1218 T3 V1-V7 Lecture Slides engn1218.pdf

ENGN1218 Introduction to Electronics Slides

1. ENGN1218 Introduction to Electronics
1
Topic 3 Video 1
Equivalent Resistance
Overview
•Solving resistor combinations
•Equivalent resistance

2. ENGN1218 Introduction to Electronics
2
•In many circuits
–Some components are connected in series
•To have the same current
–Others are connected in parallel
•for the same voltage.
–Others are neither in series or parallel
–These circuits supply different currents and voltages
with one source of applied voltage.
•To analyse these circuits,
–the techniques of series and parallel circuits are
applied individually
•to produce a simplified total circuit.
–An equivalent resistance can capture the circuit
behaviour of an interconnection of resistors
Circuit Analysis: Equivalent Resistance

3. ENGN1218 Introduction to Electronics
3
Resistors in Series
•Series connected circuit elements carry the same current
–There is only one path for the current
•Total resistance of resistors in series
–Is the sum of the individual resistors in series
–For N resistors in series, the equivalent single resistor has a
resistor equal to the sum of the N resistances
????????????
????????????????????????=�
????????????=1
????????????
????????????
????????????=????????????
1+????????????
2+????????????
3+⋯+????????????
????????????

4. ENGN1218 Introduction to Electronics
4
Resistors in Parallel: Equivalent Resistance
•For two resistors in parallel
–The equivalent resistance is equal to the product of their
resistances divided by the sum of their resistances.
•For N resistors in parallel,
–the equivalent resistance is
DC
�
1
????????????
????????????????????????
=�
1
????????????
1
+�
1
????????????
2
????????????
????????????????????????=
????????????
1????????????
2
????????????
1+????????????
2
�
1
????????????
????????????????????????
=�
1
????????????
1
+�
1
????????????
2
+⋯+�
1
????????????
????????????
????????????
3????????????
2????????????
1 ????????????
????????????
…
…

5. ENGN1218 Introduction to Electronics
5
Resistors in Parallel: Example 1
•For three resistors in parallel
•If ????????????
1=18Ω,????????????
2=9Ω&????????????
3=6Ω
????????????
????????????????????????=
????????????
1????????????
2????????????
3
????????????
1????????????
2+????????????
1????????????
3+????????????
2????????????
3
=
18×9×6
18×9+18×6+9×6
Then ????????????
????????????????????????=18|
9|6=3Ω
R1 R2 R3

6. ENGN1218 Introduction to Electronics
6
Circuit Analysis: Vocabulary
Circuit elements may be connected in a way that they are
neither in series or parallel
•Ladder Circuit
•A series-parallel circuit with a topology that resembles a ladder.
•Ladder Circuit

7. ENGN1218 Introduction to Electronics
7
Circuit Analysis: Simplifying Resistor Combinations

8. ENGN1218 Introduction to Electronics
8
Example 1
•Find ????????????
????????????????????????: the equivalent resistance
•Start at far right
1. Resistors in series
•1Ω+5Ω=6Ω
2. Resistors in parallel•6Ω||3Ω=
6×3
6+3
=2Ω
3. Resistors in parallel
•(2+2)Ω||6Ω
•= 4×6
4+6
=2.4Ω
4.????????????
????????????????????????
=4+2.4+8
=14.4Ω

9. ENGN1218 Introduction to Electronics
9
•Find the equivalent resistance of this ladder circuit
Example 2
1. Resistors in series:4Ω+5Ω+3Ω=12Ω
2. Resistors in parallel:4Ω||12Ω=
4×12
4+12
=3Ω
3. Resistors in series:3Ω+3Ω=6Ω
4. Resistors in parallel: 6Ω||6Ω=
6×6
6+6
=3Ω
5. Resistors in series:????????????
????????????????????????=2Ω+3Ω+1Ω=6Ω

10. ENGN1218 Introduction to Electronics
10
Example 3
•Find ????????????
????????????????????????equivalent resistance
1. Resistors in parallel:
70Ω||30Ω=
70×30
70+30
=21Ω
21Ω
2. Resistors in parallel:
12.5Ω||17.5Ω=
12.5×17.5
12.5+17.5
=7.29Ω
3. Resistors in parallel:
15Ω||35Ω=
15×35
15+35
=10.5Ω
7.29Ω
10.5Ω
4. Resistors in series:
7.29Ω+10.5Ω
=17.79Ω
17.79Ω 21Ω
5. Resistors in parallel:
????????????
????????????????????????=17.79Ω||21Ω
=
17.79×21
17.79+21
=9.63Ω
????????????
????????????????????????

