Engineering Year 1

SECTION

4 ELECTRICAL AND
ELECTRONIC
CIRCUIT
SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

ENERGY SYSTEMS
Circuits And Machines

Introduction
Welcome to the section on circuits and machines. In this section, you will be
introduced to the fundamentals of Direct Current (DC) electrical and electronic
circuits. An electrical circuit is an interconnection of electrical elements in which
current can flow. These circuit elements form the building blocks of electrical and
electronic systems and devices that power our everyday lives and hence it is important
to know them and understand their functions. The electrical circuit components can
be classified as passive and active components. These passive and active components
are fundamental components that play essential roles in controlling and regulating the
flow of electric current. Electrical and electronic circuits are represented graphically
using circuit diagrams. The circuit diagrams are used to convey information about the
interconnections and functionality of various components within a circuit. Circuit
diagrams use electrical symbols to represent the various electrical and electronic
components. These symbols are standardised and universally recognised, making it
easier for engineers, technicians, and electricians to communicate and understand
complex circuit designs. Electrical circuit analysis involves the use of physical laws and
mathematical equations to determine the relationship between electrical components
in a circuit, the current flow through them and the voltages across them. Kirchhoff’s
laws are commonly used for analysing circuits so your understanding of Kirchhoff’s
Laws and their applications is an essential skill for studying electrical engineering
or related fields. In the field of electronics, circuit simulation software enables the
understanding, designing, and testing of electrical circuits without the need for physical
components. These tools allow users to create and simulate circuits virtually, making
them essential learning aids. Three common user-friendly circuit simulation software
tools are Proteus, LTspice, and CircuitLab. The electrical and electronic circuits can
also be built and instruments such as voltmeter, ammeter, and power meter can be
used to measure the circuit terminal quantities.

At the end of this section, you will be able to:

• Identify the basic elements of DC electric and electronic circuits and sketch their circuit
symbols.
• Classify circuit elements into passive and active elements.
• Explain Kirchhoff’s laws.
• Use Kirchhoff’s laws to find currents and voltages in DC circuits.
• Compute power in DC and single-phase AC circuits.
• Use a software tool to simulate simple circuits to derive current, voltage and power in
DC circuits.

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Key Ideas
• When a conductor is used to connect electrical components such as resistors to an
electrical power source, an electric circuit is formed. DC (Direct Current) circuits are
electrical circuits where current flows in one direction.
• Basic elements of DC circuits are the voltage source, a resistor, a switch, and a conductor.
• Power in DC circuits is a fundamental concept used to determine the rate at which
electrical energy is consumed or converted into other forms of energy.

BASIC ELEMENTS OF DC ELECTRIC AND

ELECTRONIC CIRCUITS AND SKETCH THEIR
CIRCUIT SYMBOLS
Let us begin by first introducing you to the various electrical and electronic components,
their standard symbols, and their functions/applications. The components covered
include resistors, capacitors, inductors, diodes, transistors, transformers, and integrated
circuits.

1. Resistors
A resistor is an electronic component designed to impede or restrict the flow of electrical
current in a circuit. Its primary function is to create a specific amount of resistance
to control the flow of electrons. Resistors are commonly used to limit current, divide
voltage, and protect sensitive components from excessive current flow. The resistance
of a resistor is measured in ohms (Ω).

or
The Symbols of a Resistor

Figure 4.1: A picture of resistors mounted on a circuit board

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Types of Resistors
a. Fixed Resistors: Fixed resistors have resistance values that cannot be changed by
the user.
i. Carbon Composition Resistors: They are made from a mixture of carbon
dust and a binding material.
ii. Film Resistors: They include carbon film, metal film, and metal oxide film
resistors, which have a thin film of conductive material.
iii. Wire wound Resistors: They are made by winding a wire (usually nichrome)
around an insulating core.
b. Variable Resistors (Potentiometers and Rheostats): These allow the resistance
value to be adjusted.
c. Special Resistors:
i. Thermistors: Their resistance value changes with a change in temperature.
Negative Temperature Coefficient (NTC) thermistors decrease resistance
with increasing temperature, while Positive Temperature Coefficient (PTC)
thermistors increase resistance with increasing temperature.
ii. Light-Dependent Resistors (LDRs): Their resistance values change with a
change in light intensity. They are commonly used to automatically switch on
and off outdoor lights.

