FACILITATING AND LEARNING MATERIAL FOR
AC THEORY
National Certificate II
This facilitating and learning material covers all the Learning Outcomes for AC
Theory for the National Certificate II Programme
LEARNING OUTCOMES
1
2
3
Demonstrate knowledge of alternating current, power distribution and voltage
system
Demonstrate skills in inductance/reactance
Demonstrate skills in three phase voltage system
1.0 Introduction and Preliminary Notes
In this unit you will learn more about tubing material in refrigeration and air conditioning
and to select an appropriate tubing materials in their correct sizes for a given job. After the
learning you will be able to identify the correct insulating materials for a given activity.
The knowledge gained about tubing and insulating materials will help you to the select the
appropriate refrigeration materials in the correct sizes for the right job.
This learning material should be used with the unit specification given as the unit
specification will guide you on the standards stated with all the range statement. You
should also be guided by the evidence requirements so that your learning is relevant to the
required standards.
The way the learning material is written is to encourage learner autonomy and initiative
(i.e., activities that require the learner to work independently of the facilitator and to make
decisions concerning how you might approach a task) so that you as a learner can take
ownership of your own learning. Follow the instructions and the steps indicated in the
learning material and work as independently as possible.
Table 1: Icons and their meanings
The meaning of each icon is provided in Table 1. You should know what each icon
represents. Carefully observe the icons and their meanings.
Congratulations for going through the icons and their
meanings! We will next look at the activities under LO 1.
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LO 1 Demonstrate knowledge of alternating current, power
distribution and voltage system
This LO is developed to help you acquire skills in refrigerant charging. To achieve this,
you will have to go through PCs (a) – (f).
In this learning session you will be learning refrigerant charging in refrigeration. Before
you begin, you have to know what refrigerant charging is all about.
PC(a) Explain the concept of basic alternating current
An alternating current can be defined as a current that changes its magnitude and polarity
at regular intervals of time. It can also be defined as an electrical current that repeatedly
changes or reverses its direction opposite to that of Direct Current or DC which always
flows in a single direction as shown below.
From the graph, we can see that the charged particles in AC tend to start moving from zero.
It increases to a maximum and then decreases back to zero completing one positive cycle.
The particles then reverse their direction and reach the maximum in the opposite direction
after which AC again returns to the original value completing a negative cycle. The same
cycle is repeated again and again.
Alternating currents are also accompanied usually by alternating voltages. Besides,
alternating current is also easily transformed from a higher voltage level to a lower voltage
level.
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Alternating Current Production
Alternating current can be produced or generated by using devices that are known as
alternators. However, alternating current can also be produced by different methods where
many circuits are used. One of the most common or simple ways of generating AC is by
using a basic single coil AC generator which consists of two-pole magnets and a single
loop of wire having a rectangular shape.
In this setup, the AC generator follows Faraday’s principle of electromagnetic induction
where it converts mechanical energy into electrical energy.
Meanwhile, AC is supplied to pieces of equipment using 3 wires. They are as follows;

Power is transmitted by the hot wire.

The neutral wire which is connected to the earth provides a return path for the
current in the hot wire.

The third wire that is also connected to the earth is linked to the metallic parts of
the equipment to mainly eliminate electric shock hazards.
Application of Alternating Current
AC is the form of current that are mostly used in different appliances. Some of the examples
of alternating current include audio signal, radio signal, etc. An alternating current has a
wide advantage over DC as AC is able to transmit power over large distances without great
loss of energy.
AC is used mostly in homes and offices mainly because the generating and transporting of
AC across long distances is a lot easier. Meanwhile, AC can be converted to and from high
voltages easily using transformers. AC is also capable of powering electric motors that
further convert electrical energy into mechanical energy. Due to this AC also finds its use
in many large appliances like refrigerators, dishwashers and many other appliances.
Alternating Current Waveform
Before we learn more about this topic, let us quickly understand a few key terms.
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
The time interval between a definite value of two successive cycles is the period.

