 review kvl1

is

i1

i3

i2

+

R3

+

R2

+

R1

+

_

Vs

Exam 1 Review…KVL

  • What is Kirchoff’s voltage law?

    • If Vs = 3V, what are the voltages across R1, R2, and R3?

Discussion #12 –Exam 1 Review


Exam 1 review kvl2

is

i1

i3

i2

+

R3

+

R2

+

R1

+

_

Vs

Exam 1 Review…KVL

  • What is Kirchoff’s voltage law?

    • If Vs = 3V, what are the voltages across R1, R2, and R3?

Discussion #12 –Exam 1 Review


Exam 1 review passive sign

Exam 1 Review…Passive Sign

  • What is the passive sign convention?

Discussion #12 –Exam 1 Review


Exam 1 review passive sign1

i

i

a

b

a

b

_

_

+

+

vba

vab

Exam 1 Review…Passive Sign

  • What is the passive sign convention?

    • Which element dissipates power and which generates power?

Discussion #12 –Exam 1 Review


Exam 1 review passive sign2

i

i

a

b

a

b

_

_

+

+

vba

vab

Exam 1 Review…Passive Sign

  • What is the passive sign convention?

    • Which element dissipates power and which generates power?

  • Passive Element (load)

  • power dissipated = vi

  • power generated = -vi

  • Active Element (source)

  • power dissipated = -vi

  • power generated = vi

Positive voltage

Negative voltage

Discussion #12 –Exam 1 Review


Exam 1 review passive sign3

ie = 2A

– 3V +

B

ia

+

10V

E

D

A

id =3A

C

– 5V +

Exam 1 Review…Passive Sign

  • What is the passive sign convention?

    • Find the power dissipated by each element

Discussion #12 –Exam 1 Review


Exam 1 review passive sign4

ie = 2A

– 3V +

a

B

ia

+

10V

E

D

A

id =3A

C

– 5V +

Exam 1 Review…Passive Sign

  • What is the passive sign convention?

    • Find the power dissipated by each element

+

va

+

10V

Loop1

NB: since load D and load E share the same nodes their voltages will be the same

Discussion #12 –Exam 1 Review


Exam 1 review passive sign5

Exam 1 Review…Passive Sign

  • What is the passive sign convention?

    • Find the power dissipated by each element

ie = 2A

– 3V +

B

ia = 5A

+

10V

+

12V

+

10V

E

D

A

id =3A

C

– 5V +

Discussion #12 –Exam 1 Review


Exam 1 review dividers

Exam 1 Review…Dividers

  • What is a voltage/current divider?

Discussion #12 –Exam 1 Review


Exam 1 review dividers1

Exam 1 Review…Dividers

  • What is a voltage/current divider?

Discussion #12 –Exam 1 Review


Exam 1 review dividers2

+

Vs

_

Exam 1 Review…Dividers

  • What is a voltage/current divider?

    • Using a voltage divider find the voltage across R3

      Vs = 3V, R1 = 10Ω, R2 = 6Ω, R3 = 8Ω

– v1 +

i

R1

+

v2

R2

+ v3 –

R3

Discussion #12 –Exam 1 Review


Exam 1 review dividers3

– v1 +

i

+

R1

Vs

_

+

v2

R2

+ v3 –

R3

Exam 1 Review…Dividers

  • What is a voltage/current divider?

    • Using a voltage divider find the voltage across R3

      Vs = 3V, R1 = 10Ω, R2 = 6Ω, R3 = 8Ω

Discussion #12 –Exam 1 Review


Exam 1 review dividers4

i1

i3

i2

R3

+

R1

+

R2

+

is

Exam 1 Review…Dividers

  • What is a voltage/current divider?

    • Using a current divider find i1

      R1 = 10Ω, R2 = 2 Ω, R3 = 20 Ω, Is = 4A

Discussion #12 –Exam 1 Review


Exam 1 review dividers5

i1

i3

i2

R3

+

R1

+

R2

+

is

Exam 1 Review…Dividers

  • What is a voltage/current divider?

