Introduction To Electric Circuit

INTRODUCTION TO
ELECTRIC CIRCUIT

NUR SHEEMA BAHARUDIN

JABATAN KEJURUTERAAN MEKANIKAL
POLITEKNIK SEBERANG PERAI

INTRODUCTION TO
ELECTRIC CIRCUIT

Nur Sheema Baharuddin
2022

MECHANICAL ENGINEERING DEPARTMENT

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in writing from Politeknik Seberang Perai.

ii eBook PSP | 2022

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Perpustakaan Negara Malaysia Cataloguing-in-Publication Data

Nur Sheema Baharuddin
INTRODUCTION TO ELECTRIC CIRCUIT / Nur Sheema Baharuddin.
Mode of access: Internet
eISBN 978-967-2774-19-8
1. Electric circuits.
2. Government publications--Malaysia.
3. Electronic books.
I. Title.
621.3192

eBook PSP | 2022 iii

Acknowledgment

Very thankful to Allah SWT for completing the academic writing for the production of an eBook for
students to learn this course. I have faced a lot of experiences that are very precious and
meaningful in my life in a way to publish this writing. In this opportunity, my sincere thank you in
particular to the Head of the Mechanical Department, Mr. Muhammad Nasir bin Marzuki, a credit
to Ms. Ruhil Naznin as CTTL coordinator because of her contribution in providing a lot of guidance
and incentives during completing this eBook.
I also acknowledge my family and friends for their support and cooperation in completing this book.
Last but not least, many thanks go to the Director of Politeknik Seberang Perai, Sr. Harith Fadzilah
Abd Khalid whose have invested his full effort in guiding the team in achieving the goal.

Nur Sheema Baharuddin

iv eBook PSP | 2022

Preface

Introduction to Electric Circuit eBook is written for Semester 2 students of the Mechanical
Engineering Department that take the subject of Electrical Technology (DJJ20053). This book is
focused on Chapter 1 of this subject which is very core/fundamental/basic knowledge that is most
important for the student to master this topic. Most of the problems occur from being unable to
cater to the basics fundamentals wisely so that they fail to understand the upcoming topic. The
book also consists the examples with solutions exercises which is similar to the Final Examination
question pattern. Hopefully, with the publication of this writing, the students will be able to
understand more effectively.

eBook PSP | 2022 v

Table of Content 1121

01 INTRODUCTION TO ELECTRIC CIRCUIT 2
1.1 Introduction to Electric 7
1.2 Classification of Material 8
1.3 Factor of Resistance 12
1.4 Measuring Voltage, Current, and Resistance 14
1.5 Ohm’s Law 17
1.6 Electrical Power 19
1.7 Energy Consumption 21
1.8 Watt Meter 22
1.9 Analysis Electric Circuit
36
SUMMARY
37
REFERENCES



eBook PSP | Introduction to Electric Circuit 1

01

INTRODUCTION TO
ELECTRIC CIRCUIT

This topic covers the principle and fundamental of the electrical circuit and solve the related
problem to the electrical circuit. It consists of the basic electrical quantities, resistivity, Ohm’s law,
power and energy, and analysis of series and parallel circuits.

2 eBook PSP | Introduction to Electric Circuit

1.1 Introduction to Electric

Electricity is all around us-powering technology like our cell phones, computers, lights,
soldering irons, and air conditioners. It's tough to escape it in our modern world. Even when
you try to escape electricity, it's still at work throughout nature, from the lightning in a
thunderstorm to the synapses inside our body.

Figure 1.1 Image of thunderstorms
Electrical energy can be created impact from action as friction, heat, chemical reaction,
and electromagnetic induction. Electricity is a natural phenomenon that occurs throughout
nature and takes many different forms. The energy can be converted to several sources of
energy that can be used such as light energy, heat energy, kinetic energy, sound energy,
and so on.

eBook PSP | Introduction to Electric Circuit 3

There are two types of electricity; static electricity and dynamic electricity.

Static electricity:
This type of electricity is generated when two non-conducting materials are rubbed
together, such as a glass material and a silk cloth material, in this situation the two
materials become electrically charged as one material will suffer from lacking electrons (+
charged material) and the other material will have extra electrons (- charged material) and
these charges remain fixed on the material surfaces until the two material are in touch or
connected to a conductor to form a closed circuit, in this case, the electrons will flow
otherwise there will no flow of electrons so we called it as static electricity.

Dynamic electricity:
This is the common type of electricity that we use in our homes or factories, where this
type of electricity results from the motion of free electrons from one atom to another, these
free electrons flow in one direction, we call this type direct current electricity (DC) and if
these free electrons change its direction from positive to negative periodically (in the same
time interval), we call this type as alternating current electricity (AC).