The number of cycles or number of periods per second is frequency.

The maximum value in both directions is the amplitude.
The normal waveform of AC in most of the circuits are sinusoidal in nature in which the
positive half period corresponds with the positive direction of the current and vice-versa.
In addition, a triangular or square wave can also be used to represent the alternating current
waveform.
Audio amplifiers that deal with analogue voice or music signals produce irregular AC
waves. Some electronic oscillators produce square or sawtooth waves.
Average Value of AC
The average value is usually defined as the average of the instantaneous values of
alternating current over a complete cycle. The positive half cycle of asymmetrical waves
such as a sinusoidal voltage or current waveform will be equal to the negative half cycle.
This implies that the average value after the completion of a full cycle is equal to zero.
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Since, both the cycles do some work the average value is obtained by avoiding the signs.
Therefore, the average value of alternating quantities of sinusoidal waves can be considered
by taking the positive cycle only.
RMS Value of AC Wave
RMS value is defined as the square root of means of squares of instantaneous values. It can
also be described as the amount of AC power that generates the same heating effect as an
equivalent DC power.
Phasor Diagrams
The phasor diagram is used to determine the phase relationships between two or more sine
waves propagating with the same frequency. Here, we use the terms “lead”, “lag” and also
“in-phase”, “out-of-phase” to indicate the relation between one waveform with the other.
Phasor diagrams will be of the form:
AC Circuit Containing Resistance only
The pure resistive AC circuit contains only pure resistance of R ohms. There will be no
effect of inductance and capacitance in this circuit. The alternate current and voltage
move along both directions as backwards and forwards. Therefore, current and voltage
follow a shape of sine.
In a purely resistive circuit, the power is dissipated by the resistors and the phase of both
voltage and current remains the same. This means that the voltage and current reaches a
maximum value at the same time.
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Let the supply voltage be,
v = Vm Sinωt …… (1)
The instantaneous value of current flowing through the given circuit is,
i=
v
R
=
Vsinωt
R
…… (2)
From equation (2), the value of current be maximum at t = 900, so sin t =1
Then, the instantaneous value of current will be,
i = Im sinωt …… (3)
So, by observing the equation (1) and (3), it is clear that there is no phase difference
between the applied voltage and current flowing through the circuit. Meaning, phase angle
between voltage and current is zero.
Hence, in a pure resistive ac circuit, the current is in phase with the voltage.
This can be expressed in a waveform as,
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AC Circuit Containing Inductance only
This type of circuit contains only inductance. There will not be any effect of resistance
and capacitance in this circuit. Here, the current will lag behind the voltage by an angle of
900.
The circuit will be,
The inductor will reserve electrical energy in the magnetic field when current flows through
it. When this current changes, the time-varying magnetic field causes EMF which opposes
the flow of current. This opposition to the flow of current is known as inductive reactance.
We get,
i = Im sin (ωt –
π
2
)
This implies that the current in pure inductive ac circuits lags the voltage by 900.
This can be expressed in a waveform as,
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If the voltage and current are at their peak value as a positive value, the power will also be
positive. Similarly, if the voltage and current are at a negative peak then the power will be
negative. This is because of the phase difference between them.
AC Circuit Containing Capacitor only
This type of circuit includes a pure capacitor only. It will not affect the properties of
resistance and inductance. The capacitor will store electric power in the electric field. This
is known as capacitance.
The electric field is developed across the plates of the capacitor when a voltage is applied
across the capacitor. Also, there will not be any current flows between them.
The circuit will be,
As we know, a capacitor includes two insulating plates which are separated by a dielectric
medium. Usually, a capacitor works as a storage device and it gets charged if the supply is
on and it gets discharged if the supply is off.
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i = Im sin (ωt +
π
2
)
This implies that the current flowing through the capacitor leads the voltage by 900.