Applications of Resistors
• Current Limiting: It protects components by limiting the amount of current.
• Voltage Division: It creates specific voltage drops within a circuit.
• Biasing Active Devices: It sets the operating point for transistors and other
active components.
• Signal Attenuation: It reduces signal strength in audio, radio, and other
applications.
• Pull-up and Pull-down: It ensures that inputs to logic circuits settle at expected
logic levels.

2. Capacitors
Capacitors are passive components used to store and release electrical energy in the
form of an electric field. They consist of two conductive plates separated by an insulating
material (dielectric). When a voltage is applied across the plates, electrons accumulate
on one plate, creating a negative charge, while an equal number of electrons leave the
other plate, creating a positive charge. Capacitors are used for filtering, energy storage,
coupling, and timing applications in electronic circuits. The capacitance of a capacitor
is measured in Farad (F).

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or
The Symbols of a Capacitor

Figure 4.2: A picture of Capacitors

Types of Capacitors
a. Fixed Capacitors:
i. Ceramic Capacitors: Made of ceramic materials, offering small size and high
stability. Commonly used for high-frequency applications.
ii. Electrolytic Capacitors: Have a larger capacitance-to-volume ratio, typically
used for low-frequency applications. They are polarised, meaning they have a
positive and a negative lead.
iii. Tantalum Capacitors: Known for their stability and reliability, also polarised.
iv. Film Capacitors: Made from plastic films, offering high precision and stability.
b. Variable Capacitors:
i. Trimmer Capacitors: Adjustable capacitors used for fine-tuning circuits.
ii. Variable Air Capacitors: Often used in radio tuning circuits.

Applications of Capacitors
• Energy Storage: Stores energy for use in applications such as power supplies
and camera flashes.
• Filtering: Removes unwanted frequencies from signals, such as in power
supply smoothing and audio crossover networks.
• Coupling and Decoupling: Blocks DC components while allowing AC signals
to pass, used in signal processing.
• Timing Circuits: Used in conjunction with resistors to create time delays in
circuits.
• Tuning Circuits: Adjusts the frequency response of radio and TV receivers.

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3. Inductors
Inductors are also passive components and are designed to store energy in the form
of a magnetic field when an electric current flows through them. They consist of a
coil of wire wound around a core material. When the current changes, the magnetic
field induces a voltage across the inductor, resisting changes in current. Inductors are
commonly used in filters, transformers, and various energy storage applications. The
inductance of an inductor is measured in Henry, (H).

The Symbol of an Inductor

Figure 4.3: A picture of Inductors

Types of Inductors
a. Air Core Inductors: These have no magnetic core, only air inside the coil. They
are used for high-frequency applications due to their low losses.
b. Iron Core Inductors: Use an iron core to increase inductance, suitable for low-
frequency applications.
c. Ferrite Core Inductors: Use ferrite material as the core, providing higher
inductance and used in applications like transformers and noise filters.
d. Toroidal Inductors: The wire is wound on a toroidal (doughnut-shaped) core,
offering high inductance and low electromagnetic interference (EMI).

Applications of Inductors
• Filtering: Used in power supplies and audio circuits to filter out unwanted
frequencies.
• Energy Storage: Store energy in switching power supplies and DC-DC
converters.

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• Transformers: Inductors with multiple windings that transfer energy between

circuits through electromagnetic induction.
• Tuning Circuits: Adjust the frequency response in radio receivers and
transmitters.
• Chokes: Block high-frequency AC signals while allowing DC or low-frequency
signals to pass.

4. Diode
Diodes allow current to flow in one direction only and block it in the opposite direction.
They are used for rectification, signal demodulation, and voltage regulation in both DC
circuits. It has two terminals: the anode and the cathode. When a positive voltage is
applied to the anode relative to the cathode, the diode becomes forward-biased and
allows current to pass through. When a negative voltage is applied, the diode becomes
reverse-biased and blocks current.