As an example, DC is produced by the car battery and AC is produced by the car alternator.

1.1.1 Electrical Quantities
The SI system of units is a modern form of the metric system. It is widely used in the
electrical field throughout the world.

In this section, the SI unit is classified into:
1. Base units
2. Derived units

4 eBook PSP | Introduction to Electric Circuit

Base units are the seven foundational units. Originally length, mass, and time were

identified as base quantities. Then, electric current was added as the base unit to

represent the electrical quantities. After some time, units for temperature along with

substance and luminous intensity were also added. Nowadays, this system contains 7-unit

quantities.

Table 1.1 S1 Base Unit

SI Base Unit

Quantity Symbol Unit Abbreviation

Length Ɩ meter m

Mass m kilogram kg

Time t second s

Temperature T kelvin K

Electric Current I ampere A

Amount n mole mole

Luminous Intensity Iv cd Candela

Derived units are a combination of base units that are formed by combining, multiplying,
or by taking powers of different numbers.

Table 1.2 Derived Unit Derived Unit Unit Abbreviation
Symbol coulomb C
Quantity Ω
Charge Q ohm V
Resistance R volt A
Voltage V ampere W
Current I watt J
Power P joule F
Energy E/W farad H
Capacitance C henry Hz
Inductance L hertz Wb
Frequency f weber T
Magnetic flux Ф tesla
Magnetic flux density B

eBook PSP | Introduction to Electric Circuit 5

Definitions of the units are explained on the following Table 1.3.

Table 1.3 Definition of electrical units

Unit Definition

Charge The essential property of electrons and protons

Resistance The opposition of the body against the current flow

Voltage The potential difference between the two points

Current The flow of charges from one point to another

Power The product of current and voltage

Energy Power per unit time

Capacitance The ability of the body to store charge

Frequency Number of cycles covered by sine wave per second

Magnetic flux Integral of the magnetic field passing through surface

1.1.2 Basic Electrical Quantities

1.1.2.1 Electromotive Force (EMF)

Electromotive Force (emf) is a measurement of force or electrical pressure that cause the

flow of electrons or the flow of current into an electric device or circuit. Electromotive force,

abbreviation E or emf, is energy per unit of electric charge that is imparted by an energy

source, such as an electric generator or a battery. The unit of EMF is in voltage and

measured in volts.

Symbol E / emf / Vs

Unit Volts, V

1.1.2.2 Electrical Charge

Electric charge is a basic property of electrons, protons, and other subatomic particles.

Electrons are negatively charged while protons are positively charged. Any material that

has the same charge pushes each other away (they repel each other). Electrical charge is

measured in Coulomb.

Symbol Q
Unit Coulomb, C

6 eBook PSP | Introduction to Electric Circuit

1.1.2.3 Current
An electric current is a flow of electric charge in a circuit. More specifically, the electric
current is the rate of charge flow past a given point in an electric circuit. The charge can
be negatively charged electrons or positive charge carriers including protons, positive ions,
or holes.

Symbol I
Unit Ampere, A

1.1.2.4 Voltage /Potential Difference
Voltage is a property that causes the electrical charges to move in a wire or other electrical
conductor. It can be thought of as the force that pushes the charges, but it is not a force.
Voltage can cause charges to move, and since moving charges is current, the voltage can
cause a current. Voltage is also the change in Electric Potential between two places.

Symbol V
Unit Volt, A

1.1.2.5 Resistance
Resistance is a property of a material that limits the amount of current flow and at the
same time act to produce the desired drop in voltage and current within the circuit.

Symbol R
Unit Ohm, Ω

1.1.2.6 Resistivity
The resistivity of a substance is the resistance of a cube of that substance having edges
of unit length, with the understanding that the current flows normally to opposite faces
and is distributed uniformly over them. The electrical resistivity is the electrical resistance
per unit length and per unit of cross-sectional area at a specified temperature.

Symbol Ρ (rho)
Unit Ohm Meter, Ωm

eBook PSP | Introduction to Electric Circuit 7

1.2 Classification of Materials

1.2.1 Conductor
Conductors are substances that permit easy flow of electric energy through them. More
specifically, we can say, it permits an easy flow of electrons from one atom to the other
when a proper electric field is applied to it. Examples of conductors are metals such as
silver, copper, and gold.

1.2.2. Insulator
Insulators are materials that do not allow current and electrical charges to flow through
them. The energy band gap is so high in the case of insulators that even applied potential
does not excite the electrons from the valence band to the conduction band.