11. ENGN1218 Introduction to Electronics
11
Example 4
•Find ????????????
????????????????????????equivalent resistance
1. Resistors in parallel:20Ω||5Ω=
20×5
20+5
=4Ω
2. Resistors in series:1 Ω+4Ω=5Ω
3. Resistors in parallel:20Ω||5Ω=
20×5
20+5
=4Ω
20Ω5Ω
1Ω
4Ω
5Ω
20Ω

12. ENGN1218 Introduction to Electronics
12
Example 4
•Find ????????????
????????????????????????equivalent resistance
5. Resistors in parallel:18 Ω9Ω6Ω
=
18×9×6
(18×9)+(18×6)+(9×6)
=3Ω
4. Resistors in series:
2Ω+4Ω=6Ω
4Ω
2Ω
6Ω18Ω 9Ω
3Ω
8Ω
????????????
????????????????????????
6. Resistors in series:
????????????
????????????????????????=8Ω+3Ω=11Ω

13. ENGN1218 Introduction to Electronics
13
Example 5
Find the equivalent resistance ????????????
????????????????????????.
5Ω4Ω
12Ω
1Ω
6Ω3Ω
10Ω 1Ω

14. ENGN1218 Introduction to Electronics
14
Example 5 contd
•Find the equivalent resistance:
????????????
????????????????????????=11.2Ω
12Ω4Ω6Ω=2Ω
1Ω+5Ω=6Ω
5Ω4Ω
12Ω
1Ω
6Ω3Ω
10Ω 1Ω
4Ω12Ω
1Ω
6Ω3Ω
10Ω
6Ω
10Ω
1Ω
6Ω3Ω
10Ω
1.2Ω
6Ω3Ω
2Ω
3Ω
3Ω6Ω3Ω=1.2Ω
1Ω+2Ω=3Ω

15. ENGN1218 Introduction to Electronics
15
In our next video…
We will be introduced to dependent voltage and current
sources

16. ENGN1218 Introduction to Electronics
16
Topic 3 Video 2
Dependent Sources
Overview
•Independent vs dependent sources
•Revisit valid interconnections
•Five problems for your viewing pleasure

17. ENGN1218 Introduction to Electronics
17
Independent vs Dependent Sources
•Ideal Independent Source
–Circle symbol
–Establishes a voltage or current in a circuit
•Independent of voltages or currents
elsewhere in the circuit.
–Active circuit element
•Models a device capable of generating
electrical energy
•Ideal Dependent source
–Diamond symbol
–Establishes a voltage or current in a circuit
•whose value depends on the value of a
voltage or current elsewhere in a circuit
Independent
Voltage Source
Independent
Current Source
Dependent
Voltage Source
Dependent
Current Source

18. ENGN1218 Introduction to Electronics
18
Ideal Dependent Sources
•Ideal dependent voltage source
•Voltage-controlled (VCVS)
•????????????
????????????=????????????????????????
????????????
•????????????is dimensionless
•Ideal dependent current source
•Voltage-controlled (VCCS)
•????????????
????????????=????????????????????????
????????????
•????????????amps/volts
Current-controlled (CCVS)
•????????????
????????????=????????????????????????
????????????
–????????????volts/amps
Current-controlled (CCCS)
•????????????
????????????=????????????????????????
????????????
–????????????is dimensionless

19. ENGN1218 Introduction to Electronics
19
Real World Perspective
•Dependent sources
–Ohm’s Law and KCL, KVL (with passive sign convention) can be used
–Can’t buy a dependent source
•Not a real world device
–Used in circuit theory as a theoretical model
•of complex real world electronic devices and components.
Large-signal BJT DC model Small-signal BJT AC model
Example: the bipolar junction transistor (BJT) is modelled as a VCCS

20. ENGN1218 Introduction to Electronics
20
Voltage Sources in Series
•Connecting voltage sources in series
•Can obtain higher applied voltage
•The total voltage available
•Is equal to the sum of the voltage sources in series
•The current capacity for voltage sources in series is the same as
for one of the voltage sources
•The same current flows through all of the voltage sources
BT1 BT2 BT3 BT4 BT5


21. ENGN1218 Introduction to Electronics
21
Voltage Sources in Series
•Addition of voltage sources in series
•Need to account for the polarities of the voltage sources,
20V
8V
5V
6V
4V
15V≡≡
20V
8V
5V
6V
4V
43V


22. ENGN1218 Introduction to Electronics
22
Voltage Sources in Parallel
•Same voltage: equivalent to increasing the size
of the electrodes and electrolyte
–For more current capacity
•Connect all +veterminal together
•Connect all – veterminals together
•Voltage sources of different potentials should
never be connected in parallel.
–Violates Kirchhoff’s voltage law.
–A source with a lower voltage can act as a
resistance and drain excessive current from
the cells with higher output voltage

ONLYvoltage sources with equal output voltage can be connected in parallel.

23. ENGN1218 Introduction to Electronics
23
•Connecting current sources in parallel
–Can be simplified by a single current source
–Magnitude and direction of the resultant current source
•Determined by adding the currents in one direction and
subtracting those currents in the other direction.
Current sources in Parallel
3A 3A3A 3A≡


24. ENGN1218 Introduction to Electronics
24
Current Sources in Series
•Current sources of different values are never placed in series
–Using Kirchhoff's current law at the node in-between the
current sources
•the current entering the node would be a different value to that
leaving the node
•This is a violation of KCL and is INVALID

3A 5A


25. ENGN1218 Introduction to Electronics
25
Interconnection of Independent Sources: Valid?
Both sources across same terminals a and b.
•KVL states voltage from both sources must be the same.
•The independent source supplies 5 V and the dependent
source supplies 15V.
•This interconnection violates KVL
Both sources across the same terminals a and b.
•the voltage source is independent of current,
•This interconnection is: VALID
VS
VCVS
VS
VCCS
NOT VALID
VALID