This can be expressed in a waveform as,
PC(b) Explain power distribution
Electric power distribution is the final stage in the delivery of electric power; it carries
electricity from the transmission system to individual consumers. Distribution substations
connect to the transmission system and lower the transmission voltage to medium voltage
ranging between 2 kV and 35 kV with the use of transformers
PC (c) Explain three phase voltage system
The three-phase system is an economical way of bulk power transmission over long
distances and for distribution. The three-phase system consists of a three-phase voltage
source connected to a three-phase load by means of transformers and transmission lines.
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PC (d) Explain three phase delta system
Delta connection is an arrangement of three of same or different passive components. It is
also called a mesh connection. The three passive element is connected with each other; the
input supply is given through the two junctions of the element. Or the starting ends of the
three phases or coils are connected to the finishing ends of the coil.
In Delta connection, the three windings interconnection looks like a short circuit, but this
is not true if the system is balanced, then the value of the algebraic sum of all voltages
around the mesh is zero (from Kirchhoff’s voltage rule).
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In delta connection, there is three wires alone and no neutral terminal is taken. Normally
delta connection is preferred for short distance due to the problem of unbalanced current in
the circuit.
PC (e) Explain three phase star/wye system
Initially, we explored the idea of three-phase power systems by connecting three voltage
sources together in what is commonly known as the “Y” (or “star”) configuration.
This configuration of voltage sources is characterized by a common connection point
joining one side of each source.
Three-phase “Y” connection has three voltage sources connected to a common point.
If we draw a circuit showing each voltage source to be a coil of wire (alternator or
transformer winding) and do some slight rearranging, the “Y” configuration becomes
more obvious in figure below.
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Three-phase, four-wire “Y” connection uses a “common” fourth wire.
The three conductors leading away from the voltage sources (windings) toward a load are
typically called lines, while the windings themselves are typically called phases.
In a Y-connected system, there may or may not (Figure below) be a neutral wire attached
at the junction point in the middle, although it certainly helps alleviate potential problems
should one element of a three-phase load fail open, as discussed earlier.
Three-phase, three-wire “Y” connection does not use the neutral wire
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LO 2 Demonstrate skills in inductance/reactance
PC (a) Explain inductance
Inductance is the tendency of an electrical conductor to oppose a change in the electric
current flowing through it. L is used to represent the inductance, and Henry is the SI unit
of inductance. 1 Henry is defined as the amount of inductance required to produce an EMF
of 1 volt in a conductor when the current change in the conductor is at the rate of 1 Ampere
per second.
An electric current flowing through a conductor creates a magnetic field around it. The
strength of the field depends upon the magnitude of the current. The generated magnetic
field follows any changes in the current, and from Faraday’s law of induction, we know
that changing the magnetic field induces an electromotive force in the conductor.
Considering this principle, inductance is defined as the ratio of the induced voltage to the
rate of change of current causing it. The electronic component designed to add inductance
to a circuit is an inductor.
Factors Affecting Inductance
The following factors affect the inductance in a circuit:
Number of Wire Turns in the Coil: Inductance is greater when the number of turns of
wire in the coil is greater. More coils of wires indicate a greater amount of magnetic field
force for a given amount of coil current.
Coil Area: Inductance is proportional to the coil area. Greater the coil area, the greater the
inductance. Greater coil area presents less opposition to the formation of magnetic field
flux for a given amount of field force
Core Material: The greater the magnetic permeability of the core to which the coil is
wrapped around, the greater the inductance.
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Coil Length: The longer the coil’s length, the lesser the inductance. The shorter the coil’s
length, the greater the inductance.
PC (b) Explain inductive reactance
Reactance can be defined as the opposition which is offered through a capacitor & inductor
within a circuit to the AC flow. It is quite related to resistance however reactance changes
through the AC voltage source’s frequency which is measured in Ohms. If we notice
current-carrying conductors, we can discover that reactance is present always with
resistance. Additionally, reactance also shows in shorter gaps because the DC changes
while approaching from a stable flow.