1.2.3. Semi-conductor
Semiconductors are materials that possess the property of electrical conductivity less than
conductors. The charge carriers in the case of semiconductors are electrons and holes.
When the temperature is absolute zero, then no movement of charge carriers takes place
in the case of semiconductors. In such cases, it acts as an insulator. But to have a
considerable flow of charge carriers take place certain potential must be provided to them
that can excite the electrons to another energy level. Thereby, generating electric
current.

Table 1.4 Classification of material Specification Material
Item Copper

Conductor Material that easily allows current flow Iron

Semiconductor Material that has conductance value Silicon
between conductor and insulator germanium

Insulator Material that does not allow current Rubber
flow in normal condition Glass

Air

8 eBook PSP | Introduction to Electric Circuit

1.3 Factor of Resistance

The resistance of given materials depends on the physical properties of the material. Four
factors influence the value of resistance.

1. Length of conductor, ℓ
The value of resistance increases due to the length of the conductor. The longer a wire
is, the higher the resistance value.

Rαℓ

2. Cross Sectional Area, A
Resistance is inversely proportional to an area. The larger area, the lower resistance.

Rα 1



3. Temperature, T
The resistance increases due to the increase in temperature.

RαT

4. Resistivity, ρ
The value of resistance is proportional to resistivity. The higher the resistance is, the
higher the resistivity value

Rαρ

eBook PSP | Introduction to Electric Circuit 9

1.3.1 Combination of Resistance Factors in Mathematics Form
Mathematically, the formula for the resistance of a resistivity, ρ, wire length ℓ and cross-
section area, A, can be defined as the equation below:

Where is; R= Resistance (Ω)
Ρ = Resistivity (Ωm)
A= Cross section area (m²)
ℓ = Length of the conductor (m)

Example 1.1

Calculate the resistance of a 1.5km length of aluminium wire. Given the diameter of the
wire is 10 mm and the resistivity of aluminium is 0.025 µΩm.

Solution
Given d=10 10−3 , ℓ= 1500 m, ρ=0.025 10−6Ω

= ( )2 = (10 10−3)2= 78.54 10−6 ²

22

Knowing,

= ℓ = (0.025 10−6Ω )(1500) = 0.477Ω
78.54 10−6 ²


10 eBook PSP | Introduction to Electric Circuit

Exercise 1.1

1. The resistance of a conductor 1mm² in cross-section area and 20 m length is 0.76Ω.
Determine the specific resistivity of the conducting material.
(Ans: 38 nΩm)

2. Calculate the resistance of a 100 m long wire with a uniform cross-sectional area of
0,1mm² if the wire is made of iron and has a resistivity of 50 10−8Ω .
(Ans: 500 Ω)

3. Determine the specific resistivity of an aluminium wire having a circular cross-section
with a diameter of 1.5 mm, length of 2m, and resistance of 0.0359 Ω.
(Ans: 3.172 10−8 Ω )

Comprehension Test 1.1

1. Define the electric unit and symbol of:

a) Electromotive force _______________________

b) Charge _______________________

c) Current _______________________

d) Voltage _______________________

e) Resistance _______________________

2. Explain factors that affect the resistance of conductor materials.
i. _____________________________________________________________
ii. _____________________________________________________________
iii. _____________________________________________________________
iv. _____________________________________________________________
v. _____________________________________________________________

eBook PSP | Introduction to Electric Circuit 11

3. Given the length of the wire is 900m and resistivity of 0.03 µΩm. Determine the
diameter of the wire if the resistance is 0.2 Ω is produced.
(Ans: 13.11 mm)

4. Given the diameter of manganese wire is 47mm and resistivity is 90mΩm. Determine
the length of the wire if the resistance has produced 0.7Ω.
(Ans: 0.0135 m)

5. Calculate the resistance of a 1.5 km length of wire having a uniform diameter of 10
mm if the wire is made of aluminium having a resistivity of 0.025 µΩm.
(Ans: 0.477 Ω)

6. Calculate the resistance value if the length of copper wire is 2 km with a diameter of
20 mm and has a resistivity of 0.28 μΩ.m.
(Ans: 1.78 Ω)

1.3.2 Types of Electric Circuits
A circuit is defined as a complete and closed path around which a circulating electric
current can flow. It can also mean a system of electrical conductors and components
forming such a path. Every time the switch is flipped (functioning), the circuit is complete
and electrical charge can flow through it. The circuit can be divided into complete circuit
and incomplete circuit

a) Complete circuit
A closed circuit has a complete path that allows current in proper ways. The circuit
must consist of the supply voltage (V), electric current (I), and resistance (R).

b) In-complete circuit
The circuit lacks one of the three elements either voltage, current, or, resistance. So,
the current flow does not occur in the circuit. The incomplete circuit consists of two
types:
i. Open Circuit: The load in that circuit will open. No current flow occurs. The
resistance value is higher (∞)

12 eBook PSP | Introduction to Electric Circuit

ii. Short Circuit: Connection at the load will short with a conductor which no
resistance. The current which goes through is high. The fuse will be burned.