26. ENGN1218 Introduction to Electronics
26
Interconnection of Independent Sources: Valid?
Both sources across the same terminals a and b.
•The independent current source supplies current through
terminals a and b, regardless of the voltage.
•This interconnection is: VALID
Two current sources, one independent, the other dependent,
supply current through terminals a and b.
•KCL states each source must supply the same current at the
nodes.
•In this circuit the independent source supplies 2A while
the dependent source supplies 6A.
•This interconnection violates KCL.
CCVS
CS
CCCS
CS
VALID
INVALID

27. ENGN1218 Introduction to Electronics
27
In our next video…
We will solve resistive circuits with independent and
dependent sources

28. ENGN1218 Introduction to Electronics
28
Topic 3 Video 3
Solving Circuits with Dependent Sources
Overview
•Problems solved for resistive circuits with
independent and dependent sources

29. ENGN1218 Introduction to Electronics
29
Circuit Analysis Technique

30. ENGN1218 Introduction to Electronics
30
Problem 1: Textbook Assessment 2.1
•Textbook Assessment
•What kind of circuit is this?
•Single-node-pair circuit
•Same voltage drop across
the three branches
•????????????
????????????=�
????????????
????????????
4
Ans:
•a) Value of ????????????
????????????=−8????????????
•Calculate ????????????
????????????=�
????????????
????????????
4=−2????????????
•Therefore for this circuit to
be valid????????????
????????????=−2????????????
•b) ????????????
????????????????????????=−????????????
????????????.????????????
????????????
•=−(−2 ×−8)=−16????????????
•Delivered/generated (-ve)
VSCCVS CS

31. ENGN1218 Introduction to Electronics
31
Problem 2: Textbook P2.6
•Textbook P2.6
•What kind of circuit is this?
•Single-loop circuit
•Same current through
every element
•Ans:
•a) we know ????????????=400????????????????????????
•????????????=⁄
????????????1
50=400????????????????????????
•????????????
1=20????????????
•b) ????????????=????????????.????????????
•=20×0.4
•=8????????????(????????????????????????????????????????????????????????????????????????????????????????????????)
VCCSCS
VS

32. ENGN1218 Introduction to Electronics
32
Problem 3
•Is this interconnection valid?
This is neithera single loop or
single node-pair
•It is not possible to determine
the voltage between the top and
bottom node
•Cannot know voltage drop
across a current source.
•Ans:
•????????????
1=50????????????????????????
•3????????????
1=150????????????????????????
•????????????
????????????=100????????????????????????
•Use KCL at top node
•????????????
????????????−3????????????
1+????????????
1=0
–If this equation is correct then
the circuit is valid.
•100????????????−150????????????+50????????????=0
•This is CORRECT so the
circuit is valid
????????????
????????????
3????????????
1


33. ENGN1218 Introduction to Electronics
33
Problem 4: Textbook P2.9
•Is this interconnection valid?
•This is neithera single loop or
single node-pair
•We can determine the voltage
between the top and bottom
node for two branches
•Ans:
•We know the values of voltage
????????????
????????????& ????????????
????????????.
•????????????
????????????=30????????????
•????????????
????????????=1800????????????
????????????+60=
1800
50????????????+60=150????????????
•Use KVL
•for the circuit to be valid
•????????????
????????????=????????????
????????????
•But 30????????????≠150????????????
•The interconnection is NOT
VALID.
(1800????????????
????????????+60)????????????
????????????????????????????????????????????????
????????????
???????????? ????????????
????????????


34. ENGN1218 Introduction to Electronics
34
Problem 5: Week 3 Q2
gv1
DC
Find ????????????
????????????in the circuit shown
????????????
????????????
????????????
????????????
10???????????????????????? 4????????????
????????????????????????
????????????
2????????????Ω
4????????????Ω
3????????????Ω
+
−
+
−
????????????
1
????????????
????????????is the same voltage drop between the 2 nodes
Ans:
•Use KCL at top node
•10????????????+????????????
1+????????????
????????????−4????????????
????????????=0
•Use Ohm’s Law
•????????????
????????????=????????????
????????????×3????????????=????????????
1
2k+4k
•????????????
????????????=�
????????????????????????
3????????????
•????????????
1=�
????????????????????????
6????????????
•Substitute back into KCL
•10????????????+�
????????????????????????
6????????????+�
????????????????????????
3????????????−4�
????????????????????????
3????????????=0
•????????????
????????????=12????????????
•Calculate ????????????
????????????using Ohm’s Law
•????????????
????????????=????????????
1×4????????????=�
????????????????????????
6????????????×4????????????
•=⁄
12
6????????????
×4????????????=8????????????
CCCS

35. ENGN1218 Introduction to Electronics
35
Problem 6: Week 3 Q5
•Use Kirchhoff’s and Ohm’s
laws to find voltage ????????????
????????????
•Ohm’s law????????????=????????????.????????????
•????????????
????????????=⁄
????????????
????????????
=⁄
10
6
=⁄
5
3
????????????
•????????????
????????????=????????????
????????????.3
Ans:
Kirchhoff’s voltage law
•−3????????????
????????????+2????????????
????????????+3????????????
????????????=0
•−3×⁄
5
3
+5????????????
????????????=0
•????????????
????????????=1????????????
•Substitute into Ohms law
•????????????
????????????=????????????
????????????.3=3????????????
•Question: Is there a current
between the two circuits?
•Ans: No
+ −
CCVS

