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Discussion #12 –Exam 1 Review

Examine Yourselves

2 Cor. 13: 5

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

Discussion #12 –Exam 1 Review

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

- 15 multiple choice (answer on bubble sheet!)
- 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

- 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

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

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

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

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

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

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

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

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

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

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

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 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

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

- Using a voltage divider find the voltage across R3

– v1 +

i

R1

+

v2

–

R2

+ v3 –

R3

Discussion #12 –Exam 1 Review

– 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

- Using a voltage divider find the voltage across R3

Discussion #12 –Exam 1 Review

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

- Using a current divider find i1

Discussion #12 –Exam 1 Review

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

- Using a current divider find i1

Discussion #12 –Exam 1 Review

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

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

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

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

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

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

- What is the node voltage method of circuit analysis?

Discussion #12 –Exam 1 Review

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

- Find all unknown voltages

Discussion #12 –Exam 1 Review

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

- Find all unknown voltages

- 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

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

- Find all unknown voltages

- Apply KCL at nodes a and b

+

ia

–

Discussion #12 –Exam 1 Review

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

- Find all unknown voltages

- Express currents in terms of voltages

+

ia

–

Discussion #12 –Exam 1 Review

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

- Find all unknown voltages

- Solve the n – 1 – m equations

+

ia

–

Discussion #12 –Exam 1 Review

Exam 1 Review…Mesh Current

- What is the mesh current method of circuit analysis?

Discussion #12 –Exam 1 Review

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

- Find the mesh currents

Discussion #12 –Exam 1 Review

+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

- Find the mesh currents

- 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

+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

- Find the mesh currents

- Apply KVL at nodes b and c

Discussion #12 –Exam 1 Review

+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

- Find the mesh currents

- Express voltages in terms of currents

Discussion #12 –Exam 1 Review

+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

- Find the mesh currents

- Solve the n – m equations

Discussion #12 –Exam 1 Review

Exam 1 Review…Superposition

- What is the superposition method of circuit analysis?