Figure 1.2 Types of an electric circuit; closed circuit, open circuit, and short circuit

1.4 Measuring Voltage, Current, and Resistance

Some instruments are used to measure the basic quantities of electricity. The basic
quantities of electricity are voltage, current, and resistance. Every element needs its
respective device such as the following explanation.
1.4.1 Voltmeters
The voltmeter is a device used to measure voltage which is the voltage measured in volts.
Voltmeters are connected in parallel across components and have very high resistance.

Figure 1.3 Connecting a voltmeter in parallel
1.4.2 Ammeter
Ammeters measure current. Current is measured in amps (amperes), A. 1A is quite large,
so mA (milliamps) and µA (microamps) are often used. 1000mA = 1A, 1000µA = 1mA,
1000000µA = 1A. Ammeters are connected in series.

eBook PSP | Introduction to Electric Circuit 13

To connect in series, you must break the circuit and put the ammeter across the gap, as
shown in Figure 1.4. Ammeters have very low resistance.

Figure 1.4 Connecting an ammeter in series
1.4.3 Ohmmeter
An ohmmeter is used to measure resistance in ohms ( ). Ohmmeters are rarely found as
separate meters but all standard multimeters have an ohmmeter setting. 1 is quite small
so k and M are often used.

k = 1000
1M = 1000k = 1000000
1.4.4 Multimeter
Multimeters are very useful to test instruments. By operating a multi-position switch on the
meter, they can be quickly and easily set to be a voltmeter, an ammeter, or an ohmmeter.
They have several settings (called 'ranges') for each type of meter and the choice of AC or
DC.
Some multimeters have additional features such as transistor testing and ranges for
measuring capacitance and frequency.

Figure 1.5 Multimeter

14 eBook PSP | Introduction to Electric Circuit

1.5 Ohm’s Law

Ohm’s principal discovery was that the amount of electric current through a metal
conductor in a circuit is directly proportional to the voltage impressed across it, for any
given temperature. Ohm expressed his discovery in the form of a simple equation,
describing how voltage, current, and resistance interrelate:

V=IR

In this algebraic expression, voltage (E) is equal to current (I) multiplied by resistance (R).
Using algebra techniques, we can manipulate this equation into two variations, solving for
I and R, respectively:

OHMS LAW

=

The relationship between current and voltage is shown on the graph in Figure 1.6. This is
the situation for a constant value of resistance and temperature and it’s named linear
resistance. The constant value of resistance will result in the condition which is by
increasing voltage will increase the current and vice versa.

Figure 1.6 Graph voltage (V) versus current (I) for constant resistance

eBook PSP | Introduction to Electric Circuit 15

For the non-constant or changing value of resistance, the relationship between voltage and
current is nonlinear as shown in Figure 1.7. The changing value of R will result in the
condition which is by increasing voltage will increase the current to a constant level and
vice versa.

Figure 1.7 Graph voltage (V) versus current (I) for non-constant resistance
1.5.1. Analyzing Simple Circuits with Ohm’s Law

Figure 1.8 Ohm’s Law Circuit
In the above circuit (Figure 1.8) there is only one source of voltage (the battery, on the left)
and only one source of resistance to current (the lamp, on the right). This makes it very
easy to apply Ohm’s Law. If we know the values of any two of the three quantities (voltage,
current, and resistance) in this circuit, we can use Ohm’s Law to determine the third.

16 eBook PSP | Introduction to Electric Circuit

Example 1.2

Figure 1.9
What is the amount of current (I) in the circuit shown in Figure 1.9?
In this second example, calculate the amount of resistance (R) in a circuit, given values of
voltage (E) and current (I):

Figure 1.10
Referring to Figure 1.10, what is the amount of resistance (R) offered by the lamp?
In the last example, we will calculate the amount of voltage supplied by a battery, given
values of current (I) and resistance (R):

eBook PSP | Introduction to Electric Circuit 17

Figure 1.11
Based on Figure 1.11 what is the amount of voltage provided by the battery?