The Symbol of a Diode

Figure 4.4: A picture of Diodes

Types of Diodes
a. Standard (Silicon) Diodes: General-purpose diodes used for rectification and
other applications.
b. Zener Diodes: Designed to conduct in the reverse direction when a specific
breakdown voltage is reached, used for voltage regulation.
c. Schottky Diodes: Have a lower forward voltage drop and faster switching speed,
used in high-frequency applications.
d. Light Emitting Diodes (LEDs): Emit light when forward biased, used for
indicators and displays.
e. Photodiodes: Generate current when exposed to light, used in sensors and
photovoltaic cells.
f. Avalanche Diodes: Operate in reverse breakdown with controlled breakdown
characteristics, used in high-voltage applications.
g. Varactor Diodes: Variable capacitance diodes used in tuning circuits.

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Applications of Diodes
• Rectification: Converting AC to DC in power supplies using diodes in rectifier
circuits (half-wave, full-wave, and bridge rectifiers).
• Voltage Regulation: Zener diodes maintain a constant voltage across loads.
• Signal Demodulation: Extracting audio or data from modulated carrier waves
in radios and communication devices.
• Protection: Clamping diodes protect circuits from voltage spikes and transients.
• Switching: Diodes in switching applications like logic gates and relay drivers.
• Light Emission: LEDs provide visual indicators and lighting.

Example Circuits
• Half-Wave Rectifier: Uses a single diode to rectify an AC signal, allowing only
one half-cycle (positive or negative) of the AC voltage to pass through, resulting
in pulsating DC.
• Full-Wave Rectifier: Uses multiple diodes (typically four in a bridge
configuration) to rectify both halves of the AC signal, producing a smoother DC
output.

Diode Characteristics
• Forward Bias: When the anode is more positive than the cathode, the diode
conducts. The current-voltage relationship is exponential for small voltages and
linear at higher currents.
• Reverse Bias: When the cathode is more positive than the anode, the diode
blocks current, except for a small leakage current. Beyond the breakdown
voltage, the diode conducts in reverse.

5. Transistor  
Transistors are semiconductor devices that can amplify or switch electrical signals.
They are fundamental components in electronic devices like computers, amplifiers,
and other electronic circuits. Transistors come in two main types: bipolar junction
transistors (BJTs) and field-effect transistors (FETs).

The Symbol of a Transistor

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Figure 4.5: A picture of a transistor

Types of Transistors
Bipolar Junction Transistors (BJTs)
• NPN Transistors: Consist of two N-type semiconductor materials separated
by a thin layer of P-type material.
• PNP Transistors: Consist of two P-type semiconductor materials separated by
a thin layer of N-type material.
Operation:
• Active Mode: For NPN, the base-emitter junction is forward-biased, and the
base-collector junction is reverse-biased. For PNP, the polarities are reversed.
• Saturation Mode: Both junctions are forward-biased.
• Cutoff Mode: Both junctions are reverse-biased.
Key Parameters:
• Current Gain (β or h𝐹𝐸​): The ratio of collector current (I𝐶​) to base current (I𝐵​).
• Collector-Emitter Voltage (V𝐶𝐸​): The voltage difference between the collector
and emitter.
• Field-Effect Transistors (FETs)
• Junction FETs (JFETs): Use a voltage applied to the gate terminal to control
current through the channel between the source and drain.
• Metal-Oxide-Semiconductor FETs (MOSFETs): Have an insulated gate that
can control the conductivity of a channel.
Operation:
• Depletion Mode: Current flows without gate voltage; applying a voltage
depletes the channel.
• Enhancement Mode: No current flows without gate voltage; applying a
voltage enhances the channel.

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Key Parameters:
• Transconductance (g𝑚​): The rate of change of the drain current with respect
to the gate-source voltage.
• Drain-Source Voltage (V𝐷𝑆​): The voltage difference between the drain and
source.

Applications of Transistors
• Amplification: Used in amplifiers to increase the power, voltage, or current of
a signal.
• Switching: Used in digital circuits, power supplies, and motor controllers to
turn current on and off.
• Oscillators: Generate oscillating signals in radios, clocks, and signal generators.
• Regulation: Stabilise voltage and current in power supply circuits.

Example Circuits
Common Emitter Amplifier (using NPN BJT)
• Configuration: The emitter is common to both input and output circuits.
• Operation: Input signal at the base, amplified output is taken from the collector.
• Biasing: Requires proper biasing to set the transistor in active mode.