Discussion #12 –Exam 1 Review

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

- Use superposition to find vR

Discussion #12 –Exam 1 Review

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

- Use superposition to find vR

- Remove all sources except is
- Source vs is replaced with short circuit

–

R2

+

i2

+

R1

–

R3

+

vR1

–

i1

i3

Discussion #12 –Exam 1 Review

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

- Use superposition to find vR

Node a

–

R2

+

i2

+

R1

–

R3

+

vR1

–

i1

i3

Discussion #12 –Exam 1 Review

–

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

- Use superposition to find vR

- Remove all sources except vs
- Source is is replaced with open circuit

–

R2

+

i2

+

R1

–

R3

+

vR2

–

i1

i3

Discussion #12 –Exam 1 Review

–

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

- Use superposition to find vR

Node a

–

R2

+

i2

+

R1

–

R3

+

vR2

–

i1

i3

Discussion #12 –Exam 1 Review

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

- Use superposition to find vR

Discussion #12 –Exam 1 Review

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

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

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

- find iL by finding the Thévenin equivalent circuit

R1

R3

iL

RL

R2

Discussion #12 –Exam 1 Review

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

- find iL by finding the Thévenin equivalent circuit

- Compute RT
- Remove RL

+R1–

+ R3 –

+

R2

–

Discussion #12 –Exam 1 Review

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

- find iL by finding the Thévenin equivalent circuit

- Compute RT
- Remove RL
- Zero sources

+R1–

+ R3 –

+

R2

–

Discussion #12 –Exam 1 Review

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

- find iL by finding the Thévenin equivalent circuit

- Compute RT
- Remove RL
- Zero sources
- Compute RT = REQ

REQ

Discussion #12 –Exam 1 Review

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

- find iL by finding the Thévenin equivalent circuit

- Compute RT
- Compute vT

iL

Discussion #12 –Exam 1 Review

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

- find iL by finding the Thévenin equivalent circuit

- Compute RT
- Compute vT
- Remove the load
- Define voc

+R1–

+ R3 –

+

voc

–

+

R2

–

Discussion #12 –Exam 1 Review

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

- find iL by finding the Thévenin equivalent circuit

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

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

- find iL by finding the Thévenin equivalent circuit

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

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

- find iL by finding the Thévenin equivalent circuit

RT

iL

iL

RL

NB: iL is the same in both circuits

Discussion #12 –Exam 1 Review

–

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

- find iL by finding the Thévenin equivalent circuit

RT

iL

RL

Discussion #12 –Exam 1 Review

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

- Find the Norton equivalent circuit

vs

R3

is

RL

R2

R1

Discussion #12 –Exam 1 Review

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

- Find the Norton equivalent circuit

vs

vs

- Compute RN
- Remove RL

R3

is

R2

R1

Discussion #12 –Exam 1 Review

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

- Find the Norton equivalent circuit

- Compute RN
- Remove RL
- Zero sources

R3

R2

R1

Discussion #12 –Exam 1 Review

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

- Find the Norton equivalent circuit

- Compute RN
- Remove RL
- Zero sources
- Compute RN = REQ

REQ

Discussion #12 –Exam 1 Review

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

- Find the Norton equivalent circuit

vs

- Compute RN
- Compute iN

R3

is

RL

R2

R1

Discussion #12 –Exam 1 Review

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

- Find the Norton equivalent circuit

vs

- Compute RN
- Compute iN
- Short circuit the load
- Define isc

R3

is

R2

R1

isc

Discussion #12 –Exam 1 Review

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

- Find the Norton equivalent circuit

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…Norton

- What is the Norton theorem?
- Find the Norton equivalent circuit
vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

- Find the Norton equivalent circuit

i3

vs

Node a

Node b

- Compute iN
- Choose a network analysis method
- Node voltage

- Choose a network analysis method

+ 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…Norton

- What is the Norton theorem?
- Find the Norton equivalent circuit
vs= 6V, is = 2A, R1= 6Ω, R2= 3Ω, R3 = 2Ω, RL = 10Ω

- Find the Norton equivalent circuit

i3

vs

Node a

Node b

- Compute iN
- Choose a network analysis method
- Node voltage

- Choose a network analysis method

+ R3 –

is

iv

+

R2

–

+

R1

–

isc

i1

i2

Node d

Discussion #12 –Exam 1 Review

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

- Find the Norton equivalent circuit

i3

vs

- Compute iN
- Choose a network analysis method
- Node voltage

- Choose a network analysis method

Node a

Node b

+ R3 –

is

iv

+

R2

–

+

R1

–

isc

i1

i2

Node d

Discussion #12 –Exam 1 Review

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

- Find the Norton equivalent circuit

i3

vs

- Compute iN
- Choose a network analysis method
- Node voltage

- Choose a network analysis method

Node a

Node b

+ R3 –

is

iv

+

R2

–

+

R1

–

isc

i1

i2

Node d

Discussion #12 –Exam 1 Review

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

- Find the Norton equivalent circuit

i3

vs

- Compute iN
- Choose a network analysis method
- Node voltage

- Choose a network analysis method

Node a

Node b

+ R3 –

is

iv

+

R2

–

+

R1

–

isc

i1

i2

Node d

Discussion #12 –Exam 1 Review

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

- Find the Norton equivalent circuit

i3

vs

- Compute iN
- Choose a network analysis method
- Node voltage

- iN = isc

- Choose a network analysis method

+ R3 –

is

iv

+

R2

–

+

R1

–

isc

i1

i2

Discussion #12 –Exam 1 Review

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

- Find the Norton equivalent circuit

vs

R3

is

RL

RL

R2

R1

RN

Discussion #12 –Exam 1 Review

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

- Find the maximum power delivered to the load

Discussion #12 –Exam 1 Review

–

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 the maximum power delivered to the load

- Find Thévenin equivalent circuit
- (previously found)

RT

RL

Discussion #12 –Exam 1 Review

–

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 the maximum power delivered to the load

- Find Thévenin equivalent circuit
- Set RL = RT
- Calculate PLMax

RT

RL

Discussion #12 –Exam 1 Review

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

R4

R3

R1

R5

R2

+

v

–

+

vout

–

+

–

vin

–

+

2v

Exam 1 Review… Controlled Sources14. find the gain (Av = vout/vin)

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

Discussion #8 – Network Analysis

+R4–

ib

+R3 –

+ R1–

R5

R2

+

v

–

+

vout

–

+

–

vin

–

+

ia

2v

ic

Exam 1 Review… Controlled Sources14. 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

+R4–

ib

+R3 –

+ R1–

R5

R2

+

v

–

+

vout

–

+

–

vin

–

+

ia

2v

ic

Exam 1 Review… Controlled Sources14. 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

+R4–

ib

+R3 –

+ R1–

R5

R2

+

v

–

+

vout

–

+

–

vin

–

+

ia

2v

ic

Exam 1 Review… Controlled Sources14. 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

+R4–

ib

+R3 –

+ R1–

R5

R2

+

v

–

+

vout

–

+

–

vin

–

+

ia

2v

ic

Exam 1 Review… Controlled Sources14. 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

+R4–

ib

+R3 –

+ R1–

R5

R2

+

v

–

+

vout

–

+

–

vin

–

+

ia

2v

ic

Exam 1 Review… Controlled Sources14. 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

–

vin

–

+

Exam 1 Review… Controlled Sources14. 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

vs

+

–

Exam 1 Review…Thévenin P.114Find 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

vs

+

–

Exam 1 Review…Thévenin P.114Find 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…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…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…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…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…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…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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