Unit I of BEEE Subject

1. BASIC ELECTRICAL AND
ELECTRONICS ENGINEERING
UNIT- I

2. TOPIC: BASIC CIRCUIT COMPONENTS
&
OHM’S LAW

3. ELECTRIC CIRCUIT
An electric circuit is an interconnection of
electrical elements

4. ELECTRIC CURRENT
Electric current is the time rate of flow of
Electric charge. It is measured in amperes(A).
Mathematical Relationship between current i, charge q
and time t is
1 ampere= 1 coulomb/Second
dt
dq
i 

5. • A direct current(dc) is a current that remains
constant with time
• An alternating current (ac) is a current that
varies sinusoidally with the time.

6. ELECTRIC VOLTAGE
The voltage vab between two points a and b in
an electric circuit is the energy (or work) needed
to move a unit charge from a to b.
Or
Voltage or potential difference is the energy
required to move a unit charge through an
element. It is measured in volts(V)
Mathematically
1 volt= 1 joule/coulomb
dq
dw
vab


7. ELECTRIC POWER
Power is the time rate of expending or
absorbing energy. It is measured in watts(W).
Mathematically
P=VI or p=vi
dt
dw
p 

8. ELECTRIC ENERGY
Energy is the capacity to do work. It is
measured in Joules(J).
Mathematically
Energy=P*t
1 Wh =3600 J
Que: How much energy does a 100 W electric
bulb will consume in two hours?

9. VOLTAGE SOURCE
Ideal Voltage Source :
Practical Voltage Source :

10. CURRENT SOURCE
Ideal current Source :
Practical current Source :

11. BASIC CIRCUIT COMPONENTS
• Resistor
• Inductor
• Capacitor

12. Resistor
• The resistance R of an element denoted its
ability to resist the flow of electric current.
• It is measured in ohms.
R- resistivity of the material is ohm-meter
l- length of the material in meter
A-cross section area of the material in meter
A
l
R 

13. OHM’S LAW
Ohm’s law states that the voltage V across a
resistor is directly proportional to the current i,
flowing through the resistor.
iv
iRv 

14. Limitations of Ohm’s law
• Ohm’s law does not applicable for all the non-metallic
conductors.
• It is not applicable to non-linear devices such as zener diode,
Vacuum tubes etc.
• Ohm’s law is true for metal conductors at constant
temperature. If the temperature changes, the law is not
applicable.

15. NETWORK DEFINITION
BRANCH: A branch represents a single element
such as a voltage source or a resistor.
Node: A node is the point of connection
between two or more branches.
Loop: A loop is any closed path in a circuit.
Fundamental theorem of network topology
A nework with b branches,n nodes, and l
independent loops will satisfy the fundamental
theorem of network topology
b=l+n-1

16. Problem 1 : What will be the current drawn by a lamp
rated at 230 V, 60 W connected to the
230 V supply?
Problem 2 : What is amount of current, if the lamp is
connected to 250 V and 415 V?
Problem 3 : What is the value of resistance of the
lamp given in Problem 1?

17. Problem 4 :
A circuit consists of three resistors 3Ω, 4Ω and 6Ω in parallel and
a fourth resistor 4Ω in series. A battery of emf 12 V and internal
resistance 6Ω is connected across the circuit. Find the total
current in the circuit and terminal voltage across the battery.

18. KIRCHHOFF’S LAWS
Kirchhoff’s Voltage Law states that the algebraic
sum of all voltages around the closed path or loop is
zero.
Sum of voltage rises = sum of voltage drops
M= Number of voltages(Number of branches) in
the loop


M
m
m
v
1
0

19. Problem 5
• Find the voltage across
resistors.

20. Kirchhoff’s Current Law states that the algebraic
sum of currents entering at a node (or a closed is
zero.
Sum of Currents = Sum of Currents
entering at a node leaving at a node
N= Number of branches connected to the node


N
n
n
i
1
0

21. PROBLEMS IN KVL

22. Problem 6
For the circuit shown in figure, determine the
unknown voltage drop V1
(ANS: V1=19 V)

23. Problem 7
In the circuit of figure find using “krichhoff’s
laws” the currents in the various elements.
Find also the power delivered by the battery.
(Ans: 3 A, 2 A & 1 A, 54 W)