    • Using a current divider find i1

      R1 = 10Ω, R2 = 2 Ω, R3 = 20 Ω, Is = 4A

Discussion #12 –Exam 1 Review


Exam 1 review wheatstone

c

R1

R3

va

vb

a

b

+

vs

R2

Rx

_

d

Exam 1 Review…Wheatstone

  • What is the voltage across the terminals a and b of the Wheatstone bridge?

Discussion #12 –Exam 1 Review


Exam 1 review wheatstone1

c

R1

R3

va

vb

a

b

+

vs

R2

Rx

_

d

Exam 1 Review…Wheatstone

  • What is the voltage across the terminals a and b of the Wheatstone bridge?

Discussion #12 –Exam 1 Review


Exam 1 review measuring

Exam 1 Review…Measuring

  • How do measuring devices connect to circuits?

Discussion #12 –Exam 1 Review


Exam 1 review measuring1

R

Ω

Exam 1 Review…Measuring

  • How do measuring devices connect to circuits?

NB: the resistance of an element can only be measured when the element is disconnected from all other circuit elements

Discussion #12 –Exam 1 Review


Exam 1 review measuring2

R1

A

+

vs

_

i

R2

Exam 1 Review…Measuring

  • How do measuring devices connect to circuits?

NB: 1. the ammeter must be connected in series with the circuit element

2. the ammeter should not restrict the flow of current (i.e. cause a voltage drop)

– an ideal ammeter has zero resistance

Discussion #12 –Exam 1 Review


Exam 1 review measuring3

+

R2

+

v2

V

+

vs

_

i

Exam 1 Review…Measuring

  • How do measuring devices connect to circuits?

NB: 1. the voltmeter must be connected in parallel with the circuit element

2. the voltmeter should not draw any current away from the element

– an ideal voltmeter has infinite resistance

Discussion #12 –Exam 1 Review


Exam 1 review measuring4

R1

+

R2

W

+

vs

_

i

Exam 1 Review…Measuring

  • How do measuring devices connect to circuits?

NB: 1. the wattmeter must be connected in parallel with the circuit element,

but also in series with the circuit.

– a wattmeter is simply the combination of a voltmeter and an ammeter

Discussion #12 –Exam 1 Review


Exam 1 review node voltage

Exam 1 Review…Node Voltage

  • What is the node voltage method of circuit analysis?

Discussion #12 –Exam 1 Review


Exam 1 review node voltage1

R2

ia

ib

R4

R3

R1

Exam 1 Review…Node Voltage

  • What is the node voltage method of circuit analysis?

    • Find all unknown voltages

      ia = 1mA, ib = 2mA, R1 = 1kΩ, R2= 500Ω, R3 = 2.2kΩ, R4 = 4.7kΩ

Discussion #12 –Exam 1 Review


Exam 1 review node voltage2

i2

vb

Node b

Node a

va

+ R2 –

+

ib

+

R4

+

R3

+

R1

i1

i3

i4

vc

Node c

Exam 1 Review…Node Voltage

  • What is the node voltage method of circuit analysis?

    • Find all unknown voltages

      ia = 1mA, ib = 2mA, R1 = 1kΩ, R2= 500Ω, R3 = 2.2kΩ, R4 = 4.7kΩ

  • Label currents and voltages (polarities “arbitrarily” chosen)

  • Choose Node c (vc) as the reference node (vc = 0)

  • Define remaining n – 1 (2) voltages

    • va is independent

    • vb is independent

  • Apply KCL at nodes a and b

+

ia

Discussion #12 –Exam 1 Review


Exam 1 review node voltage3

i2

vb

Node b

Node a

va

+ R2 –

+

ib

+

R4

+

R3

+

R1

i1

i3

i4

vc

Node c

Exam 1 Review…Node Voltage

  • What is the node voltage method of circuit analysis?

    • Find all unknown voltages

      ia = 1mA, ib = 2mA, R1 = 1kΩ, R2= 500Ω, R3 = 2.2kΩ, R4 = 4.7kΩ

  • Apply KCL at nodes a and b

+

ia

Discussion #12 –Exam 1 Review


Exam 1 review node voltage4

i2

vb

Node b

Node a

va

+ R2 –

+

ib

+

R4

+

R3

+

R1

i1

i3

i4

vc

Node c

Exam 1 Review…Node Voltage

  • What is the node voltage method of circuit analysis?