6. Integrated circuits (IC)                                            

An integrated circuit (IC), also known as a microchip or chip, is a compact arrangement
of electronic components such as transistors, capacitors, resistors, and diodes, fabricated
on a single piece of semiconductor material, typically silicon. The components are
interconnected in a way that allows them to perform specific functions, such as
amplification, signal processing, logic operations, or memory storage. Integrated circuits
are fundamental to modern electronics and are used in all electronic equipment.

The Symbol of an Integrated Circuit

Figure 4.6: A picture of an Integrated circuit (IC)

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Types of Integrated Circuits

a. Microprocessors: The brain of computers and many other devices, executing a
sequence of stored instructions.
b. Microcontrollers: Contain a microprocessor along with memory and input/
output peripherals on a single chip.
c. Memory ICs: Include RAM (Random Access Memory) and ROM (Read-Only
Memory).
d. Digital Signal Processors (DSPs): Specialised in processing digital signals in
real-time.
e. Application-Specific Integrated Circuits (ASICs): Custom-designed for a
specific application.
f. Power Management ICs: Manage power requirements of the host system.
g. Sensors and Actuators ICs: Integrate sensory functions and can directly interact
with physical devices.

Applications of Integrated Circuits

• Computing: Microprocessors, memory, and GPUs in computers, tablets, and
smartphones.
• Communication: Signal processing in phones, radios, and networking
equipment.
• Consumer Electronics: Embedded systems in TVs, cameras, and home
appliances.
• Automotive: Engine control units, safety systems, and infotainment.
• Industrial: Automation, robotics, and process control.
• Medical Devices: Imaging systems, portable diagnostics, and patient
monitoring.

Advantages of Integrated Circuits

• Size and Weight: Significantly smaller and lighter than discrete component
circuits.
• Cost: Lower production costs due to mass manufacturing.
• Performance: Higher speed and efficiency due to reduced parasitic elements.
• Reliability: Enhanced reliability with fewer interconnections and solder joints.
• Power Consumption: Lower power consumption compared with equivalent
discrete circuits.

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7. Transformer
A transformer is a device used to transfer electrical energy between two or more
circuits through electromagnetic induction. It is commonly used to step up or step
down voltage levels in power distribution systems. Transformers are crucial in power
transmission and distribution systems, as well as in various electronic devices.

The Symbol of a Transformer

Figure 4.7: A picture of a Transformer

Types of Transformers
a. Power Transformers:
i. Step-Up Transformers: Increase voltage for efficient long-distance power
transmission.
ii. Step-Down Transformers: Decrease voltage for safe distribution and usage in
homes and businesses.
b. Distribution Transformers: Used in the distribution network to deliver electricity
at usable voltage levels to end consumers.
c. Isolation Transformers: Provide electrical isolation between circuits without
changing voltage levels significantly, enhancing safety.
d. Autotransformers: Have a single winding that acts as both primary and secondary
winding, with a tap point. They are more efficient but lack isolation.
e. Current Transformers (CTs): Used to measure high currents by producing a
lower, proportional current.
f. Potential Transformers (PTs): Used to measure high voltages by producing a
lower, proportional voltage.

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Applications of Transformers
• Power Transmission and Distribution: Stepping up and down voltages for
efficient power transmission and safe distribution.
• Electrical Isolation: Isolating various parts of a circuit to prevent direct
electrical connection and increase safety.
• Voltage Regulation: Maintaining constant voltage levels in power systems.
• Signal Processing: In audio equipment and telecommunications for impedance
matching and signal coupling.
• Measurement: Using current and potential transformers in metering and
protective relays.

8. Switches (S)
Switches are electrical components that can open or close a circuit, interrupting or
allowing the flow of current. They can be either mechanical or electronic. When a
switch is closed (turned ON), it allows current to flow through the circuit. When it is
open (turned OFF), it interrupts the current path, preventing current flow. Switches
play a crucial role in controlling the operation of electronic devices and systems.
Switches are fundamental components in electronic and electrical systems, used to
control devices, direct signals, and ensure safety.