36. ENGN1218 Introduction to Electronics
36
In our next video…
We will calculate equivalent resistance

37. ENGN1218 Introduction to Electronics
37
Topic 3 Video 4
Calculating Equivalent Resistance
Overview
•Problems solved for resistive circuits with a single source
•Series and parallel resistance examples
•Delta and Y configurations and conversions

38. ENGN1218 Introduction to Electronics
38
Circuit Analysis Technique

39. ENGN1218 Introduction to Electronics
39
Voltage Division
•The voltage drop across any resistor is
proportional to the magnitude of the resistor
•Any series circuit is a voltage divider
–The current is the same in all resistances in a
series circuit
•The IR drops are proportional to the applied
voltage
–the largest R has the highest V
•For N resistors connected in series the
voltage drop across each resistor is given by
Voltage Divider Rule
We can calculate the voltage drop even when the current is unknown
????????????
????????????=(
????????????
????????????
????????????
????????????????????????
)????????????
????????????????????????
????????????????????????=????????????
1+????????????
2+⋯+????????????
????????????

40. ENGN1218 Introduction to Electronics
40
•Find ????????????
????????????????????????
•Ans: Voltage divider
•????????????
????????????????????????=????????????
????????????????????????−????????????
????????????????????????
•????????????
????????????????????????=
300
100+300
????????????
????????????=
3
4
×40=30????????????
•????????????
????????????????????????=
200
50+200
????????????
????????????=
4
5
×40=32????????????
•????????????
????????????????????????=30−32=−2????????????
Voltage Divider: Example 1
100Ω
200Ω
50Ω
300Ω40V
100Ω
200Ω
50Ω
300Ω40V
a
b
b
a
c
c

41. ENGN1218 Introduction to Electronics
41
•Principle of current division:
–If current ????????????
????????????enters a parallel network of resistors,
•the smallest value of resistor in the network will have the largest
amount of current
•Inversely the largest value of the resistance will have the smallest
amount of current.
•In general if N resistors are connected in parallel, the current
through each resistor is given by:
Resistors in Parallel: Current Divider Rule
????????????
????????????=(
????????????
????????????????????????
????????????
????????????
)????????????
????????????
�
1
????????????
????????????????????????
=�
1
????????????
1
+�
1
????????????
2
+⋯+�
1
????????????
????????????
????????????
????????????∝
1
????????????
????????????
????????????
???????????? ????????????
????????????
DC ????????????
3????????????
2????????????
1
????????????
????????????
…
…

42. ENGN1218 Introduction to Electronics
42
•Solve for ????????????
0&????????????
????????????
•Using current divider rule
•For resistors in parallel
•????????????
????????????=(
????????????
????????????????????????
????????????????????????
)????????????
????????????
•�
1
????????????
????????????????????????
=�
1
????????????
1
+�
1
????????????
2
•????????????
????????????????????????=
????????????
1????????????
2
????????????
1+????????????
2
=
2????????????×8????????????
2????????????+8????????????
=1.6????????????Ω
•????????????
????????????=
1.6????????????
2????????????
2????????????=1.6????????????????????????
•????????????
????????????=
1.6????????????
8????????????
2????????????=0.4????????????=400????????????????????????
Current Divider: Example 2
2mA
2mA
1????????????+4????????????+3????????????
=8????????????Ω
????????????
????????????
????????????
????????????

43. ENGN1218 Introduction to Electronics
43
Find a)????????????
????????????, b)????????????
1and ????????????
2in circuit
•Ans:
•a) ????????????
0=0????????????
•b) use voltage divider to calculate ????????????
∆
•????????????
∆=
????????????
∆
????????????
????????????????????????
????????????
????????????=
6
12+6
18=6????????????
•????????????
∆→????????????
????????????????????????????????????????????????=
????????????
∆
2
=
6
2
=3????????????=−????????????
????????????
•With 2 resistors in parallel current divider
•????????????
1=
10||5)
10
−3=−1????????????
•????????????
2=
10||5)
5
−3=−2????????????
Problem 1: Textbook Problem 2.35
10||5=
????????????
1????????????
2
????????????
1+????????????
2
=
10×5
10+5
=
50
15
????????????
????????????
????????????
????????????=(
????????????
????????????????????????
????????????
????????????
)????????????
????????????
VCCS

44. ENGN1218 Introduction to Electronics
44
•There are circuits where resistors are not in parallel or series
•Y(orT)and Delta(∆????????????????????????????????????)configurations show us how we
can convert these circuits so they can be analysed
Resistors: Neither in Parallel or Series
•For example:
–Note resistor in centre.
–How can we calculate the
equivalent resistance?