24. Problem 8
Calculate the currents supplied by the batteries
in the network shown in figure.
(Ans: I1=5 A, I2=-1 A & I3=4 A)

25. MESH CURRENT METHOD

26. Problem 9
Give mesh and branch currents shown in figure.
(Ans: I1=2.86 A, I2=-0.521 A, 3.381 A)

27. Problem 10
In the circuit shown in figure, obtain the load
current and power delivered to the load.
(Ans: 2 A, 60 W)

28. Source Transformation

29. NODE VOLTAGE METHOD

30. Problem 11
Using nodal analysis, determine the current in
the 20 Ω resistor.
(Ans:I=0.6 A)

31. Problem 12
Using nodal analysis, obtain the currents
flowing in all the resistors of the circuit shown
in figure.
(Ans:I=4.25 A, 6.38 A, 8.51 A)

32. Problem 13
Using nodal analysis, obtain the current
flowing in the 15 ohm resistor of the circuit
shown in figure.
(Ans:I=2.78A)

33. Electrical Measurements
• Operating Principles of moving iron
instruments (Ammeters and voltmeters)
• Dynamometer type watt meters and energy
meters
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34. Measurement
• Measurement is an act or the result of
quantitative comparison between an unknown
magnitude and pre defined standard. Since two
quantities are compared the results is expressed
in numerical values.
• If the result is to be meaningful two requirements
must be met viz.
1. The standard which is used for comparison must
be accurately known and commonly accepted.
2. The procedure and equipment used for
obtaining this comparison must be provable.

35. Methods of Measurements
• Direct comparison method.
• Indirect comparison method.

36. Methods of Measurements
Direct comparison method:
• In this method, the unknown quantity
(measurand) is directly compared against a
standard. The result is expressed as a numerical
value and a unit. It is common for the
measurement of physical quantities like mass and
time.
• This method is not always possible, feasible and
practicable. It is inaccurate because they involve
human factors and less sensitive. Hence direct
methods are not preferred and are rarely used.

37. Methods of Measurements
Indirect comparison method:
• In this method, the parameter to be measured
is compared with the standard through the
use of a calibrated system. These methods are
mostly used in industries.

38. Types of Measurements
• Primary measurements
• secondary measurements
• Tertiary measurements

39. Types of Measurements
• Primary measurements:
In this case the sought value of a parameter is
determined by comparing it directly with
reference standard. This type of measurement is
called primary measurements.
Example:
• Measuring the length of a line with a scale.
• Judging the weight of unknown mass.
• Matching of two colours and light intensities

40. Types of Measurements
• Secondary measurements:
This type of measurements involves one conversion since
the measured quantity is not observable (like the
temperature of fluid). It is necessary to make indirect
comparison using the calibrated system. The following
requirements are satisfied by this method.
a) It should be converted temperature changes into length
changes.
b) A length scale calibrated interms of known changes in
temperature.
Example:
In a mercury thermometer the primary signal
(temperature) is transmitted to a transducer (mercury)
and the secondary signal (length) is read by observer)

41. Types of Measurements
• Tertiary measurements:
This type of measurements involves two
conversion. This measurements involves the
conversion of the measured quantity into another
quantity which is again converted into length and
thus involves two conversion of the quantity to
be measured. Measurement of temperature by
thermocouple is an example of this type of
measurements.

42. Types of Measurements
• Tertiary measurements:
• The primary signal is sensed by the transducer which
generates a voltage directly proportional to the
temperature difference. It is the first conversion
(temperature into voltage). This voltage is then
converted into length (second conversion) by means
of suitable meter which is transmitted to observer’s
eye.

43. Types of instruments
• An instrument is a device for measuring the
values or magnitude of a quantity or variable.
1. Mechanical instruments
2. Electrical instruments
3. Electronic instruments

44. Types of instruments
• Mechanical instruments:
The mechanical instruments were the first
instruments in nature and the principles on which
they worked are even used today.
Advantage:
These instruments are very reliable for static and
stable operation.
Disadvantages:
1. It is unable to response rapidly to measurement of
dynamic and transient conditions. This is because of
the rigid, heavy and bulk moving parts and
consequently have a large mass.
2. These instruments are potential source of noise and
hence cause pollution of silence.

45. Types of instruments
• Electrical instruments:
These instruments are more rapid in indicating
the output of detector than mechanical
instruments. Unfortunately electrical
instruments have to depend on mechanical
instruments (i.e., meter) as indicating device.
Since mechanical instruments have some inertia,
they have limited time and hence frequency
response.

