This document discusses conductors, insulators, semiconductors, direct current, alternating current, current, voltage, resistance, Ohm's law, series circuits, parallel circuits, series-parallel circuits, electric power, inductors, inductive reactance, and time constants in LR series circuits. Key concepts covered include the definitions of conductors, insulators, and semiconductors; Ohm's law formulas; formulas for calculating total resistance, current, and voltage in series, parallel, and series-parallel circuits; power formulas; inductance formulas for inductors in series and parallel; and expressions for calculating current and induced emf in LR series circuits.

1. PRINCIPLE OF
ELECTRICITY AND
ELECTRONICS
Roldan T. Quitos
Assistant Professor I

2. Conductors, Insulators and Semiconductors
Conductors
An electric current is produced when free electrons move from one atom to the next. Materials that
permit many electrons to move freely are called conductors. Copper, silver, aluminum, zinc, brass,
and iron.

3. I. Conductors, Insulators and Semiconductors
Insulators
Materials that allow few free electrons are called insulators. Materials such as plastic, rubber, glass,
mica, and ceramic are good insulators.

4. Conductors, Insulators and Semiconductors
Semiconductors
Semiconductor materials, such as silicon, can be used to manufacture devices that have
characteristics of both conductors and insulators. Many semiconductor devices will act like a
conductor when an external force is applied in one direction. When the external force is applied in the
opposite direction, the semiconductor device will act like an insulator. This principle is the basis for
transistors, diodes, and other solid state electronic devices.

5. Direct Current (DC)
• Constant voltage and/or current sources
• one-directional flow of electric charge

6. Alternating Current, AC

7. II. Current, Voltage and Resistance
Current
Electricity is the flow of free electrons in a conductor from one atom to the next atom in the same
general direction. This flow of electrons is referred to as current and is designated by the symbol “I”.
Electrons move through a conductor at different rates and electric current has different values. Current
is determined by the number of electrons that pass through a cross-section of a conductor in one
second.. For this reason current is measured in amperes which is abbreviated “amps”. The letter “A” is
the symbol for amps. A current of one amp means that in one second about 6.24 x 1018 electrons
move through a cross-section of conductor.

8. Current, Voltage and Resistance
Voltage
• Electricity can be compared with water flowing through a pipe. A force is required to get water to flow
through a pipe. This force comes from either a water pump or gravity. Voltage is the force that is applied to a
conductor that causes electric current to flow. Electrons are negative and are attracted by positive charges.
They will always be attracted from a source having an excess of electrons, thus having a negative charge, to
a source having a deficiency of electrons which has a positive charge. The force required to make electricity
flow through a conductor is called a difference in potential, electromotive force (emf), or more simply referred
to as voltage. voltage is designated by the letter “E”, or the letter “V”. The unit of measurement for voltage is
volts which is also designated by the letter “V”.

9. Current, Voltage and Resistance
Resistance
A third factor that plays a role in an electrical circuit is resistance. All material impedes the flow of
electrical current to some extent. The amount of resistance depends upon composition, length, cross-
section and temperature of the resistive material. As a rule of thumb, resistance of a conductor
increases with an increase of length or a decrease of crosssection. Resistance is designated by the
symbol “R”. The unit of measurement for resistance is ohms (Ω).

11. 1000 5% or 1K

13. George Simon Ohm and Ohm’s Law
The relationship between current, voltage and resistance was and studied by the 19th century
German mathematician, George Simon Ohm. Ohm formulated a law which states that current varies
directly with voltage and inversely with resistance. From this law the following formula is derived:
Ohm’s Law is the basic formula used in all electrical circuits. Electrical designers must decide how
much voltage is needed for a given load, such as computers, clocks, lamps and motors. Decisions
must be made concerning the relationship of current, voltage and resistance. All electrical design and
analysis begins with Ohm’s Law. There are three mathematical ways to express Ohm’s Law. Which of
the formulas is used depends on what facts are known before starting and what facts need to be
known.

14. Examples of Solving Ohm’s Law
Using the simple circuit below, assume that the voltage supplied by the battery is 10 volts, and the
resistance is 5 Ω
To find how much current is flowing through the circuit, cover the “I” in the triangle and use the
resulting equation.
Using the same circuit, assume the ammeter reads 200 mA and the resistance is known to be 10 Ω.
To solve for voltage, cover the “E” in the triangle and use the resulting equation.