45. ENGN1218 Introduction to Electronics
45
•The Y or T configuration
•Look like the English letter Y or T
•They are the same
Y(orT)and Delta( ∆????????????????????????????????????)Configurations
•Delta (∆)or pi ( ????????????)configuration
•Look like Greek letter delta or pi
•They are the same
There are resistor configurations that are neither in series or parallel

46. ENGN1218 Introduction to Electronics
46
•Circuit analysis
–May be helpful to convert a Y to
a delta configuration or vice
versa.
•Analysis may be impossible
without the conversion
•Can make the analysis much
simpler.
–The formulas used to convert
between these configurations are
derived using Kirchhoff’s Law
•Proofs not assessable in this
course
Y(orT)and Delta( ∆????????????????????????????????????)Configurations: Conversion

47. ENGN1218 Introduction to Electronics
47
•In some cases circuit analysis is simpler by converting a Delta
(∆)to a Y configuration
•Formula for conversion ∆to Y
•????????????
1=
????????????
????????????????????????????????????
????????????
????????????+????????????
????????????+????????????
????????????
•????????????
2=
????????????????????????????????????????????????
????????????????????????+????????????
????????????+????????????????????????
•????????????
3=
????????????????????????????????????
????????????
????????????????????????+????????????
????????????+????????????????????????
Delta( ∆)to Y Conversion
????????????
????????????=
??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????∆
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????∆

48. ENGN1218 Introduction to Electronics
48
Delta( ∆)to Y Conversion: Example 3
•Convert this Delta to a Y configuration, calculate ????????????
1,????????????
2, ????????????
3
•????????????
????????????=
??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????∆
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????∆
•????????????
1=
30×60
30+60+90
=10Ω
•????????????
2=
30×90
30+60+90
=15Ω
•????????????
3=
60×90
30+60+90
=30Ω

49. ENGN1218 Introduction to Electronics
49
•In some cases circuit analysis is simpler by converting a Y to a
Delta(∆)configuration
•Formula for conversion of Y to ∆
•????????????
????????????=
????????????1????????????2+????????????2????????????3+????????????1????????????3
????????????
1
•????????????
????????????=
????????????
1????????????
2+????????????
2????????????
3+????????????
1????????????
3
????????????2
•????????????
????????????=
????????????
1????????????
2+????????????
2????????????
3+????????????
1????????????
3
????????????3
Y to Delta( ∆)Conversion
????????????
∆=
Σ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

50. ENGN1218 Introduction to Electronics
50
•Convert this Y configuration to a delta configuration
–Note configuration has been flipped around point c
•????????????
∆=
Σ????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
•????????????
????????????=
????????????
1????????????
2+????????????
2????????????
3+????????????
1????????????
3
4.8????????????
•=
3.6????????????×4.8????????????+4.8????????????×2.4????????????+3.6????????????×2.4????????????
4.8????????????
=
37.44????????????
4.8
=7.8????????????Ω
•????????????
????????????=
37.44????????????????????????
3.6????????????
=10.4????????????Ω
•????????????
????????????=
37.44????????????????????????
2.4????????????
=15.6????????????Ω
Y to Delta( ∆)Conversion: Example 4
????????????
1????????????
2
????????????
3

51. ENGN1218 Introduction to Electronics
51
•What is the formula for the equivalent resistance of this
circuit?
–the resistors are in neither in series or parallel
–Delta(∆)to Y Conversion
Delta( ∆)to Y Conversion: Example 5
????????????
???????????? ????????????
????????????
????????????
????????????
????????????
1 ????????????
2
????????????
3
????????????
???????????? ????????????
????????????
????????????
???????????? ????????????
????????????
????????????
1 ????????????
2
????????????
3
????????????
???????????? ????????????
????????????
????????????
????????????????????????
????????????
????????????????????????=????????????
3+(????????????
1+????????????
????????????)||(????????????
2+????????????
????????????)

52. ENGN1218 Introduction to Electronics
52
•Find the current ????????????though ????????????
5for the circuit ∆
–Simple series and parallel combination
Delta( ∆)to Y Conversion: Example 6
????????????=
30????????????
6Ω+2Ω+3.6Ω
=2.59????????????
∆to Y transformation

53. ENGN1218 Introduction to Electronics
53
•Calculate the current ????????????
•First conversion from Y to ∆
•The sides of the resulting ∆are in parallel
Y to Delta( ∆)Conversion: Example 7
15Ω
20Ω
22.5Ω ????????????
????????????????????????=15Ω||
20Ω+22.5Ω=11.09Ω
????????????=
30????????????
11.09Ω
=2.706????????????
????????????

54. ENGN1218 Introduction to Electronics
54
•Calculate the current ????????????
•Y to ∆ transformation
Y to Delta( ∆)Conversion: Example 8

55. ENGN1218 Introduction to Electronics
55
In our next video…
We will look at practical measurement of voltage and current

56. ENGN1218 Introduction to Electronics
56
Topic 3 Video 5
Measuring DC Voltage, Current and
Resistance
Overview
•Practical measurement
•Ammeter
•Voltmeter
•Ohmmeter

57. ENGN1218 Introduction to Electronics
57
Practical Measurement
Often need to measure current, voltage and resistance
•Ammeter
–Measuring current
–Schematic circle with I or A
•Voltmeter
–Measuring voltage
–Schematics: circle with V
•Ohmmeter
–Measuring resistance
•Multimeter
–Measures all three
–Digital or Analogue

58. ENGN1218 Introduction to Electronics
58
•Analogue meters are based on the d’Arsonvalmeter movement,
–a movable coil placed in the field of a permanent magnet.
Analogue Multimeters
•When current flows in the coil,
•it creates a torque on the coil,
•causes it to rotate
•moves the pointer across the scale.
•The coil has both a current and voltage rating,
•in one commercially available meter the rating
is 50mV and 1mA.
•when it has a 50mV drop the coil is carrying
1mA,
•the pointer will be deflected into the full scale
position.