    • Find all unknown voltages

      ia = 1mA, ib = 2mA, R1 = 1kΩ, R2= 500Ω, R3 = 2.2kΩ, R4 = 4.7kΩ

  • Express currents in terms of voltages

+

ia

Discussion #12 –Exam 1 Review


Exam 1 review node voltage5

i2

vb

Node b

Node a

va

+ R2 –

+

ib

+

R4

+

R3

+

R1

i1

i3

i4

vc

Node c

Exam 1 Review…Node Voltage

  • What is the node voltage method of circuit analysis?

    • Find all unknown voltages

      ia = 1mA, ib = 2mA, R1 = 1kΩ, R2= 500Ω, R3 = 2.2kΩ, R4 = 4.7kΩ

  • Solve the n – 1 – m equations

+

ia

Discussion #12 –Exam 1 Review


Exam 1 review mesh current

Exam 1 Review…Mesh Current

  • What is the mesh current method of circuit analysis?

Discussion #12 –Exam 1 Review


Exam 1 review mesh current1

R4

ic

R3

R1

R2

vs

Is

ia

ib

+

Exam 1 Review…Mesh Current

  • What is the mesh current method of circuit analysis?

    • Find the mesh currents

      Vs = 6V, Is = 0.5A, R1= 3Ω, R2= 8Ω, R3 = 6Ω, R4 = 4Ω

Discussion #12 –Exam 1 Review


Exam 1 review mesh current2

+R4–

ic

+R3 –

+ R1–

+

R2

vs

Is

ia

ib

+

Exam 1 Review…Mesh Current

  • What is the mesh current method of circuit analysis?

    • Find the mesh currents

      Vs = 6V, Is = 0.5A, R1= 3Ω, R2= 8Ω, R3 = 6Ω, R4 = 4Ω

  • Mesh current directions given

  • Voltage polarities chosen and labeled

  • Identify n – m (3) mesh currents

    • ia is dependent (ia = is)

    • ia is independent

    • ic is independent

  • Apply KVL around meshes b and c

Discussion #12 –Exam 1 Review


Exam 1 review mesh current3

+R4–

ic

+R3 –

+ R1–

+

R2

vs

Is

ia

ib

+

Exam 1 Review…Mesh Current

  • What is the mesh current method of circuit analysis?

    • Find the mesh currents

      Vs = 6V, Is = 0.5A, R1= 3Ω, R2= 8Ω, R3 = 6Ω, R4 = 4Ω

  • Apply KVL at nodes b and c

Discussion #12 –Exam 1 Review


Exam 1 review mesh current4

+R4–

ic

+R3 –

+ R1–

+

R2

vs

Is

ia

ib

+

Exam 1 Review…Mesh Current

  • What is the mesh current method of circuit analysis?

    • Find the mesh currents

      Vs = 6V, Is = 0.5A, R1= 3Ω, R2= 8Ω, R3 = 6Ω, R4 = 4Ω

  • Express voltages in terms of currents

Discussion #12 –Exam 1 Review


Exam 1 review mesh current5

+R4–

ic

+R3 –

+ R1–

+

R2

vs

Is

ia

ib

+

Exam 1 Review…Mesh Current

  • What is the mesh current method of circuit analysis?

    • Find the mesh currents

      Vs = 6V, Is = 0.5A, R1= 3Ω, R2= 8Ω, R3 = 6Ω, R4 = 4Ω

  • Solve the n – m equations

Discussion #12 –Exam 1 Review


Exam 1 review superposition

Exam 1 Review…Superposition

  • What is the superposition method of circuit analysis?

Discussion #12 –Exam 1 Review


Exam 1 review superposition1

R2

R1

R3

+

vR

+

vs

is

Exam 1 Review…Superposition

  • What is the superposition method of circuit analysis?

    • Use superposition to find vR

      is= 12A, vs= 12V, R1= 1Ω, R2= 0.3Ω, R3 = 0.23Ω

Discussion #12 –Exam 1 Review


Exam 1 review superposition2

is

Exam 1 Review…Superposition

  • What is the superposition method of circuit analysis?