1.6 Electrical Power

Electric power is the rate at which energy is transferred to or from a part of an electric
circuit. A battery can deliver energy, or a circuit element like a resistor can release energy
as heat. For any circuit element, the power is equal to the voltage difference across the
element multiplied by the current. By Ohm's Law, V = IR, and so there are additional forms
of the electric power formula for resistors. Power is measured in units of Watts (W), where
a Watt is equal to a Joule per second (1 W = 1 J/s).

General form:

P=I V

P= electric power (Watt)
V= voltage (Volt)
I = Current (Ampere)

18 eBook PSP | Introduction to Electric Circuit

Resistors:

P = electric power (W)
V = voltage difference (V = J/C)
I = electric current (A = C/s)
R = resistance (Ω = V/A)

Figure 1.12 Formula wheel

Example 1.3

Question 1
If the battery of a cell phone operates at 12.0 V, and it has to deliver a current of 0.9 A
while playing music, what is the power required?

Solution

P = VI
P = (12.0 V) (0.9 A)
P = 10.8 J/s
P = 10.8 W

eBook PSP | Introduction to Electric Circuit 19

Question 2
A resistor with a 24.0 V potential difference across it is radiating heat. The thermal energy
is being generated at a rate of 16.0 W. What is the resistance value?
Solution: The resistance value can be found by rearranging one of the forms of the electric
power formula. The applicable form relates to power, voltage, and resistance:

R = 36.0 Ω

1.7 Energy Consumption

Energy or work is an ability to do the work. Electrical energy is a product of power and time.
Through unit of energy is normally in Joules (J), the equation of energy consumption
produces Watt-second (Ws), Watt-hour (Wh) or Kilowatt-hour (kWhr)

1 Joule = 1 Watt Second

T/E = Power (W) x Time (s)
T/E = P x t

Thus, the equation of Energy;
From Ohm’s Law, V=IR, I=V/R and P=IV, it can also be rearranged in other forms

as shown as follows.

/ =

Energy (T) = Voltage (V) x Current (I) x Time (hour/sec)

20 eBook PSP | Introduction to Electric Circuit

/ =

Energy (T) = Current2 (I) x Resistance (R) x Time (hour/sec)


/ =

Energy (T) = [Voltage2 (V) / Resistance (R) ] x Time (hour/sec)

Apart from being measured in joules, watt second, or kilowatt-hour units, energy is also
possible in the unit of Calories (Cal) but this unit is infrequently used for energy
determination in Electric terms.

1 joule/Ws = 0.239 Cal
1 Cal = 4.184 joule/Ws

Example 1.4

Question 1
A fan with a current of 5 A and supplied voltage of 240 v takes a duration of 15 minutes.
Calculate:

i. Power dissipated
ii. Energy used in Ws and kWhr

Solution:
Given I=1.5 A, V=240 and t = 15 x 60 = 900s

i. P = I V = 5 x 240 = 1200 W
ii. E= Pt = 1200 x 900 = 1080000 Ws @ 1080 kWs

E = Pt = 1200 x (15/60) = 300 Whr @ 0.3kWhr

eBook PSP | Introduction to Electric Circuit 21

1.8 Watt Meter

The wattmeter is an instrument for measuring the electric power (or the supply rate of
electrical energy) in watts of any given circuit. Electromagnetic wattmeters are used for
the measurement of utility frequency and audio frequency power; other types are
required for radio frequency measurements.

Figure 1.13 Connection of Wattmeter

Comprehension Test 1.2

1. A 100 W electric fan is connected to a 250V supply. Determine the current flowing
through the fan and the resistance of the fan.
(Ans: I=0.4V, R=62 Ω)

2. Calculate the power dissipated when a current of 4mA flows through a resistor of 5 kΩ.
(Ans: 80 mW)

3. The hot resistance of a 240 V heater is 960 Ω. Determine:
i. Current that has been taken by the heater
ii. Its power rating
(Ans: I=0.24 A, P = 60 W)

22 eBook PSP | Introduction to Electric Circuit

4. A 12 V battery is connected across a bulb having a resistance of 40 Ω. Determine:
i. Current flowing in the bulb
ii. Power consumed
iii. Energy dissipated in 2 minutes
(Ans: I=0.3 A, P=3.6 W, E=432 J)

1.9 Analysis Electric Circuit

There are three types of electric circuits:
• Series Circuit
• Parallel Circuit
• Combination Circuit

1.9.1 Series Circuit
A series circuit is a circuit in which resistors are arranged in a chain, so the current circuit
is found by simply adding up the resistance values of the individual resistors:
Equivalent resistance of resistors in series: R = R1 + R2 + R3 + ...

Figure 1.14 Series Circuit

In a series circuit, the amount of current entering a circuit is equivalent to the value of
current leaving the circuit. In other words, the current through each resistor is equal to the
total current.