59. ENGN1218 Introduction to Electronics
59
•Ideal Meters
–Ideal ammeter
•Equivalent resistance of zero
•No voltage drop across the ammeter
–Ideal voltmeter
•Equivalent resistance that is infinite
•No current through voltmeter
•Practical(real) Meters
–Real ammeter
•Equivalent resistance greater than zero
–Adds resistance in series with the element whose current is being
measured
–Real voltmeter
•Equivalent resistance is not infinite
–Adds resistance in parallel with the element whose voltage is being
read.
Ideal and Practical(real) Meters

60. ENGN1218 Introduction to Electronics
60
•Rule of thumb for practical (real) meters
–The circuit is negligibly disturbed when the following rules of
thumb are satisfied
–Ammeter
•Effective resistance should be no more than ⁄
1
10
??????????????????the value of
the smallest resistance in the circuit
–Voltmeter
•Effective resistance should be more than 10 times the value of the
largest resistance in the circuit
•The error introduced by a real meter in the circuit
•%????????????????????????????????????????????????????????????=(
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
????????????????????????????????????????????????????????????????????????????????????????????????????????????
−1)×100
Practical(real) Meters

61. ENGN1218 Introduction to Electronics
61
•An analogue voltmeter
–includes a d’Arsonvalmovement in
serieswith a resistor
•This resistor limits the voltage drop
across the meter’s coil
•An analogue ammeter
–includes a d’Arsonvalmovement in
parallelwith a resistor:
–This resistor limits the amount of
current flowing into the movement coil
Practical (Real) Analogue Meters
•In both meters the added resistor determines the full-scale reading
of the meter movement

62. ENGN1218 Introduction to Electronics
62
Realanalogue ammeter
Resistors are in parallel with the
d’Arsonalmovement
Real analogue voltmeter
Resistors are in series with the d’Arsonal
movement
Single range
Multiple range
Practical Meters

63. ENGN1218 Introduction to Electronics
63
Ammeter: Textbook Example 3.5
a) ????????????
????????????=?When ????????????
????????????=10mA
•KCL at top node
•????????????
????????????=10????????????−1????????????=9????????????????????????
•Ohm’s Law: ????????????=⁄
????????????
????????????
•????????????
????????????=????????????
????????????=50????????????????????????
•????????????
????????????= ⁄
50????????????????????????
9????????????????????????
=5.55Ω
b) full- scale reading ????????????
????????????=1A, ????????????
????????????=?
•KCL at top node
•????????????
????????????=1−1????????????=999????????????????????????
•Ohm’s Law:????????????
????????????=�
????????????????????????
????????????????????????
•????????????
????????????=50????????????????????????
•????????????
????????????= ⁄
50????????????????????????
999????????????????????????
=50.05mΩ
Note: for good meter accuracy, at this full
scale current the smallest resistor in circuit
should be
=10×50.05????????????=0.5????????????
1????????????????????????
−
+
50????????????????????????
????????????
????????????
????????????
????????????

64. ENGN1218 Introduction to Electronics
64
Ammeter: Textbook Example 3.5 contd
c) ????????????
????????????=10mA What is the meter
equivalent resistance ????????????
?????????????????????????
•????????????
????????????????????????=????????????
????????????||????????????
????????????=
????????????????????????????????????????????????
????????????????????????+????????????????????????
•????????????
????????????= ⁄
50????????????????????????
9????????????????????????
=5.55Ω
•????????????
????????????= ⁄
50????????????????????????
1????????????????????????
=50Ω
•????????????
????????????????????????=
????????????????????????????????????????????????
????????????????????????+????????????????????????
=
5.55×50
5.55+50
=5Ω
(for good accuracy of the meter, the smallest
R in the circuit should be
=5×10=50???????????? )
d) ????????????
????????????=1A What is the meter
equivalent resistance ????????????
?????????????????????????
•????????????
????????????= ⁄
50????????????????????????
999????????????????????????
=50.05mΩ
•????????????
????????????????????????=
50.05????????????×50????????????
50.05????????????+50????????????
=25.01mΩ
1????????????????????????
−
+
50????????????????????????
????????????
????????????
????????????
????????????????????????
????????????????????????

65. ENGN1218 Introduction to Electronics
65
Ammeter Problem: Textbook Ass 3.5
Textbook Ass 3.5
•a) Find the current in the circuit
•b) If the ammeter is used to
measure the current, what will it
read? Use prevex. ????????????
????????????????????????value.
•c) What is the error?
Ans:
•a) Ohm’s Law ????????????=⁄
????????????
????????????
????????????=�
1
100
=10????????????????????????
•b) using ammeter
•????????????
????????????????????????=5Ω(fromprevexample)
•????????????
????????????????????????????????????????????????????????????????????????????????????????????????=�
????????????
????????????
????????????????????????
•=�
1
(5+100)
=9.53????????????????????????
c) Calculating error introduce by A
•%????????????????????????????????????????????????????????????=
????????????????????????????????????????????????????????????????????????????????????????????????
????????????????????????????????????????????????
−1×100
=
9.53????????????
10????????????
−1×100=−4.76%