    • Use superposition to find vR

      is= 12A, vs= 12V, R1= 1Ω, R2= 0.3Ω, R3 = 0.23Ω

  • Remove all sources except is

    • Source vs is replaced with short circuit

R2

+

i2

+

R1

R3

+

vR1

i1

i3

Discussion #12 –Exam 1 Review


Exam 1 review superposition3

is

Exam 1 Review…Superposition

  • What is the superposition method of circuit analysis?

    • Use superposition to find vR

      is= 12A, vs= 12V, R1= 1Ω, R2= 0.3Ω, R3 = 0.23Ω

Node a

R2

+

i2

+

R1

R3

+

vR1

i1

i3

Discussion #12 –Exam 1 Review


Exam 1 review superposition4

+

vs

Exam 1 Review…Superposition

  • What is the superposition method of circuit analysis?

    • Use superposition to find vR

      is= 12A, vs= 12V, R1= 1Ω, R2= 0.3Ω, R3 = 0.23Ω

  • Remove all sources except vs

    • Source is is replaced with open circuit

R2

+

i2

+

R1

R3

+

vR2

i1

i3

Discussion #12 –Exam 1 Review


Exam 1 review superposition5

+

vs

Exam 1 Review…Superposition

  • What is the superposition method of circuit analysis?

    • Use superposition to find vR

      is= 12A, vs= 12V, R1= 1Ω, R2= 0.3Ω, R3 = 0.23Ω

Node a

R2

+

i2

+

R1

R3

+

vR2

i1

i3

Discussion #12 –Exam 1 Review


Exam 1 review superposition6

R2

R1

R3

+

vR

+

vs

is

Exam 1 Review…Superposition

  • What is the superposition method of circuit analysis?

    • Use superposition to find vR

      is= 12A, vs= 12V, R1= 1Ω, R2= 0.3Ω, R3 = 0.23Ω

Discussion #12 –Exam 1 Review


Exam 1 review source transform

Rs

a

a

+

Rp

vs

is

b

b

Exam 1 Review…Source Transform

  • How are voltage sources transformed to current sources (and vice-versa)?

Discussion #12 –Exam 1 Review


Exam 1 review source transform1

Rs

a

a

+

Rp

vs

is

b

b

Exam 1 Review…Source Transform

  • How are voltage sources transformed to current sources (and vice-versa)?

Discussion #12 –Exam 1 Review


Exam 1 review th venin

Exam 1 Review…Thévenin

  • What is the Thévenin theorem?

Discussion #12 –Exam 1 Review


Exam 1 review th venin1

vs

+

Exam 1 Review…Thévenin

  • What is the Thévenin theorem?

    • find iL by finding the Thévenin equivalent circuit

      vs= 10V, R1= 4Ω, R2= 6Ω, R3 = 10Ω, RL = 10Ω

R1

R3

iL

RL

R2

Discussion #12 –Exam 1 Review


Exam 1 review th venin2

vs

+

Exam 1 Review…Thévenin

  • What is the Thévenin theorem?

    • find iL by finding the Thévenin equivalent circuit

      vs= 10V, R1= 4Ω, R2= 6Ω, R3 = 10Ω, RL = 10Ω

  • Compute RT

    • Remove RL

+R1–

+ R3 –

+

R2

Discussion #12 –Exam 1 Review


Exam 1 review th venin3

Exam 1 Review…Thévenin

  • What is the Thévenin theorem?

    • find iL by finding the Thévenin equivalent circuit

      vs= 10V, R1= 4Ω, R2= 6Ω, R3 = 10Ω, RL = 10Ω

  • Compute RT

    • Remove RL

    • Zero sources

+R1–

+ R3 –

+

R2

Discussion #12 –Exam 1 Review


Exam 1 review th venin4

Exam 1 Review…Thévenin

  • What is the Thévenin theorem?

    • find iL by finding the Thévenin equivalent circuit

      vs= 10V, R1= 4Ω, R2= 6Ω, R3 = 10Ω, RL = 10Ω

  • Compute RT

    • Remove RL

    • Zero sources

    • Compute RT = REQ

REQ

Discussion #12 –Exam 1 Review


Exam 1 review th venin5

R1

R3

vs

RL

R2

+

Exam 1 Review…Thévenin

  • What is the Thévenin theorem?