Calculation of Reactance
In an AC circuit, the inductor offers the opposition to the AC supply is known as inductive
reactance. This reactance is denoted by XL and measured in ohms (Ω). Mostly, this
reactance is high for high frequencies and low for low frequencies. For steady DC, it is
small. The main formula for inductive reactance is given as
XL = 2 π x f x L.
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where,
‘XL’= inductive reactance that is measured in Ohms
‘2π’ = constant (2 x 3.1416 = 6.28)
‘f’ = AC frequency in Hertz
‘L’ = inductance value of the coil in Henrys.
PC (b) Explain semi-conductor circuits
Semiconductors, sometimes referred to as integrated circuits (ICs) or microchips, are made
from pure elements, typically silicon or germanium, or compounds such as gallium
arsenide. In a process called doping, small amounts of impurities are added to these pure
elements, causing large changes in the conductivity of the material.
PC(b) Explain capacitive reactance
Capacitive reactance is the opposition by a capacitor or a capacitive circuit to the flow of
current. The current flowing in a capacitive circuit is directly proportional to the
capacitance and to the rate at which the applied voltage is changing. The rate at which the
applied voltage is changing is determined by the frequency of the supply; therefore, if the
frequency of the capacitance of a given circuit is increased, the current flow will increase.
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It can also be said that if the frequency or capacitance is increased, the opposition to current
flow decreases; therefore, capacitive reactance, which is the opposition to current flow, is
inversely proportional to frequency and capacitance.
Capacitive reactance Xc, is measured in Ohms, as is inductive reactance.
Xc =
1,000,000
2πfc
Where
c = capacitance (farads)
f = frequency (hertz)
PC (e) Perform basic calculation involving inductance reactance, capacitive reactance
and impedance
Example: A 10µF capacitor is connected to a 120V, 60Hz power source. Find the
capacitive reactance.
Solution:
Capacitive reactance XC =
XC =
1,000,000
2πfc
1,000,000
2 x 3.142 x 60 x10
XC = 265Ω
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LO 3 Demonstrate skills in three phase voltage system
PC(a) Perform basic calculations on line voltage, phase voltage, power factor
In a three-phase balanced system, the voltage across the phase with respect to another phase
is always equal in the magnitude of the voltage and phase angle and the vector sum of the
three-phase is always zero.
The line voltage or phase voltage above 440Volts can be measured with the help of a
potential transformer. Potential meter reduces the voltage from a higher level to low level
typically 110 Volts to 63.5Volts.
At the same time the line current or phase current above 25Amps, Current transformer is
used to reduce the current level from high to low typically 1A or 5A.
Example: our domestic power supply is three phases, 440 Volts. Here 440 volts means the
phase to phase voltage is 440.
Note: If they mention in single phase 230 volts, then it means the potential difference the
phase to neutral is 230 volts.
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In star connection: VL-L = √3 x VPh
Line voltage = 1.732 times of phase voltage.
In delta connection: VL-L = VPh
Line voltage = Phase voltage.
Phase current is the measure of the current inside of star connection or delta connection of
the three phase system. It is denoted by Iph.
In star connection: Iph = IL
Phase current = Line current
In delta connection line current: IPh =
IL
1.732
NB: Value of √3 = 1.732.
PC (b) State the advantages and disadvantages of three phase system
Three phase power’s advantages
1) It delivers 1.73 times as much power to a load with a given amount of supply conductors
as single phase. (Particularly advantageous on transmission lines).
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2) It provides inherently for rotation in a definite direction for motors. 3) It reduces the
amount of iron required in transformers for a given power flow.
The only significant disadvantage is that motor starters and disconnect switches need to
have three poles rather than one, though for a given amount of power the contacts can be
much lighter duty than an equivalent single phase unit.
PC(c) Explain the 277/480 volts system
277V is a standard single phase voltage derived from 480V three phase voltage
system available in commercial applications. It can be achieved by three transformers
connected in Wye (Star – connection) having a neutral point. The transformer’s secondary
provides 277V single phase and 480V single phase and three phase voltage levels
PC (e) Compare three phase systems to single phase systems
In electrical systems, we use the terms “single-phase” and “three-phase” fairly often, so a
brief description of them will help us moving forward.