IT = I1 = 12 = I3…….= In

eBook PSP | Introduction to Electric Circuit 23

However, the total resistance in the circuit is the sum of the resistance from each resistor
in the circuit. Therefore;

RT = R1+R2+R3

The total sum of the voltage supply is equal to the sum of the voltage drop on each
resistor in the circuit. Therefore;

VT=V1+V2+V3

The magnitude of the voltage drop across each resistor can be found by applying Ohm’s
Law using only the resistor. Therefore;

Vn = IT Rn

Example 1.5

Figure 1.15

Refer to Figure 1.15 above, and calculate the:
i. Total Resistance, RT
ii. Current in the circuit, IT
iii. Voltage drops for each resistor

Solution Total resistance RT
i. RT = R1 +R2+ R3 = (3 + 10+5) = 18 Ω

24 eBook PSP | Introduction to Electric Circuit

ii. Current Circuit, IT:
I T = V = 9 = 0.5 A

Rt 18

iii. Voltage drop for each resistor:
VR1 = IT R1 = (0.5 x 3) = 1.5 V
VR2 = IT R2 = (0.5 x 10) = 5 V
VR3 = IT R3 = (0.5 x 5) = 2.5 V

1.9.1.1Voltage Divider Rules
The voltage division rule (voltage divider) is a simple rule which can be used in solving
circuits to simplify the solution. Applying the voltage division rule can also solve simple
circuits thoroughly. The statement of the rule is simple:

Voltage Division Rule: The voltage is divided between two series resistors in direct
proportion to their resistance.

=


It is easy to prove this. In the following circuit;

V1 = ( R1 R1 )VT
+ R2

V2 = ( R2 )VT
R1 + R2

Figure 1.16

eBook PSP | Introduction to Electric Circuit 25

Example 1.6

Figure 1.17

Refer to the circuit shown in Figure 1.17 above, and calculate the voltage drop for each
resistor using Voltage Divider Rule.

Solution

Comprehension Test 1.3

1. Refer to Figure 1.18 to calculate
a) Voltage drop at R1 and R2
b) Value of resistor R1
c) Total power dissipated of
resistors R1 and R2

Figure 1.18

26 eBook PSP | Introduction to Electric Circuit

2. Refer to Figure 1.19, and calculate the:
a) Total Resistance, RT
b) Current in the circuit, IT
c) Voltage drops for each resistor
d) Total power in the circuit

Figure 1.19

1.9.2 Parallel Circuit
The parallel circuit is the connection of the resistor which is against each other. Each
component across the voltage source provides a separate path or branch for current flow.
These are three principles regarding parallel circuits:

1. Voltage: Voltage is equal across all components in a parallel circuit.
2. Current: The total circuit current is equal to the sum of the individual branch

currents.
3. Resistance: Individual resistances diminish to equal a smaller total resistance

rather than add to make the total.

Figure 1.20 Parallel Connection
In a parallel circuit, the total sum of current is equal to the sum of current at each junction,
Therefore:

IT = I1 + I 2 + I3…..+In

eBook PSP | Introduction to Electric Circuit 27

The amount of voltage in a circuit is calculated using the equation:

1 111 1
= 1 + 2 + 3 … . . +

The amount of voltage in a circuit element is the same, therefore:
VT = V1 = V2= V3 ……. = Vn

The magnitude of the voltage drop across each resistor can be found by applying Ohm’s
Law using only the resistance of each resistor. Therefore:

Vn = In Rn

1.9.2.1 Current Divider Law
Current divider law refers to the splitting of current between the branches of the divider.
The currents in the various branches of such a circuit will always divide in such a way as
to minimize the total energy expended. The formula describing a current divider is similar
in form to that of the voltage divider.

Where: = ( )

RT is the total resistance of the parallel branches
Rn is the resistance at the related branch
In is current to be measured
IT is the total current

28 eBook PSP | Introduction to Electric Circuit

Example 1.7

Refer to Figure 1.21, calculate:
i) Total resistance RT
ii) Total current, IT
iii) Current I1 and I2 using
two different method

Figure 1.21

Solution

i) 1 =1+1 = = ( 12+114) = 1.33 Ω

1 2

ii) = = 240 = 180

1.33

iii) Method 1:
240

1 = 1 = 2 = 120

240
2 = 2 = 4 = 60

Method 2:

1 = ( 1 ) = 1.33 180 = 120
(2)

2 = ( 2 ) = 1.33 = 60
( 4 ) 180

eBook PSP | Introduction to Electric Circuit 29

Comprehension Test 1.4

1. Refer to Figure 1.22, and calculate the:
i. Total Resistance
ii. Voltage drop for each
resistor R1, R2, and R3
iii. Current through each resistor
iv. Total power