    • find iL by finding the Thévenin equivalent circuit

      vs= 10V, R1= 4Ω, R2= 6Ω, R3 = 10Ω, RL = 10Ω

  • Compute RT

  • Compute vT

iL

Discussion #12 –Exam 1 Review


Exam 1 review th venin6

vs

+

Exam 1 Review…Thévenin

  • What is the Thévenin theorem?

    • find iL by finding the Thévenin equivalent circuit

      vs= 10V, R1= 4Ω, R2= 6Ω, R3 = 10Ω, RL = 10Ω

  • Compute RT

  • Compute vT

    • Remove the load

    • Define voc

+R1–

+ R3 –

+

voc

+

R2

Discussion #12 –Exam 1 Review


Exam 1 review th venin7

vs

+

Exam 1 Review…Thévenin

  • What is the Thévenin theorem?

    • find iL by finding the Thévenin equivalent circuit

      vs= 10V, R1= 4Ω, R2= 6Ω, R3 = 10Ω, RL = 10Ω

i3 = 0

  • Compute RT

  • Compute vT

    • Remove the load

    • Define voc

    • Choose a network analysis method

      • Voltage divider

+R1–

+ R3 –

+

voc

+

R2

i

Discussion #12 –Exam 1 Review


Exam 1 review th venin8

vs

+

Exam 1 Review…Thévenin

  • What is the Thévenin theorem?

    • find iL by finding the Thévenin equivalent circuit

      vs= 10V, R1= 4Ω, R2= 6Ω, R3 = 10Ω, RL = 10Ω

i3 = 0

  • Compute RT

  • Compute vT

    • Remove the load

    • Define voc

    • Choose a network analysis method

      • Voltage divider

    • VT = Voc

+R1–

+ R3 –

+

voc

+

R2

i

Discussion #12 –Exam 1 Review


Exam 1 review th venin9

R1

R3

vs

RL

R2

+

+

vT

Exam 1 Review…Thévenin

  • What is the Thévenin theorem?

    • find iL by finding the Thévenin equivalent circuit

      vs= 10V, R1= 4Ω, R2= 6Ω, R3 = 10Ω, RL = 10Ω

RT

iL

iL

RL

NB: iL is the same in both circuits

Discussion #12 –Exam 1 Review


Exam 1 review th venin10

+

vT

Exam 1 Review…Thévenin

  • What is the Thévenin theorem?

    • find iL by finding the Thévenin equivalent circuit

      vs= 10V, R1= 4Ω, R2= 6Ω, R3 = 10Ω, RL = 10Ω

RT

iL

RL

Discussion #12 –Exam 1 Review


Exam 1 review norton

Exam 1 Review…Norton

  • What is the Norton theorem?

Discussion #12 –Exam 1 Review


Exam 1 review norton1

– +

Exam 1 Review…Norton

  • What is the Norton theorem?

    • Find the Norton equivalent circuit

      vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

vs

R3

is

RL

R2

R1

Discussion #12 –Exam 1 Review


Exam 1 review norton2

– +

Exam 1 Review…Norton

  • What is the Norton theorem?

    • Find the Norton equivalent circuit

      vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

vs

vs

  • Compute RN

    • Remove RL

R3

is

R2

R1

Discussion #12 –Exam 1 Review


Exam 1 review norton3

Exam 1 Review…Norton

  • What is the Norton theorem?

    • Find the Norton equivalent circuit

      vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

  • Compute RN

    • Remove RL

    • Zero sources

R3

R2

R1

Discussion #12 –Exam 1 Review


Exam 1 review norton4

Exam 1 Review…Norton

  • What is the Norton theorem?

    • Find the Norton equivalent circuit

      vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

  • Compute RN

    • Remove RL

    • Zero sources

    • Compute RN = REQ

REQ

Discussion #12 –Exam 1 Review


Exam 1 review norton5

– +

Exam 1 Review…Norton

  • What is the Norton theorem?

    • Find the Norton equivalent circuit

      vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

vs

  • Compute RN

  • Compute iN

R3

is

RL

R2

R1

Discussion #12 –Exam 1 Review


Exam 1 review norton6

– +

Exam 1 Review…Norton

  • What is the Norton theorem?