46. Types of instruments
Electronic Instruments:
• The requirements to step up response time and also the
direction of dynamic changes in certain parameters,
requires the monitoring time of the order of milliseconds
and quite often microseconds, have led to the development
of electronic instruments.
• For example a CRO can follow dynamic and transient
changes of the order of nanoseconds
• Advantages:
1. More reliable, Light weight, compact, very fast response,
power consumption is very low
• Disadvantages:
1. High cost
2. Complex circuit

47. Classification of Instruments
1. Absolute instruments
2. Secondary instruments

48. Classification of Instruments
• Absolute instruments:
It measures the quantity in terms of physical
constants of the instruments. Use of these
instruments is time consuming since every time a
measurement is made, it takes lot of time to
complete the magnitude of measurand.
Examples of absolute instruments are:
1. Tangent galvanometer.
2. Rayleigh’s current balance.

49. Classification of Instruments
• Secondary instruments:
This type of instruments are designed in such a
manner that measurand can be measured by
observing the output indicated by the instrument.
The examples of secondary instruments are
voltmeter, ammeter, glass thermometer and
pressure gauge etc.
Secondary instruments are mainly used in every
sphere of measurement while absolute
instruments are rarely used for examples in
standard institutions.

50. Functional classification of
instruments
• Indicating instruments
• Recording instruments
• Controlling instruments

51. Functional classification of instruments
Indicating instruments:
• These instruments indicate the magnitude of
the quantity being measured, with the help of
dial and pointer. The moving system of such
an instrument is filled with a pointer that
moves over a calibrated scale to indicate the
reading. Examples of this instruments are
voltmeter, ammeters, wattmeter's etc.

52. Functional classification of instruments
Recording instruments:
• They give a continuous record of the quantity
being measured over a specified period. The
moving part connected to a pen, records the
variation in the quantity being measured on a
paper (e.g. X-Y recorders).

53. Functional classification of instruments
Controlling instruments:
• In these instruments, the information is used
by the instruments to control the original
measured quantity. For example thermostat
for temperature control and floats for liquid
level control.

54. Classification of analog instruments
• Direct current instrument
• Alternating current instrument
• Universal instruments ( both DC and AC measurements)
some other classification
• Indicating instrument
• Recording instrument
• Integrating instrument
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55. Principles of operation of analog
instruments
• Magnetic effect
• Thermal effect
• Electrostatic effect
• Induction effect
• Hall effect
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56. • Force of Attraction or Repulsion ( Moving iron instruments)
• Force between a current carrying coil and a permanent
magnet (moving coil instruments)
• Force between two current carrying coil (dynamometer
type instruments)
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57. Operating forces needed for indicating
instruments
• Deflecting force
• Controlling force
• Damping force
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58. Operating system
• Deflecting system
The system or device which produces
deflecting force to move the pointer from it
zero position is known as deflecting system.
The effects used to produce deflecting force
are
1. Magnetic effect – generally for ammeter and
voltmeter
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59. 2.Heating effect – for ammeters and voltmeters
3.Electrodynamic effect – for ammeter,
voltmeters and wattmeters
4.Chemical effect – for DC ampere hour meters
5.Electromagnetic effect – for ammeters,
voltmeters, wattmeters and watthour meter
6 . Electrostatic effect – for voltmeters only
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60. • Controlling system
The system that produces a force equal and
opposite to deflecting force. Controlling forces
are applied in two ways
1. Spring control (used in modern instruments)
2. Gravity control ( not popularly used)
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61. Spring control
• A hair spring attached to the moving system
produces a controlling torque.
• Requirements for spring are
1. They should be non-magnetic (phosphor bronze)
2. They should be free from mechanical fatigue
3. They should have a small resistance, where
springs are used to lead the current into
moving system.
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62. 24-Dec-20 62