Figure 1.22

2. Based on Figure 1.23, calculate:
i. Voltage drop at resistor R3
ii. Current through
resistor R2 (I2)
iii. Total current, IT
iv. Resistor of R1 and R3

Figure 1.23

3. Based on Figure 1.24, calculate:
i. Total resistance, RT
ii. Voltage R2
iii. Current flow
through R2 and R3
iv. Total power PT

Figure 1.24

Ans: Q1 = (RT=923.077 Ω, R1=R2=R3=15V, I1=3.75 mA, I2=7.5 mA, I3=5 mA, PT=0.244 W)
Q2= (VR3=20 V, IR2=6.667 mA, IT=36.667 mA, R1=2 kΩ and R3=1 kΩ)
Q3= (RT=1.143 Ω, VR2=240 V, IR2=60 A, IR3=30 A, PT=28.8 kW)

30 eBook PSP | Introduction to Electric Circuit

1.9.3 Combination Circuit (Series-Parallel Circuit)
Most electric circuits are a combination of series and parallel circuits. Both formulas of
series and parallel circuits will be used to determine the value of current, voltage, and total
resistance. Since both types of connections are used in combination circuits, the concepts
associated with both types of circuits apply to the respective parts of the circuit.

Example 1.8

1. Refer to Figure 1.25, a 120 V supply is connected through a resistor with R1=10Ω,
R2=20 Ω and R3=15 Ω, calculate:
a) Total Resistance, RT
b) Total Current, IT
c) Current I2 and I3

Figure 1.25

Solution

eBook PSP | Introduction to Electric Circuit 31

2. Based on Figure 1.26 below, find:
i. The total resistance of the circuit.
ii. The total current and current of R2 and R34
iii. The voltage drops for each resistor R1, R2, R34 & R5

Figure 1.26

Solution
i. Combine R3 and R4 (resistor in series) to R34
R34=R3 + R4 = 5 Ω + 15 Ω = 20 Ω

Combine R2 and R34 (resistor in parallel 1 = 1 + 1 = 1 + 1 = 15 Ω

234 2 34 60 20

= 1 + 234 + 5 = 60 Ω

ii. Applying Ohm's Law for the whole circuit

= = 120 = 2
60

• Current at R2 (Using current divider law-parallel circuit)

2 = ( 234) = (15) 2 = 0.5

2 60

• Current at R34 (Using current divider law-parallel circuit)

34 = ( 23344) = (5 15 = 1.5
+ 15) 2

iii. Then applying Ohm's Law to each element

V1 = IT R1 = 2(25) = 50 V
V2 = I2 R2 = 0.5 (60) = 30 V
V34 = I34 R34 =1.5 (20) = 30 V
V5 = IT R5 = 3 (20) = 40 V

32 eBook PSP | Introduction to Electric Circuit

Comprehension Test 1.4
1. Based on Figure 1.27 below, the voltage across R1 = 72 V. Specify the following values:

i. The current flow each resistor R1, R2, R3, and R4
ii. The voltage across each resistor R2, R3, and R4
iii. Supply voltage, Vs

Figure 1.27
2. By using Ohm’s Law, Current Divider Law and Voltage Divider Law calculate Total

Current, IT, Current I1, Current I2, and, the Voltage drop at each resistor in Figure 1.28
below.

(RT =22.92 Ω, IT=0.87A, I1=0.507A, I2=0.363A, VR1=17.4V, VR2 = 2.6V=VR3 because of parallel)
Figure 1.28

eBook PSP | Introduction to Electric Circuit 33

Revision

1. Describe the electrical quantities below:
i. Current
ii. Electrical Charge
iii. Resistance

2. Explain FOUR (4) factors that affect the value of resistance in a conductor.

3. Give the definition, symbol, and unit for electric quantities below:
i. Voltage
ii. Resistivity
iii. Power

4. Describe Ohm’s Law and sketch a graph to show the relationship between voltage and
current if the resistance is constant.