    • Find the Norton equivalent circuit

      vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

vs

  • Compute RN

  • Compute iN

    • Short circuit the load

    • Define isc

R3

is

R2

R1

isc

Discussion #12 –Exam 1 Review


Exam 1 review norton7

– +

Exam 1 Review…Norton

  • What is the Norton theorem?

    • Find the Norton equivalent circuit

      vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

i3

vs

Node a

Node b

  • Compute RN

  • Compute iN

    • Short circuit the load

    • Define isc

    • Choose a network analysis method

      • Node voltage

+ R3 –

is

iv

+

R2

+

R1

isc

i1

i2

Node d

Discussion #12 –Exam 1 Review


Exam 1 review norton8

– +

Exam 1 Review…Norton

  • What is the Norton theorem?

    • Find the Norton equivalent circuit

      vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

i3

vs

Node a

Node b

  • Compute iN

    • Choose a network analysis method

      • Node voltage

+ R3 –

is

iv

+

R2

+

R1

  • va is independent

  • vb is dependent (actually va and vb

  • are dependent on each other but choose vb) vb = va + vs

isc

i1

i2

Node d

Discussion #12 –Exam 1 Review


Exam 1 review norton9

– +

Exam 1 Review…Norton

  • What is the Norton theorem?

    • Find the Norton equivalent circuit

      vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

i3

vs

Node a

Node b

  • Compute iN

    • Choose a network analysis method

      • Node voltage

+ R3 –

is

iv

+

R2

+

R1

isc

i1

i2

Node d

Discussion #12 –Exam 1 Review


Exam 1 review norton10

– +

Exam 1 Review…Norton

  • What is the Norton theorem?

    • Find the Norton equivalent circuit

      vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

i3

vs

  • Compute iN

    • Choose a network analysis method

      • Node voltage

Node a

Node b

+ R3 –

is

iv

+

R2

+

R1

isc

i1

i2

Node d

Discussion #12 –Exam 1 Review


Exam 1 review norton11

– +

Exam 1 Review…Norton

  • What is the Norton theorem?

    • Find the Norton equivalent circuit

      vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

i3

vs

  • Compute iN

    • Choose a network analysis method

      • Node voltage

Node a

Node b

+ R3 –

is

iv

+

R2

+

R1

isc

i1

i2

Node d

Discussion #12 –Exam 1 Review


Exam 1 review norton12

– +

Exam 1 Review…Norton

  • What is the Norton theorem?

    • Find the Norton equivalent circuit

      vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

i3

vs

  • Compute iN

    • Choose a network analysis method

      • Node voltage

Node a

Node b

+ R3 –

is

iv

+

R2

+

R1

isc

i1

i2

Node d

Discussion #12 –Exam 1 Review


Exam 1 review norton13

– +

Exam 1 Review…Norton

  • What is the Norton theorem?

    • Find the Norton equivalent circuit

      vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

i3

vs

  • Compute iN

    • Choose a network analysis method

      • Node voltage

    • iN = isc

+ R3 –

is

iv

+

R2

+

R1

isc

i1

i2

Discussion #12 –Exam 1 Review


Exam 1 review norton14

– +

iN

Exam 1 Review…Norton

  • What is the Norton theorem?

    • Find the Norton equivalent circuit

      vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

vs

R3

is

RL

RL

R2

R1

RN

Discussion #12 –Exam 1 Review


Exam 1 review max power

Exam 1 Review…Max Power

  • What is the maximum power theorem?

Discussion #12 –Exam 1 Review


Exam 1 review max power1

R1

R3

vs

RL

R2

+

Exam 1 Review…Max Power

  • What is the maximum power theorem?

    • Find the maximum power delivered to the load

      vs= 18V, R1= 3Ω, R2= 6Ω, R3 = 2Ω

Discussion #12 –Exam 1 Review


Exam 1 review max power2

+

vT

Exam 1 Review…Max Power

  • What is the maximum power theorem?

    • Find the maximum power delivered to the load

      vs= 18V, R1= 3Ω, R2= 6Ω, R3 = 2Ω

  • Find Thévenin equivalent circuit

    • (previously found)

RT

RL

Discussion #12 –Exam 1 Review


Exam 1 review max power3

+

vT

Exam 1 Review…Max Power

  • What is the maximum power theorem?