63. Gravity Control
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64. Damping System
• The device that produces a damping force to
reduce the oscillations when the pointer
comes to final steady value.
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65. Methods of producing damping torque
1. Eddy current damping
2. Air damping
3. Fluid damping
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66. Eddy current damping
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67. Air Friction damping
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68. Fluid Damping
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69. Permanent Magnet Moving Coil
Instruments (PMMC)
• Operating principle
• When a current carrying conductor is placed in a magnetic field, a force
acts upon the conductor which tends to move it.
• If the strength of the magnetic field is constant, force exerted on the
conductor will be proportional to the current carried by it.
• Hence deflecting force will be proportional to the current to be measured.
Deflecting torque = N.B.A.I
= K.I
Where,
K = NBA – constant
I – current flowing through the meter
N – No. of turns in the coil
B – flux density in wb/m2
A – Area of the coil in m2
24-Dec-20 69

70. • Controlling Torque is provided by spiral
springs. This Torque is proportional to the
angular deflection.
T c = Cθ
T c = controlling torque
C = spring constant
θ = angular deflection
• For steady state deflection
KI = C θ
θ = KI/C
current I = (C/K) θ
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71. Construction
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72. Core magnet construction
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73. Advantages of moving coil Instruments
• The scale is uniform
• The power consumption is very low as 20μW to 200 μW
• The torque/weight ratio is high which gives a high accuracy
( 2% of full scale deflection)
• A single instrument can be used for many different current,
voltage ranges
• Errors due to stray magnetic fields are small, because of the
large operating forces
24-Dec-20 73

74. Disadvantages of moving coil
Instruments
• These instruments are useful only for DC. If
the instrument is used in AC, the deflecting
torque reverses when the current reverses;
the pointer cannot follow such rapid reversals
• The cost of the moving coil instrument is
higher than that of moving iron instrument
24-Dec-20 74

75. Errors in PMMC instruments
The main sources of errors are due to
• Weakening of permanent magnet due to
ageing and temperature effect
• Weakening of springs due to ageing and
temperature effect
• Change of moving coil with temperature
24-Dec-20 75

76. Applications of the PMMC instrument
• These instruments can be used as voltmeter
and ammeter with multiranges
• Self shielding magnets make the core magnet
mechanism particularly useful in aircrafts and
other aerospace applications where more
number of instruments are mounted in one
case to form a unified display. Thereby
considerable amount of weight is reduced.
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77. Moving iron instrument
• The most common ammeter and voltmeter
are the moving iron instrument. These type of
instruments are generally used for laboratory
or switch-board power frequencies.
• There are two types of MI instruments
1. Attraction type
2. Repulsion type
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78. Attraction type
24-Dec-20 78

79. Repulsion type
• In this type of MI instrument, there are two
vanes inside the coil. These vanes are similarly
magnetized when the current flows through
the coil and there is a force of repulsion
between the two vanes resulting in the
movement of moving vane.
• There are two types of vanes
1. Radial vane type
2. Co-axial vane type
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80. Radial vane type
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81. Co-axial vane type
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82. Torque equation
• Expression for the torque of a moving iron instrument can be
derived by considering a small increment in the current, di supplied
to the coil in the instrument. Because of this, there will be a small
deflection, 𝑑Ө and some mechanical work will be done. If 𝑇𝑑 is the
deflection torque, then
• Mechanical work done = 𝑇𝑑 .𝑑Ө
• As the vane tries to occupy the position of minimum reluctance
either by the principle as in repulsion type instrument, there will be
a change in the energy stored in the magnetic field due to the change
in inductance.
• Let I = initial current in A
L = Instrument inductance in H
Ө = deflection in radians
dI = increase in current in A
dL= change in inductance in H
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83. Torque equation
• If the current increases by dI, the deflection
changes by dӨ which changes the inductance by
dL. In order to increase the current by dI, there
must be an increase in the applied voltage given
by e =
𝑑
𝑑𝑡
(LI)
Since , both L and I are variables,
e = I
𝑑𝐿
𝑑𝑡
+ L
𝑑𝐼
𝑑𝑡
Where, e is the applied voltage.
Electrical energy supplied is given by
24-Dec-20 83