5. Calculate the current flowing through the aluminium wire with a length of 3 km and a
diameter of 25 mm if the 240 V supply voltage. The resistivity of the wire is 0.28 μΩm.
Calculate the power used.
(R = 1.71 Ω, I = 140.35 A, P = 33684 W)

6. Determine the resistance of a 30 m length iron wire having a resistivity of
1.229x10−7 Ω and diameter of 2 mm.
(R = 1.174 Ω)

7. Calculate the power dissipated when a current of 5 mA flows through a resistance of 6
kΩ.
(P = 0.15 W)

34 eBook PSP | Introduction to Electric Circuit

8. A bread maker with 5 kW power, 240 voltage is used to bake 25 pieces of bread for
half an hour. Calculate:
i. Current used
ii. Resistance
iii. Electrical energy if the circuit used for half an hour
(I = 21.74 A, R =10.58 Ω, E = 9000 kJ)

9. A 100 W electric light bulb is connected to a 250 V supply. Determine:
i. Current flowing in the bulb
ii. The resistance of the bulb
(I = 0.4 A, R = 625 Ω)

10.Referring to the circuit in Figure 1.29, the given values are R1 = 15 Ω, R2 = 1 kΩ, R3
= 100 Ω, R4 = 150 Ω and VT = 12 V, calculate:
i. Total resistance, RT
ii. Total Current, IT
iii. Current flow through R4 using the current divider law, I4

Figure 1.29
(RT = 1075 Ω, IT = 11 = 11 = mA; I4 = 4.4 mA)

11.

Figure 1.30
Simplify the combination circuit in Figure 1.30 above to identify the following value:

i. The total resistance (RT) in the circuit,
ii. The total current (IT) in the circuit
iii. Current flows in each resistor R1 and R4
iv. Voltage drop across resistor R2
(RT=58.76Ω, IT= 0.17A; I4=0.17A. I2=0.106A, V2=3.18V)

eBook PSP | Introduction to Electric Circuit 35

12.Refer to the circuit in Figure 1.31, and calculate:
i. Total resistance, RT
ii. Current flow through R1, R2, R3 and R4
iii. Voltage drop at R1, R2, R3, and R4
iv. Power dissipated at R1 and R3 (PR1 and PR3)
v. Total energy of resistor R4 in 2 minutes

Figure 1.31
(RT = 3.96 A Ω, I1 = 2.5 A, I2 = 2.917 A, I3 = 0.883 A, I4 = 2.08 A, VR1 = 20V,
VR2 = 11.668 V, VR3 = VR4 = 8.33V, PR1 = 50 W, PR3 = 6.936 W, ER4 = 0.579W)
13.Refer to Figure 1.32, calculate

i. Voltage supply, Vs
ii. Voltage drop at R1
iii. Value of resistor R2 and R3
iv. Total resistance, RT
v. Power dissipated at R1 and R2

Figure 1.32
(Vs=30V, VR1=30FVi,gRu2re=13..3811Ω, R3=1.905Ω, RT=5.001Ω, PR1=22.5W, PR2=105W)

36 eBook PSP | Introduction to Electric Circuit

Summary

This Introduction to Electric Circuit eBook exposes the reader to basic electrical circuit
fundamentals and problem-solving. The writing is using simple words and the explanation
is also clear thus, the student will easily understand. The problem-solving solution is also
shown step by step makes the student can follow it properly. This book is very suitable as
a reference for students at polytechnics, colleges, or institutions of higher education.

eBook PSP | Introduction to Electric Circuit 37

References

Bird, J. O. (2017). Electrical Circuit Theory and Technology. Routledge.

Bolton, W. (2019). Mechatronics: Electronic Control Systems in mechanical and electrical
engineering. Pearson Education Limited.

Floyd, T. L., & Buchla, D. M. (2010). Electric Circuits Fundamentals. Prentice Hall.

Mazur, G. A., & Proctor, T. E. (2010). Troubleshooting electrical/electronic systems.
American Technical Publishers, Inc.

Power and energy. Electronics Club. (n.d.). Retrieved October 27, 2022, from
https://electronicsclub.info/power.htm

Schultz, M. E. (2021). Grob's Basic Electronics. McGraw-Hill Education.

Technology, E. (2022, September 29). Introduction to series, parallel and series-parallel
connections. ELECTRICAL TECHNOLOGY. Retrieved October 27, 2022, from
https://www.electricaltechnology.org/2015/03/parallel-connection-is-preferred-
over-series.html

Wikimedia Foundation. (2022, October 23). Lightning. Wikipedia. Retrieved October 27,
2022, from https://en.wikipedia.org/wiki/Lightning

Wikimedia Foundation. (2022, September 12). Ohm's Law. Wikipedia. Retrieved October
27, 2022, from https://en.wikipedia.org/wiki/Ohm%27s_law

Wikimedia Foundation. (2022, September 29). Series and Parallel Circuits. Wikipedia.
Retrieved October 27, 2022, from
https://en.wikipedia.org/wiki/Series_and_parallel_circuits

Wildi Thoď ore. (2014). Electrical Machines, drives, and Power Systems. Pearson.

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