16. DC Series Circuit
A series circuit is formed when any number of resistors are connected end-to-end so that there is only
one path for current to flow. The resistors can be actual resistors or other devices that have
resistance. The following illustration shows four resistors connected end-to-end. There is one path of
current flow from the negative terminal of the battery through R4, R3, R2, R1 returning to the positive
terminal.

18. Current in a Series Circuit
The equation for total resistance in a series circuit allows us to simplify a circuit. Using Ohm’s Law, the
value of current can be calculated. Current is the same anywhere it is measured in a series circuit.

19. Voltage in a Series Circuit
Voltage can be measured across each of the resistors in a circuit. The voltage across a resistor is referred to
as a volt age drop. A German physicist, Kirchhoff, formulated a law which states the sum of the voltage drops
across the resistances of a closed circuit equals the total voltage applied to the circuit. In the following
illustration, four equal value resistors of 1.5 Ω each have been placed in series with a 12 volt battery. Ohm’s
Law can be applied to show that each resistor will “drop” an equal amount of voltage.
First, solve for total resistance:
Rt = R1 + R2 + R3 + R4
Rt = 1.5 + 1.5 + 1.5 + 1.5
Rt = 6 Ω
Second, solve for current:
Third, solve for voltage across any resistor:
E = I x R
E = 2 x 1.5
E = 3 Volts

20. Voltage Division in a Series Circuit
It is often desirable to use a voltage potential that is lower than the supply voltage. To do this, a
voltage divider, similar to the one illustrated, can be used. The battery represents Ein which in this
case is 50 volts. The desired voltage is represented by Eout, which mathematically works out to be 40
volts. To calculate this voltage, first solve for total resistance.
Finally, solve for voltage:
Second, solve for current:

21. Resistance in a Parallel Circuit
A parallel circuit is formed when two or more resistances are placed in a circuit side-by-side so that
current can flow through more than one path. The illustration shows two resistors placed side-by-side.
There are two paths of current flow. One path is from the negative terminal of the battery through R1
returning to the positive terminal. The second path is from the negative terminal of the battery through
R2 returning to the positive terminal of the battery.

22. Formula for Equal Value Resistors in a Parallel Circuit
To determine the total resistance when resistors are of equal value in a parallel circuit, use the
following formula:
In the following illustration there are three 15 Ω resistors. The total resistance is:

23. Formula for Unequal Resistors in a Parallel Circuit
There are two formulas to determine total resistance for unequal value resistors in a parallel circuit.
The first formula is used when there are three or more resistors. The formula can be extended for any
number of resistors.
In the following illustration there are three resistors, each of different value. The total resistance is:

24. Voltage in a Parallel Circuit
When resistors are placed in parallel across a voltage source, the voltage is the same across each
resistor. In the following illustration three resistors are placed in parallel across a 12 volt battery. Each
resistor has 12 volts available to it

25. Current in a Parallel Circuit
Current flowing through a parallel circuit divides and flows through each branch of the circuit.
Total current in a parallel circuit is equal to the sum of the current in each branch. The following
formula applies to current in a parallel circuit.

26. Current Flow with Equal Value Resistors in a Parallel Circuit
When equal resistances are placed in a parallel circuit, opposition to current flow is the same in each
branch. In the following circuit R1 and R2 are of equal value. If total current (It) is 10 amps, then 5
amps would flow through R1 and 5 amps would flow through R2.

27. Current Flow with Unequal, Value Resistors in a Parallel Circuit
When unequal value resistors are placed in a parallel circuit opposition to current flow is not the same
in every circuit branch. Current is greater through the path of least resistance. In the following circuit
R1 is 40 Ω and R2 is 20 Ω. Small values of resistance means less opposition to current flow. More
current will flow through R2 than R1.
Using Ohm’s Law, the total current for each circuit can be calculated.
Total current can also be calculated by first calculating total resistance,
then applying the formula for Ohm’s Law.

28. Series-Parallel Circuits
Series-parallel circuits are also known as compound circuits. At least three resistors are required to
form a series-parallel circuit. The following illustrations show two ways a series-parallel combination
could be found.

29. Simplifying a Series-Parallel
The formulas required for solving current, voltage and resistance problems have already been
defined. To solve a series-parallel circuit, reduce the compound circuits to equivalent simple circuits.
In the following illustration R1 and R2 are parallel with each other. R3 is in series with the parallel
circuit of R1 and R2.
First, use the formula to determine total resistance of a parallel circuit
to find the total resistance of R1 and R2. When the resistors in a
parallel circuit are equal, the following formula is used:
Second, redraw the circuit showing the equivalent values. The result is
a simple series circuit which uses already learned equations and
methods of problem solving.