    • Find the maximum power delivered to the load

      vs= 18V, R1= 3Ω, R2= 6Ω, R3 = 2Ω

  • Find Thévenin equivalent circuit

  • Set RL = RT

  • Calculate PLMax

RT

RL

Discussion #12 –Exam 1 Review


Exam 1 review controlled sources

Exam 1 Review… Controlled Sources

  • Network analysis with controlled sources:

    • Initially treat controlled sources as ideal sources

    • In addition to equations obtained by node/mesh analysis there will be the constraint equation (the controlled source equation)

    • Substitute constraint equation into node/mesh equations

Discussion #8 – Network Analysis


Exam 1 review controlled sources1

R4

R3

R1

R5

R2

+

v

+

vout

+

vin

+

2v

Exam 1 Review… Controlled Sources

14. find the gain (Av = vout/vin)

  • R1= 1Ω, R2= 0.5Ω, R3 = 0.25Ω, R4 = 0.25Ω , R5 = 0.25Ω

Discussion #8 – Network Analysis


Exam 1 review controlled sources2

+R4–

ib

+R3 –

+ R1–

R5

R2

+

v

+

vout

+

vin

+

ia

2v

ic

Exam 1 Review… Controlled Sources

14. find the gain (Av = vout/vin)

  • R1= 1Ω, R2= 0.5Ω, R3 = 0.25Ω, R4 = 0.25Ω , R5 = 0.25Ω

Choose mesh analysis – simpler than node analysis

  • Mesh current directions chosen

  • Voltage polarities chosen and labeled

  • Identify n – m (3) mesh currents

    • ia is independent

    • iais independent

    • ic is independent

  • Apply KVL around meshes a, b, and c

Discussion #8 – Network Analysis


Exam 1 review controlled sources3

+R4–

ib

+R3 –

+ R1–

R5

R2

+

v

+

vout

+

vin

+

ia

2v

ic

Exam 1 Review… Controlled Sources

14. find the gain (Av = vout/vin)

  • R1= 1Ω, R2= 0.5Ω, R3 = 0.25Ω, R4 = 0.25Ω , R5 = 0.25Ω

  • Apply KVL at nodes a, b, and c

Discussion #8 – Network Analysis


Exam 1 review controlled sources4

+R4–

ib

+R3 –

+ R1–

R5

R2

+

v

+

vout

+

vin

+

ia

2v

ic

Exam 1 Review… Controlled Sources

14. find the gain (Av = vout/vin)

  • R1= 1Ω, R2= 0.5Ω, R3 = 0.25Ω, R4 = 0.25Ω , R5 = 0.25Ω

  • Solve the n – m equations

Discussion #8 – Network Analysis


Exam 1 review controlled sources5

+R4–

ib

+R3 –

+ R1–

R5

R2

+

v

+

vout

+

vin

+

ia

2v

ic

Exam 1 Review… Controlled Sources

14. find the gain (Av = vout/vin)

  • R1= 1Ω, R2= 0.5Ω, R3 = 0.25Ω, R4 = 0.25Ω , R5 = 0.25Ω

  • Solve the n – m equations (Matrices)

Discussion #8 – Network Analysis


Exam 1 review controlled sources6

+R4–

ib

+R3 –

+ R1–

R5

R2

+

v

+

vout

+

vin

+

ia

2v

ic

Exam 1 Review… Controlled Sources

14. find the gain (Av = vout/vin)

  • R1= 1Ω, R2= 0.5Ω, R3 = 0.25Ω, R4 = 0.25Ω , R5 = 0.25Ω

  • Solve the n – m equations (Matrices)

Discussion #8 – Network Analysis


Exam 1 review controlled sources7

+

vin

+

Exam 1 Review… Controlled Sources

14. find the gain (Av = vout/vin)

  • R1= 1Ω, R2= 0.5Ω, R3 = 0.25Ω, R4 = 0.25Ω , R5 = 0.25Ω

+R4–

  • Find the gain

ib

+R3 –

+ R1–

R5

R2

+

v

+

vout

ia

2v

ic

Discussion #8 – Network Analysis


Exam 1 review th venin p 114

vs

+

Exam 1 Review…Thévenin P.114

Find the Thévenin equivalent resistance

vs= 20V, R1= 1MΩ, R2= 2kΩ, R3 = 3kΩ, R4 = 6kΩ, R5 = 6kΩ, R6 = 3kΩ, R7 = 2kΩ, RL = 10Ω

R5

R7

R3

R1

R2

R4

R6

RL

NB: the answer to this problem in the book is wrong!!