66. ENGN1218 Introduction to Electronics
66
Voltmeter: Textbook Example 3.6
Ans:
a) ????????????
????????????= ⁄
50????????????????????????
1????????????????????????
=50Ω
•Use voltage divider
????????????
????????????=50????????????????????????=
50
50+????????????
????????????
×150
????????????
????????????=149.95????????????Ω
c) What is the equivalent resistance ????????????
?????????????????????????
????????????
????????????????????????=????????????
????????????+50=149.95????????????+50=150????????????Ω
For good meter accuracy, the largest resistor in the
circuit should be
150????????????
10
=15????????????????????????
d) Fullscale5V
50????????????????????????=
50
50+????????????
????????????
×5
????????????
????????????=4.95????????????Ω
????????????
????????????????????????=????????????
????????????+50=4.95????????????+50=5????????????Ω
For good meter accuracy, the largest resistor in the
circuit should be
5????????????
10
=500????????????
????????????
????????????=50Ω−
+
50mV
50Ω

67. ENGN1218 Introduction to Electronics
67
d’ArsonvalVoltmeter: Textbook Assessment 3.6
Ans:
a) 2 resistors in series, u
se voltage
divider rule
????????????=
75????????????
75????????????+15????????????
×60=50????????????
b) Place voltmeter that has been rated
for 150V across the 75Ω.
????????????
????????????????????????=75????????????||150????????????=
75????????????×150????????????
75????????????+150????????????
=50????????????Ω
????????????
????????????????????????????????????????????????????????????????????????????????????????????????=
50????????????
15????????????+50????????????
×60=46.15????????????
%????????????????????????????????????????????????????????????=
????????????????????????????????????????????????????????????????????????????????????????????????
????????????????????????????????????????????????
−1×100
=
46.15
50
−1×100=−7.7%
????????????
????????????
????????????????????????(????????????)
=150????????????Ω

68. ENGN1218 Introduction to Electronics
68
In our next video…
We will measure voltage, current and resistance

69. ENGN1218 Introduction to Electronics
69
Topic 3 Video 6
Measuring Voltage, Current and Resistance
Overview
•Ammeter
•Voltmeter
•Ohmmeter
•Ground
•Electrical Safety

70. ENGN1218 Introduction to Electronics
70
Practical Measurement
Often need to measure current, voltage and resistance
•Ammeter
–Measuring current
–Schematic circle with I or A
•Voltmeter
–Measuring voltage
–Schematics: circle with V
•Ohmmeter
–Measuring resistance
•Multimeter
–Measures all three
–Digital or Analogue

71. ENGN1218 Introduction to Electronics
71
Digital Multimeters (DMM)
•Most digital multimeters
automatically select the correct range
for measurement.
–auto-ranging or auto-scaling
•Digital multimeters measure the
continuous voltage at discrete time
points
–The signal is converted from
analogue to digital
•Digital multimeters are widely used
–generally more accurate
Main dial to select
the different modes.
Select resistance,
voltage and current
over different
ranges

72. ENGN1218 Introduction to Electronics
72
•Good practice
–Turn off before connecting to circuit
–Always start with the meter set to the highest range
•Can move down the range if needed
•Avoids damaging the multimeter
•Observe proper polarity
–When measuring DCcurrent or voltage
•To avoid damage always set to correct mode
–AC, DC, V, A, ohms
•Turn off when measurement is complete
–avoids draining the battery.
How to Properly Use a Multimeter

73. ENGN1218 Introduction to Electronics
73
•To measure voltage
–Place the voltmeter leads across the component
•Correctly use the red and black leads
–Insert the red lead into the + socket
–Insert the black lead into the –(or COM) socket
–The point where the red lead is connected is
positive with respect to the point where the black
lead is connected.
How to Measure Voltage?
Voltage is the potential difference between two points

74. ENGN1218 Introduction to Electronics
74
•If reading is positive,
–the point where the red lead is connected is
positive with respect to the point where the black
lead is connected.
How to measure current?
To measure the current, we connect the
ammeter in series with the element.
Current to be measured
Ammeter correctly inserted

75. ENGN1218 Introduction to Electronics
75
•When using an Ohmmeter to measure resistance:
–Ohmmeter has its own battery
–Remove all power supplies from the circuit being
tested
•If not could damage ohmmeter
•If not, result is nonsense
–Isolate the component from the rest of the circuit
•Disconnect at least one terminal
–Connect the two probes across the component
•For resistors, the black and red leads are
interchangeable
•For other components, the resistance is dependent
on the current direction
–Check correct range on Ohmmeter
•For analogue: Most accurate when dial is close to
centre
–Turn off after measurement complete
How to Use an Ohmmeter

76. ENGN1218 Introduction to Electronics
76
•Ground
–Point of reference or a common point in a circuit
–Voltage must always be measured from a reference potential .
–We make this reference potential 0V
•commonly referred to as ground.
–The most frequently used reference potential is the Earth
•or more specifically the ground that your building is embedded in.
Earth Ground
•a) Signal Ground:
•circuit reference point where we assume 0V
•b) Earth Ground:
•the earth is used as reference point
•c) ChasisGround:
•when use the case or chasisas the circuit
reference point.