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Single-phase systems are the simplest electrical circuits. They require only two wires: one
for power to go in and the other is a return path for current to go out. These are often called
Line 1 and Line 2, or Line 1 and Neutral. Current only has one path to travel in a singlephase circuit, and all of the control circuits that we will be looking at are single-phase.
An AC single-phase circuit.
Three-phase systems are bit more complex. They use three current carrying conductors,
called Line 1, Line 2, and Line 3, which have a 120° phase shift in
the voltage and current waveforms between them. Each of these conductors are connected
to a three-phase load, like a three-phase motor.
When in operation, a balanced three-phase load (such as a motor) has each of its three line’s
current values cancel each other out, and so it does not require a return conductor. These
loads can be connected in Wye or Delta configuration.
A three-phase circuit
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Unbalanced three-phase loads are mainly connected in the Wye configuration where the
central point is used as a neutral conductor to carry any stray return currents. In practice a
motor is almost always a balanced three-phase load.
Only large industrial and commercial loads will be supplied by three-phase systems. Most
heating and cooling loads, especially those used in residential applications, will be singlephase.
PC (f) Adhere to safety measures
Ensure the strict adherence to all safety protocol so as to safeguard: Self, Others,
Instruments. Tools, Environment
Self-Assessment 1
This learning outcome (LO) has a little quiz at the end. I recommend you take
this whole quiz without looking back for any of the answers. This is meant to
help you determine how well you have understood this learning outcome. Now assess
yourself with the questions below:
1. Alternating current can be defined as current that changes its …………. at regular
intervals of time.
a. Magnitude and Current
b. Magnitude and Polarity
c. Polarity and Resistance
d. Current and Reluctance
2. In electric power distribution, substations connected to the transmission system
use …………. to lower the transmission voltage to medium voltage ranging
between 2 kV and 35 kV.
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a. Transformers
b. Transducers
c. Condensers
d. Evaporators
3. The three-phase system is an economical way of bulk power transmission over
long distances and for distribution. TRUE or FALSE
4. In Delta connection, the three windings interconnection looks like a short circuit,
but this is not true if the system is balanced, then the value of the algebraic sum
of all voltages around the mesh is zero.
a. Ohm’s current rule
b. Kirchhoff’s resistance rule
c. Ohm’s capacitance rule
d. Kirchhoff’s voltage rule
5. Three-phase “Y” connection has three ……………. sources connected to a
common point
a. Current
b. Resistance
c. Voltage
d. Capacitance
6. The ratio of the induced voltage to the rate of change of current causing it is known
as………………….
a. Reluctance
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b. Inducement
c. Current
d. Inductance
7. The opposition which is offered through a capacitor & inductor within a circuit to
the AC flow is called………………
a. Voltage
b. Reactance
c. Capacitance
d. Current
8. The process of producing semi-conductors by adding small amounts of impurities
to pure elements, causing large changes in the conductivity of the material is
referred to as………………………
a. Dodging
b. Doubling
c. Doping
d. Ducting
9. The current flowing in a capacitive circuit is directly proportional to the
capacitance and to the rate at which the applied voltage is changing.
TRUE or FALSE
10. A 10µF capacitor is connected to a 120V, 60Hz power source. Find the capacitive
reactance.
a. 265Ω
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b. 275Ω
c. 625Ω
d. 526Ω
11.
12. State one the advantage of three phase system
a. ………………………………………………………………………………
………………………………………………………………………………
13. 277V is a standard single phase voltage derived from ……. three phase voltage
system available in commercial applications.
a. 220V
b. 340V
c. 480V
d. 840V
14. Three-phase systems use three current carrying conductors, which have a
……………. phase shift in the voltage and current waveforms between them.
a. 110°
b. 120°
c. 150°
d. 220°
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