A symbol of a Switch

Figure 4.8: A picture of some switches

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Types of Switches
a. Toggle Switches: Operated by a lever, commonly used in household and industrial
applications.
b. Push Button Switches: Operated by pressing a button, used in many control
applications.
c. Rotary Switches: Operated by rotating a knob, used for selecting different circuit
paths.
d. Slide Switches: Operated by sliding a button, used in small electronic devices.
e. DIP Switches: A set of small switches in a dual in-line package, used for
configuration settings on circuit boards.
f. Rocker Switches: Operated by rocking a button back and forth, commonly used
in power control.
g. Limit Switches: Automatically activated by the motion of a machine part, used
for position sensing.
h. Reed Switches: Activated by a magnetic field, used in proximity sensing.
i. Membrane Switches: A thin, flexible switch used in keyboards and control panels.
j. Proximity Switches: Detect the presence of an object without physical contact.

Applications of Switches
• Power Control: Turning devices on and off in household appliances, industrial
machinery, and consumer electronics.
• Signal Control: Directing signals in communication devices, computers, and
audio equipment.
• Safety: Ensuring safe operation in electrical circuits by disconnecting power
during faults.
• User Interface: Providing user input options in control panels, remote controls,
and keyboards.
• Automation: Sensing and responding to conditions in automated systems and
machinery.

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CLASSIFICATION OF CIRCUIT COMPONENTS

INTO PASSIVE AND ACTIVE COMPONENTS
Electrical and electronic components can be placed under two broad categories namely
the passive and active components. Your understanding of the differences between
these two types of components is crucial for designing and analysing electrical circuits.

Passive Components
These are components that do not introduce energy (on their own) into the circuit and
cannot amplify signals. They can only receive, store, or dissipate energy. Examples of
passive elements include:
1. Resistor: A resistor is a component that opposes the flow of current in an electrical
circuit. It dissipates energy in the form of heat.
2. Capacitor: A capacitor is a component that stores electrical energy in an electric
field between its plates. It can release stored energy over time.
3. Inductor: An inductor is a component that stores electrical energy in a magnetic
field created by the current flowing through its coils. It can release stored energy
over time.
4. Transformer: A transformer is a component that step-up or step-down voltage
levels for efficient power transmission. It can release stored energy over time.

Active Elements
There are two categories of active elements namely (a) components that can introduce
energy into the circuit and (b) components that can amplify or manipulate signals. In
electrical circuits, active elements are the energy-producing elements (power source).
However, in electronic circuits, active components are those that magnify or manipulate
the characteristics of signals. They can amplify signals, produce energy, and perform
complex functions that passive components cannot. They require an external power
source to operate. Examples of active components in electrical circuits include:
1. Batteries: They convert chemical energy to electrical energy.
2. Generators: They convert thermal/mechanical energy to electrical energy.
3. Solar Cells: They convert solar energy (from the sun) to electrical energy.
Examples of active components in electronic circuit include
a. Transistor: A semiconductor device that can amplify and switch electronic
signals and power. There are two main types: bipolar junction transistors (BJTs)
and field-effect transistors (FETs).
b. Diode: A diode is a semiconductor device that allows current to flow in only
one direction. It can be used for rectification (i.e. converting alternating current
(A.C.) to a direct current (D.C.)) or signal conditioning.

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Electronic circuits containing both passive and active elements are known as active
circuits. Examples include:
a. Operational Amplifier (Op-Amp): An integrated circuit that amplifies the
difference between two input voltages. It is often used for signal processing and
amplification.
b. Integrated Circuit (IC): These are active components that contain a
combination of transistors, resistors, capacitors, and other elements integrated
onto a single chip. They can perform a wide range of functions, from simple
amplification to complex digital signal processing.

Activity 4.1: Component Identification Scavenger Hunt

Objective: Learners will identify real-life examples of basic circuit elements in

everyday objects.
Instructions:
a. Learners look out for spoilt electronic boards with a list of basic circuit
elements (resistor, capacitor, inductor, diode, transistor).
b. Learners find examples of each component in electronic devices, or
circuit boards.
c. Learners should make sketches of the components they find and label
them with their names and symbols.
d. After collecting examples, learners should present their findings to
their class Facilitator and explain the function of each component.