30. Simplifying a Series-Parallel Circuit to a Parallel Circuit
In the following illustration R1 and R2 are in series with each other. R3 is in parallel with the series
circuit of R1 and R2.
First, use the formula to determine total resistance of a series
circuit to find the total resistance of R1 and R2. The following
formula is used:
Second, redraw the circuit showing the equivalent values.
The result is a simple parallel circuit which uses already learned
equations and methods of problem solving.

31. Electric Power
In an electrical circuit, voltage applied to a conductor will cause electrons to flow. Voltage is the force
and electron flow is the motion. The rate at which work is done is called power and is represented by
the symbol “P”. Power is measured in watts and is represented by the symbol “W”. The watt is defined
as the rate work is done in a circuit when 1 amp flows with 1 volt applied.
Power consumed in a resistor depends on the amount of current that passes through the resistor for a
given voltage. This is expressed as voltage times current.
P = E x I or P = VI
Power can also be calculated by substituting other components of Ohm’s Law.

32. Solving a Power Problem
In the following illustration power can be calculated using any of the power formulas.

33. Power Rating of Equipment
Electrical equipment is rated in watts. This rating is an indication of the rate at which electrical
equipment converts electrical energy into other forms of energy, such as heat or light. A common
household lamp may be rated for 120 volts and 100 watts. Using Ohm’s Law, the rated value of
resistance of the lamp can be calculated.
Using the basic Ohm’s Law formula, the amount
of current flow for the 120 volt, 100 watt lamp can be calculated.
A lamp rated for 120 volts and 75 watts has a
resistance of 192 Ω and a current of 0.625 amps
would flow if the lamp
had the rated voltage applied to it.
It can be seen that the 100
watt lamp converts energy
faster than the 75 watt lamp.
The 100 watt lamp will give off
more light and heat.

34. Review questions
1. In a parallel circuit (AC and DC), the equivalent resistance/impedance of the loads ____ as more and more
of the connected loads are turned on.
(a) Increases (b) decreases (c) remain the same (d)none of them

35. 2. If a jumper is placed across a parallel circuit, its equivalent resistance becomes ____.
(a) Smaller (b) higher (c) less than (d) zero

36. The Inductor
An Inductor is a passive electrical component consisting of a coil
of wire which is designed to take advantage of the relationship
between magnetism and electricity as a result of an electric
current passing through the coil

37. Inductors in Series
Inductors can be connected together in a series connection when
the are daisy chained together sharing a common electrical
current
The current, ( I ) that flows through the first inductor, L1 has no
other way to go but pass through the second inductor and the
third and so on. Then, series inductors have a Common
Current flowing through them, for example:
IL1 = IL2 = IL3 = IAB …etc.

38. In the example above, the inductors L1, L2 and L3 are all
connected together in series between points A and B. The sum of
the individual voltage drops across each inductor can be found
using Kirchoff’s Voltage Law (KVL) where, VT = V1 + V2 + V3

39. Inductors in Series Equation
Ltotal = L1 + L2 + L3 + ….. + Ln etc.
Inductors in Series Example
Three inductors of 10mH, 40mH and 50mH are connected
together in a series combination with no mutual inductance
between them. Calculate the total inductance of the series
combination.

40. Inductors in Parallel
Inductors are said to be connected together in Parallel when both
of their terminals are respectively connected to each terminal of
another inductor or inductors
VL1 = VL2 = VL3 = VAB …etc
IT = I1 + I2 + I3

41. Three inductors of 60mH, 120mH and 75mH respectively, are
connected together in a parallel combination with no mutual
inductance between them. Calculate the total inductance of the
parallel combination in millihenries.

42. Inductors in Parallel Example No3
Calculate the equivalent inductance of the following inductive
circuit.
Calculate the first inductor branch LA, (Inductor L5 in parallel with
inductors L6 and L7)

43. Calculate the second inductor branch LB, (Inductor L3 in parallel
with inductors L4 and LA)
Calculate the equivalent circuit inductance LEQ, (Inductor L1 in
parallel with inductors L2 and LB)

44. LR Series Circuit
All coils, inductors, chokes and transformers create a magnetic
field around themselves consist of an Inductance in series with a
Resistance forming an LR Series Circuit
A LR Series Circuit consists basically of an inductor of
inductance, L connected in series with a resistor of resistance, R.
The resistance “R” is the DC resistive value of the wire turns or
loops that goes into making up the inductors coil.