77. ENGN1218 Introduction to Electronics
77
•Electric shock
–Caused by current flow through the body
•Possible if working with power ‘on’ and touching ‘live’ conductors
–The body’s resistance is measured by holding a wire in each hand
•Between 10,000Ωand 50,000Ω.
–The tighter you hold the wires the lower the resistance
–If hold only one conductor, your resistance is higher
»The higher the body’s resistance the lower the current
»Depends on weight, skin moisture, points of contact
Electrical Safety
•Heart beat could become irregular or
stop altogether
•Electrical burns on skin and deeper tissue
•Could fall or be thrown down
•Severe muscle contraction
•Respiratory system may be paralysed

78. ENGN1218 Introduction to Electronics
78
•An electric shock can be from a current as small as 10µA
•The ‘let-go’ current
•~9mA for men
•~6mA for women
•The greatest danger to the human body
•is a source that can output more than 30V
•with enough power to maintain the load current through the body
Electrical Safety

79. ENGN1218 Introduction to Electronics
79
•High-voltage circuits are dangerous, as they can produce
dangerous amounts of current
•Example:
500????????????acrossahumanbodyofresistanceof25,000Ω
•????????????=⁄
????????????
????????????
=⁄
500
25000
=20????????????????????????which can be fatal
•The power dissipated in the body
•????????????=????????????.????????????=500×20????????????=10????????????
•The danger of shock is also determined by the power of the
supply
•If source cannot supply the 10W
•Its output voltage drops
•the current is reduced.
Electrical Safety: Example

80. ENGN1218 Introduction to Electronics
80
In our next video…
We will cross the bridge of resistance.

81. ENGN1218 Introduction to Electronics
81
Topic 3 Video 7
Measuring Resistance with Wheatstone
Bridge.
Overview
•Derive the Wheatstone bridge equation

82. ENGN1218 Introduction to Electronics
82
•How to read the colour bands of resistors
Resistors: Color Codes

83. ENGN1218 Introduction to Electronics
83
Resistors: Variable

84. ENGN1218 Introduction to Electronics
84
•Wheatstone bridge
–One of many different methods to measure resistance
–An unknown resistance ????????????
????????????is balanced against a standard
accurate variable resistor ????????????
3
•To balance the bridge, the value of ????????????
3is varied
•Balance occurs when 0A current flows through the d’Arsonval
movement called a Galvanometer (G)
Measuring Resistance: Wheatstone Bridge
Precisely measures values in
range 1Ω to 1MΩ(accuracy
0.1%)

85. ENGN1218 Introduction to Electronics
85
Deriving equation for Wheatstone bridge
•Step 1: Balance the bridge
–Vary ????????????
3until ????????????
????????????=0????????????
–KCL: When ????????????
????????????=0????????????,
•then ????????????
1=????????????
3& ????????????
2=????????????
????????????
•Step 2: Same voltage at a & b
•????????????
1????????????
1=????????????
2????????????
2& ????????????
3????????????
3=????????????
????????????????????????
????????????
•Step 3: Substituting from Step 1
•Rewrite ????????????
1????????????
1=????????????
2????????????
2as ????????????
3????????????
1=????????????
????????????????????????
2
•Step 4:
????????????3????????????1
????????????3????????????3
=
????????????????????????????????????2
????????????????????????????????????????????????
•
????????????
1
????????????
3
=
????????????
2
????????????
????????????
Wheatstone Bridge: Equation
????????????
????????????=
????????????
2
????????????
1
????????????
3

86. ENGN1218 Introduction to Electronics
86
•If ????????????
1=????????????
2, then ????????????
????????????=????????????
3
–This limits the range of resistance that can be measured
–If ????????????
????????????=1????????????Ω, but ????????????
3can only be varied over the range 0 to 100Ω,
then the bridge can never be balanced.
Wheatstone Bridge: Range of Resistance
????????????
????????????=
????????????
2
????????????
1
????????????
3

87. ENGN1218 Introduction to Electronics
87
•For wide range of resistor measurement
•vary the ratio of �
????????????2
????????????
1
•Commercially ????????????
1and ????????????
2
•consist of decimal values of resistance
•Normally the decimal values are 1, 10, 100, 1000Ω
•Thus we can vary the ratio of �
????????????2
????????????1
from 0.001 to 1000 in
decimal steps
•The variable resistor????????????
3is usually adjusted in integral values
from 1 to 11,000Ω
Wheatstone Bridge: Range of Resistance
????????????
????????????=
????????????
2
????????????
1
????????????
3

88. ENGN1218 Introduction to Electronics
88
Wheatstone Bridge: Textbook Assessment 3.7
•Solve:
????????????
????????????=
????????????
2
????????????
1
????????????
3
????????????
????????????=
1000
100
×150=1.5????????????Ω

89. ENGN1218 Introduction to Electronics
89
Real World Perspective: Strain Gauges
not assessable

90. ENGN1218 Introduction to Electronics
90
Real World Perspective: Resistive Touch Screens

91. ENGN1218 Introduction to Electronics
91
Independent Tutorial in Week03
•See: Independent Tutorial in Week03 (wattle)

92. ENGN1218 Introduction to Electronics
92
In our next video…
We will begin Topic 4