84. Torque equation
eI dt = 𝐼
𝑑𝐿
𝑑𝑡
+ L
𝑑𝐼
𝑑𝑡
𝐼 𝑑𝑡
eI dt = 𝐼2 𝑑𝐿 + 𝐿𝐼 𝑑𝐼
The stored energy due to inductance changes from
1
2
𝐿𝐼2
𝑡𝑜
1
2
(L + dL) (𝐼 + 𝑑𝐼)2
Hence, change in stored energy
1
2
(𝐿 + 𝑑𝐿)(𝐼2 + 2𝐼 𝑑𝐼 + (𝑑𝐼2) −
1
2
𝐼2 𝐿
=
1
2
𝐼2 𝐿 + 𝐼𝐿 𝑑𝐼 +
1
2
L (𝑑𝐼)2 +
1
2
𝐼2 𝑑𝐿 + IdIdL +
1
2
(𝑑𝐼)2dL -
1
2
𝐼2L
Neglecting the higher order terms,
Change in stored energy = 𝐼𝐿 𝑑𝐼 +
1
2
𝐼2 𝑑𝐿
24-Dec-20 84

85. Torque equation
From the principle of conversion of energy
Electrical energy supplied = change in stored energy + Mechanical
work done
𝐼2 𝑑𝐿 + 𝐼𝐿 𝑑𝐼 = 𝐼𝐿 𝑑𝐼 + +
1
2
𝐼2 𝑑𝐿 + 𝑇𝑑 𝑑Ө
𝑇𝑑 𝑑Ө =
1
2
𝐼2 𝑑𝐿
𝑇𝑑 =
1
2
𝐼2 𝒅𝑳
𝒅Ө
Where, Td is the deflecting torque in N-m.
I is the current through the coil in A.
Controlling torque, 𝑻 𝒅 = 𝑲 𝑺 𝜽 𝒊𝒏 𝑁 − 𝑀
Where Ks = control spring constant in N-M/rad.
Ө = deflection in radians.
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86. Torque equation
At equilibrium, 𝑇𝑐 = 𝑇𝑑
𝐾𝑆 𝜃 =
1
2
𝐼2 𝑑𝐿
𝑑𝜃
𝜃 =
1
2
𝐼2
𝐾 𝑆
𝑑𝐿
𝑑Ө
𝜃α𝐼2
From above equation, we can infer that the
deflection of pointer is directly proportional to the
square of the current to be measured. Hence the
deflection torque is unidirectional whatever may
be the polarity of the current. Hence, the moving
iron instruments can be used for both AC and DC.
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87. Errors in MI instruments
• Errors with both DC and AC
1. Hysteresis error
2. Temperature error
3. Stray magnetic fields
• Errors with AC only
1. Frequency errors
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88. Advantages of MI instruments
• Universal instruments
• Less friction errors
• Less cost
• Robustness
• Accuracy
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89. Disadvantages of MI instruments
• Due to hysteresis effect, an appreciable error
in DC measurements
• The scale of MI instruments is not uniform
and is compared at the lower end and
therefore readings are inaccurate at this end
• The instruments are subjected to serious
errors due to frequency changes, hysteresis
and stray magnetic effects
24-Dec-20 89

90. Applications of MI instruments
• Used in multiranges ammeter and voltmeter
• Used as inexpensive indicators such as
charging and discharging current indicators in
automobiles
• Extensively used in industries for
measurement of AC voltage and current
where errors of the order of 5% to 10% are
acceptable.
24-Dec-20 90

91. Wattmeter
• Types of wattmeter
1. Dynamometer type wattmeter
2. Induction type wattmeter
3. Electrostatic type wattmeter
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92. Dynamometer type wattmeter
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93. Dynamometer type wattmeter
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94. Electric Circuit of electrodynamometer
wattmeter
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95. 24-Dec-20 95

96. Disadvantages of dynamometer type
instruments
Dynamometer ammeters and voltmeters are not in
common use, especially in DC circuits, due to
following reasons.
• The magnetic field strength obtainable is small,
owing to the absence of iron. This means that a large
number of ampere turns must be used
• The scale is not uniform, since the deflecting torque
varies as the square of the current (T α I2).
• Such instruments are more expensive than the
permanent magnet type ammeter and voltmeter.
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97. Power measurements in single phase AC circuits
using dynamometer type wattmeter
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98. Induction type Energy meter
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99. Principle:
The operation of the energy meter is based on
the passage of alternating current through
two coils (current coil and pressure coil). This
coils produce the rotating magnetic field
which interacts with a aluminium disc
suspended near to the coils and makes the
disc rotates.
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100. Construction
• A single phase induction type energy meter
consists of
1. Moving system
2. Operating mechanism
3. Recording mechanism
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101. Advantages of induction type energy meter
• Simple in operation
• High torque/weight ratio
• Unaffected by temperature variations
24-Dec-20 101

102. END