45. Kirchhoff’s voltage law (KVL) gives us:
The voltage drop across the resistor, R is I*R (Ohms Law).
The voltage drop across the inductor, L is by now our familiar
expression L(di/dt)
Then the final expression for the individual voltage drops around
the LR series circuit can be given as:

46. Expression for the Current in an LR Series Circuit
Where:
V is in Volts
R is in Ohms
L is in Henries
t is in Seconds
e is the base of the Natural Logarithm = 2.71828

47. LR Series Circuit Example
A coil which has an inductance of 40mH and a resistance of 2Ω is
connected together to form a LR series circuit. If they are
connected to a 20V DC supply.
a). What will be the final steady state value of the current.
b) What will be the time constant of the RL series circuit.

48. d) What will be the value of the induced emf after 10ms.
e) What will be the value of the circuit current one time constant
after the switch is closed.

49. The Time Constant, τ of the circuit was calculated in question b)
as being 20ms. Then the circuit current at this time is given as:

50. Inductive Reactance
Inductive Reactance of a coil depends on the frequency of the
applied voltage as reactance is directly proportional to frequency
The slope shows that the “Inductive Reactance” of an inductor
increases as the supply frequency across it increases.
Therefore Inductive Reactance is proportional to frequency
giving: ( XL α ƒ )

51. A coil of inductance 150mH and zero resistance is connected
across a 100V, 50Hz supply. Calculate the inductive reactance of
the coil and the current flowing through it.

52. In a DC circuit, the ratio of voltage to current is called resistance.
However, in an AC circuit this ratio is known
as Impedance, Z with units again in Ohms. Impedance is the
total resistance to current flow in an “AC circuit” containing both
resistance and inductive reactance.
If we divide the sides of the voltage triangle above by the current,
another triangle is obtained whose sides represent the
resistance, reactance and impedance of the coil. This new
triangle is called an “Impedance Triangle”

53. The Impedance Triangle

54. A solenoid coil has a resistance of 30 Ohms and an inductance of
0.5H. If the current flowing through the coil is 4 amps. Calculate,
a) The voltage of the supply if the frequency is 50Hz.

55. b) The phase angle between the voltage and the current.

56. Power Triangle of an AC Inductor
• There is one other type of triangle configuration that we can use
for an inductive circuit and that is of the “Power Triangle”. The
power in an inductive circuit is known as Reactive
Power or volt-amps reactive, symbol Var which is measured
in volt-amps. In a RL series AC circuit, the current lags the
supply voltage by an angle of Φo.

57. Introduction to Capacitors
Capacitors are simple passive device that can store an electrical
charge on their plates when connected to a voltage source
Capacitance is the electrical property of a capacitor and is the
measure of a capacitors ability to store an electrical charge onto
its two plates with the unit of capacitance being
the Farad (abbreviated to F) named after the British physicist
Michael Faraday.
By applying a voltage to a capacitor and measuring the charge
on the plates, the ratio of the charge Q to the voltage V will give
the capacitance value of the capacitor and is therefore given
as: C = Q/V this equation can also be re-arranged to give the
familiar formula for the quantity of charge on the plates as: Q = C
x V

58. Capacitor Characteristics
The characteristics of a capacitors define its temperature, voltage
rating and capacitance range as well as its use in a particular
application

59. Calculate the charge in the above capacitor circuit.

61. Energy in a Capacitor
When a capacitor charges up from the power supply connected
to it, an electrostatic field is established which stores energy in
the capacitor. The amount of energy in Joules that is stored in
this electrostatic field is equal to the energy the voltage supply
exerts to maintain the charge on the plates of the capacitor and is
given by the formula:

62. so the energy stored in the 100uF capacitor circuit above is
calculated as:

63. Capacitors in Parallel
In the following circuit the capacitors, C1, C2 and C3 are all
connected together in a parallel branch between
points A and B as shown.
VC1 = VC2 = VC3 = VAB = 12V

64. • When adding together capacitors in parallel, they must all be converted to
the same capacitance units, whether it is μF, nF or pF. Also, we can see
that the current flowing through the total capacitance value, CT is the same
as the total circuit current, iT
• We can also define the total capacitance of the parallel circuit from the
total stored coulomb charge using the Q = CV equation for charge on a
capacitors plates. The total charge QT stored on all the plates equals the
sum of the individual stored charges on each capacitor therefore,