Discussion #12 –Exam 1 Review


Exam 1 review th venin p 1141

vs

+

Exam 1 Review…Thévenin P.114

Find the Thévenin equivalent resistance

vs= 20V, R1= 1MΩ, R2= 2kΩ, R3 = 3kΩ, R4 = 6kΩ, R5 = 6kΩ, R6 = 3kΩ, R7 = 2kΩ, RL = 10Ω

  • Compute RT

    • Remove RL

R5

R7

R3

R1

R2

R4

R6

Discussion #12 –Exam 1 Review


Exam 1 review th venin p 1142

Exam 1 Review…Thévenin P.114

Find the Thévenin equivalent resistance

vs= 20V, R1= 1MΩ, R2= 2kΩ, R3 = 3kΩ, R4 = 6kΩ, R5 = 6kΩ, R6 = 3kΩ, R7 = 2kΩ, RL = 10Ω

  • Compute RT

    • Remove RL

    • Zero sources

R5

R7

R3

R1

R2

R4

R6

Discussion #12 –Exam 1 Review


Exam 1 review th venin p 1143

Exam 1 Review…Thévenin P.114

Find the Thévenin equivalent resistance

vs= 20V, R1= 1MΩ, R2= 2kΩ, R3 = 3kΩ, R4 = 6kΩ, R5 = 6kΩ, R6 = 3kΩ, R7 = 2kΩ, RL = 10Ω

  • Compute RT

    • Remove RL

    • Zero sources

R5

R7

R3

R1

R2

R4

R6

Consider now – what resistance would the LOAD see?

Discussion #12 –Exam 1 Review


Exam 1 review th venin p 1144

Exam 1 Review…Thévenin P.114

Find the Thévenin equivalent resistance

vs= 20V, R1= 1MΩ, R2= 2kΩ, R3 = 3kΩ, R4 = 6kΩ, R5 = 6kΩ, R6 = 3kΩ, R7 = 2kΩ, RL = 10Ω

  • Compute RT

    • Remove RL

    • Zero sources

R5

R7

R3

is

R1

R2

R4

R6

Imagine we connected a 1A current source – in which branches would current flow?

Discussion #12 –Exam 1 Review


Exam 1 review th venin p 1145

Exam 1 Review…Thévenin P.114

Find the Thévenin equivalent resistance

vs= 20V, R1= 1MΩ, R2= 2kΩ, R3 = 3kΩ, R4 = 6kΩ, R5 = 6kΩ, R6 = 3kΩ, R7 = 2kΩ, RL = 10Ω

  • Compute RT

    • Remove RL

    • Zero sources

R5

R7

R3

is

R1

R2

R4

R6

Imagine we connected a 1A current source – in which branches would current flow?

Discussion #12 –Exam 1 Review


Exam 1 review th venin p 1146

Exam 1 Review…Thévenin P.114

Find the Thévenin equivalent resistance

vs= 20V, R1= 1MΩ, R2= 2kΩ, R3 = 3kΩ, R4 = 6kΩ, R5 = 6kΩ, R6 = 3kΩ, R7 = 2kΩ, RL = 10Ω

  • Compute RT

    • Remove RL

    • Zero sources

R5

R7

R3

is

R1

R2

R4

R6

No current would get to here

Discussion #12 –Exam 1 Review


Exam 1 review th venin p 1147

Exam 1 Review…Thévenin P.114

Find the Thévenin equivalent resistance

vs= 20V, R1= 1MΩ, R2= 2kΩ, R3 = 3kΩ, R4 = 6kΩ, R5 = 6kΩ, R6 = 3kΩ, R7 = 2kΩ, RL = 10Ω

  • Compute RT

    • Remove RL

    • Zero sources

    • Compute RT = REQ

R5

R7

R6

There are only 3 resistors to consider

Discussion #12 –Exam 1 Review


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