Activity 4.2: Circuit Symbol Matching Game

Objective: Learners will match circuit symbols with their corresponding

components.
Instructions:
a. Use a set of cards previously prepared by the facilitator, each with a
circuit symbol printed on one side and the name of the component on
the other side.
b. Place the cards face down on a table.
c. Join a small group of your classmates (4 or 5).
d. Each group has a set of cards to use, and the group members take turns
flipping over two cards at a time, trying to match the symbol with its
component name.
e. If a match is made, you keep the pair of cards. If not, the cards are
turned face down again, and the next learner takes a turn.
f. The game continues until all matches are made or a time limit is reached.
g. Review the matches as a class to ensure understanding.

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Activity 4.3: Circuit Building Lab

Objective: Learners will build simple DC electric circuits using breadboards and
electronic components.
Materials Needed:
• Breadboards
• Resistors
• Capacitors
• Inductors
• Diodes
• Transistors
• Jumper wires
• Power supply or batteries
• LED
• Switch
• Multimeter
Instructions:
a. The facilitator provides each group with a breadboard, a set of electronic
components (resistors, LEDs, wires, batteries, switches), and a multimeter if
available.
b. Demonstrate how to connect components on the breadboard and how to use
jumper wires to create circuits.
c. Each person or group is assigned a specific circuit configuration to build,
such as:
• Series and parallel resistor circuits
• RC time constant circuits
• Diode rectifier circuits
• Transistor amplifier circuits
d. You should sketch circuit diagrams before building them to visualise the
connections.
e. After building the circuits, you should test their functionality and measure
relevant parameters (e.g., voltage, current).
f. Then present your circuits to the class, explaining the purpose of each
component and how they function together.

Steps to build LED circuit

a. Connect the positive (red) lead from the battery holder to the positive rail on
the breadboard.
b. Connect the negative (black) lead from the battery holder to the negative rail
on the breadboard.

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c. Insert one leg of the resistor into a hole connected to the positive rail.
d. Insert the other leg of the resistor into a separate row on the terminal strip.
e. Identify the longer leg of the LED (anode) and insert it into the same row as
the resistor.
f. Insert the shorter leg of the LED (cathode) into a new row.
g. Connect a jumper wire from the row with the LED’s cathode to the negative
rail on the breadboard.
h. Connect the battery to the battery holder.
i. Observe if the LED lights up, indicating the circuit is complete and
functioning.
j. If the LED does not light up, troubleshoot by checking connections and
component placement.

Activity 4.4: Circuit Symbol Sketching Challenge

Objective: You will practice sketching circuit symbols from memory.

Instructions:
a. Pick up a list of circuit elements and their corresponding symbols from your
facilitator (e.g., resistor, capacitor, diode).
b. You will be given a set amount of time (e.g., 5 minutes) to sketch as many
circuit symbols as you can from memory.
c. After the time is up, compare your sketches with the correct symbols and
identify any discrepancies.
d. Discuss the correct symbols and their meanings as a class, emphasising any
common mistakes or misconceptions.
e. Repeat the sketching challenge periodically to reinforce learning and
improve accuracy over time.

Activity 4.5: Component Sorting Activity

Objective: You will sort a collection of circuit components into passive and active
categories based on their characteristics.
Materials Needed:
• Assorted circuit components (resistors, capacitors, inductors, diodes,
transistors)
• Sorting containers or labeled sections on a table
Instructions:
a. The facilitor will provide you with a collection of circuit components.
b. You will be instructed to examine each component and determine whether it
is passive or active.

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c. Then place each component into the appropriate sorting container or section
labelled “Passive” or “Active.”
d. Discuss your reasoning for classifying each component.
e. After sorting, review the classifications as a class, discussing the
distinguishing characteristics of passive and active elements.

Activity 4.6: Component Identification Challenge

Objective: You will identify passive and active circuit elements in real-world
circuits.
Materials Needed:
• Circuit diagrams or schematics
• Whiteboards or paper to write your answers on

Instructions:
a. You will be provided with circuit diagrams or schematics depicting various
circuits.
b. Analyse each circuit and identify the passive and active elements present.
c. You should write down your answers on whiteboards or paper.
d. After you have completed the challenge, review the circuits as a class and
discuss the correct classifications.
e. Address any misconceptions and provide explanations for why each
component is classified as passive or active.