65. Capacitors in Parallel
CT = C1 + C2 + C3 = 0.1uF + 0.2uF + 0.3uF = 0.6uF

66. Calculate the combined capacitance in micro-Farads (μF) of the
following capacitors when they are connected together in a
parallel combination:
a) two capacitors each with a capacitance of 47nF
b) one capacitor of 470nF connected in parallel to a capacitor of
1μF
a) Total Capacitance,
CT = C1 + C2 = 47nF + 47nF = 94nF or 0.094μF
b) Total Capacitance,
CT = C1 + C2 = 470nF + 1μF
therefore, CT = 470nF + 1000nF = 1470nF or 1.47μF

67. Capacitors in Series
Capacitors are connected together in series when they are daisy
chained together in a single line
• For series connected capacitors, the charging current ( iC ) flowing
through the capacitors is THE SAME for all capacitors as it only has
one path to follow.
• Then, Capacitors in Series all have the same current flowing
through them as iT = i1 = i2 = i3 etc. Therefore each capacitor will
store the same amount of electrical charge, Q on its plates
regardless of its capacitance. This is because the charge stored by a
plate of any one capacitor must have come from the plate of its
adjacent capacitor. Therefore, capacitors connected together in
series must have the same charge.
QT = Q1 = Q2 = Q3 ….etc
• Consider the following circuit in which the three
capacitors, C1, C2 and C3 are all connected together in a series
branch across a supply voltage between points A and B.

68. Capacitors in a Series Connection
Then by applying Kirchhoff’s Voltage Law, ( KVL ) to the above
circuit, we get:
• Since Q = C*V and rearranging for V = Q/C, substituting Q/C for
each capacitor voltage VC in the above KVL equation will give
us:

69. Series Capacitors Equation

70. Taking the three capacitor values from the above example, we
can calculate the total capacitance, CT for the three capacitors in
series as:

71. Find the overall capacitance and the individual rms voltage drops
across the following sets of two capacitors in series when
connected to a 12V AC supply.
a) two capacitors each with a capacitance of 47nF
Total Equal Capacitance,
Voltage drop across the two identical 47nF capacitors,

72. b) Total Unequal Capacitance,
Voltage drop across the two non-identical
Capacitors: C1 = 470nF and C2 = 1μF.

73. However, when the series capacitor values are different, the
larger value capacitor will charge itself to a lower voltage and the
smaller value capacitor to a higher voltage, and in our second
example above this was shown to be 3.84 and 8.16 volts
respectively. This difference in voltage allows the capacitors to
maintain the same amount of charge, Q on the plates of each
capacitors as shown.

74. Capacitance in AC Circuits
Capacitors that are connected to a sinusoidal supply produce
reactance from the effects of supply frequency and capacitor size
For capacitors in AC circuits, capacitive reactance is given the
symbol Xc. Then we can actually say that Capacitive
Reactance is a capacitors resistive value that varies with
frequency. Also, capacitive reactance depends on the
capacitance of the capacitor in Farads as well as the frequency
of the AC waveform and the formula used to define capacitive
reactance is given as:
Where: F is in Hertz and C is in Farads. 2πƒ can also be
expressed collectively as the Greek letter Omega, ω to denote
an angular frequency.

75. Find the rms current flowing in an AC capacitive circuit when a
4μF capacitor is connected across a 880V, 60Hz supply.

76. When a parallel plate capacitor was connected to a 60Hz AC
supply, it was found to have a reactance of 390 ohms. Calculate
the value of the capacitor in micro-farads.

77. Using the two capacitors of 10uF and 22uF in the series circuit
above, calculate the rms voltage drops across each capacitor
when subjected to a sinusoidal voltage of 10 volts rms at 80Hz.
Capacitive Reactance of 10uF capacitor
Capacitive Reactance of 22uF capacitor

78. Total capacitive reactance of series circuit – Note that reactance’s
in series are added together just like resistors in series.
Or
Circuit current

79. Then the voltage drop across each capacitor in series capacitive
voltage divider will be:

80. Using the same two capacitors, calculate the capacitive voltage
drop at 8,000Hz (8kHz).

87. Vac = 220V
R= 130 ohms
C= 12 microFarad
L= 160 mH
60Hertz

88. What are the advantages of three phase supply over single
phase supply?

89. Transformer
• device that transfers electric energy from one alternating-
current circuit to one or more other circuits, either increasing
(stepping up) or reducing (stepping down) the voltage.
Transformers are employed for widely varying purposes; e.g., to
reduce the voltage of conventional power circuits to operate
low-voltage devices, such as doorbells and toy electric trains,
and to raise the voltage from electric generators so that electric
power can be transmitted over long distances.

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