Activity 4.7: Hands-On Circuit Building

Objective: You will build circuits containing both passive and active elements to
observe their behaviour.
Materials Needed:
• Breadboards
• Resistors, capacitors, inductors, diodes, transistors
• Jumper wires
• Power supply or batteries

Instructions:
a. The facilitator will provide you with breadboards and a variety of circuit
components.
b. You will be assigned specific circuit configurations to build, incorporating
both passive and active elements.
c. Sketch the circuit diagrams before building them to plan the connections.

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d. Build and test your circuits, observing the behaviour of each component.
e. You should discuss your observations and compare the behaviour of passive
and active elements in the circuits.
f. Join a class discussion to review the circuits and reinforce the classification
of passive and active elements.

Activity 4.8: Discovering the Effects of Passive Components on Current

Flow and Energy Dissipation

Objective: You will understand how passive components such as resistors and
capacitors affect the flow of current in a circuit. You will also learn about energy
dissipation in passive components such as resistors and capacitors and understand
how this influences their classification and practical applications.
Materials Needed:
• Breadboards
• Resistors of various values
• Capacitors of various values
• Multimeters
• DC power supplies
• Connecting wires
• LED bulbs
• Worksheets for recording observations
Safety Notes:
• Always ensure the power supply is turned off while constructing
circuits.
• Double-check connections before applying power to prevent short
circuits.
• Handle resistors carefully during and after the experiment to avoid
burns from heat dissipation.
Experiment A: Resistors in Series and Parallel:
a. Step 1: Connect resistors in series on the breadboard with an LED. Use the
DC power supply to apply a constant voltage (e.g., 5V). Measure and record
the current using the multimeter.
b. Step 2: Connect resistors in parallel on the breadboard. Apply the same
voltage and measure the current.
Observation: Students should note how the total resistance changes in series
and parallel configurations and how it affects the current.
c. Step 3: Measure and record the current using the multimeter. Calculate the
power dissipation using the formula P=I2R.
d. Step 4: Touch the resistor carefully to feel the heat generated.
Observation: Students should observe the LED lighting up and the resistor
warming up due to energy dissipation as heat.

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Worksheet Questions:
i. How does the current change when resistors are added in series versus
parallel?
ii. What is the relationship between total resistance and current flow in
each configuration?
iii. How does the resistor dissipate energy?
iv. Calculate the power dissipated by the resistor.
v. What practical implications does this energy dissipation have for circuit
design?
Experiment B: Capacitors in DC Circuits and their Energy Behaviour:
a. Step 1: Connect a capacitor in series with a resistor and an LED. Apply a DC
voltage and observe the LED.
b. Step 2: Measure the voltage across the capacitor and resistor over time as the
capacitor charges and discharges.
Observation: Learners should see that the LED gradually dims as the
capacitor charges and the current decreases.
c. Step 3: Measure the voltage across the capacitor and resistor over time using
a multimeter.
Observation: You should see the LED gradually dimming as the capacitor
charges and brightening as it discharges.

Worksheet Questions:
i. What happens to the current flow when the capacitor is fully charged?
ii. How does the capacitor affect the brightness of the LED over time?
iii. Does the capacitor dissipate energy as heat? Why or why not?
iv. Describe the energy storage and release process in the capacitor.
v. How does this behaviour classify the capacitor in terms of energy
dissipation?

Conclusion and Discussion (10 minutes):

a. Discuss with the whole class the key points learned from the experiments.
b. Discuss real-world applications of resistors, capacitors, and inductors in
electronic devices.
c. Discuss the classification of passive components based on their energy
dissipation properties:
i. Resistors as energy dissipating components.
ii. Capacitors and inductors as energy-storing components.
d. You are encouraged to ask questions and share your observations.

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SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

Activity 4.9: Investigating the Role of Active Components in Signal Ampli-

fication and

Signal Processing
Objective: You will explore how active components such as transistors and
operational amplifiers (op-amps) are used in signal amplification and signal
processing within circuits.
Materials Needed:
• Breadboards
• NPN Transistors (e.g., 2N2222)
• Operational Amplifiers (e.g., LM741)
• Resistors (1kΩ, 10kΩ, 100kΩ)
• Capacitors (1µF, 10µF)
• DC power supplies (±15V and 5V)
• Signal generators
• Oscilloscopes
• Multimeters
• Connecting wires
• LEDs

Instructions:
Part 1: Understanding Transistors
Experiment 1: Transistor as a Switch
1. Circuit Setup: Connect the following components on a breadboard:
a. Collector (C) of the NPN transistor to the positive terminal of the 5V
power supply.
b. Emitter (E) to ground.
c. Base (B) through a 1kΩ resistor to the positive terminal of the power
supply.
d. LED in series with a 1kΩ resistor between the collector and ground.
2. Procedure:
a. Measure the voltage across the LED when the base is connected to the
power supply.
b. Disconnect the base and measure the voltage across the LED again.
3. Observations and Questions:
a. Record the voltage across the LED in both cases.
b. What happens to the LED when the base is connected and disconnected?
c. Explain the role of the transistor in this circuit.

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SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

KIRCHHOFF’S LAWS
Kirchhoff’s Current Law (KCL) is one of the fundamental principles used in electrical
circuit analysis. It is named after the German physicist Gustav Kirchhoff, who first
formulated it in 1845. Gustav Robert Kirchhoff (1824-1887) was a renowned physicist
and mathematician who made significant contributions to various fields of science.
In electrical circuit theory, he is best known for formulating Kirchhoff’s Laws, which
he published in 1845 while he was a university student. To understand and apply the
Kirchhoff’s Laws, let us introduce briefly the Ohm’s law.

Ohm’s Law
Ohm’s Law states that, the voltage drop (V) across a conductor or load is equivalent
to the product of current (I) and resistance (R) of the conductor or load. This can
be expressed mathematically as V = I × R. This will be useful when applying the
Kirchhoff’s Laws below.

Kirchhoff’s Current Law (KCL)

It states that at any instant, the algebraic sum of currents at any junction (or node) in
a network is zero.
Or the law states:
“The total current entering a junction (or node) in an electrical circuit must equal the
total current leaving the junction.”

Figure 4.9: A picture illustrating KCL

In simple terms, this means that the total current flowing into a junction is equal to the
total current flowing out of the junction. This is because the charge is neither created
nor destroyed at a junction; it can only flow in or out.

23
SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

In other words, the algebraic sum of currents at a node is zero. Mathematically, this
can be expressed as:
I1 + I2 + I3 – I4 – I5 = 0
I1 + I2 + I3 = I4 + I5
The currents entering the node are considered positive, and the currents leaving the
node are considered negative (or vice versa, if the sign convention is consistent).

Application of KCL
To apply Kirchhoff’s Current Law in analysing a circuit:
a. Identify Nodes: Determine all the junctions (nodes) in the circuit where
currents converge.
b. Assign Currents: Assign a direction to each current flowing into or out of
the node. The actual direction does not matter initially; if the current is in the
opposite direction, the result will be a negative value.
c. Write Equations: For each node, write an equation that represents the sum of
currents entering and leaving the node.
d. Solve the Equations: Use the system of equations to solve for the unknown
currents.
Example
Consider four gadgets in a house which are connected in parallel to a power source
namely a refrigerator, television, computer, and lamp. Given that the refrigerator draws
5A, the television draws 3A, the computer draws 2A and the lamp draws 1A. Find the
total current drawn by the three gadgets.
Solution
Using the Kirchhoff’s Current Law
Itotal = Irefrigerator + Itelevision + Icomputer + Ilamp
Itotal = 5A + 3A + 2A + 1A = 11A

Kirchhoff’s Voltage Law (KVL)

It states that at any instant in a loop, the algebraic sum of the EMFs acting around the
loop is equal to the algebraic sum of the potential differences around the loop. A loop is
a path that starts and ends at the same node/junction, without passing through any
electrical element more than once.

Application of KVL
a. Identify the Loop: Choose a closed loop within the circuit for analysis.
b. Assign Voltage Polarities: For resistors, assume a direction for the voltage drop
(from positive to negative terminal). For voltage sources, mark their polarities
according to their orientation within the loop.

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SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

c. Write the Voltage Equation: For each loop, write the Kirchhoff’s voltage
equations using KVL.
d. Solve for Equations: Use the systems of equations to solve for the unknowns.

Figure 4.10: A picture illustrating KVL

I1 = I2 + I3 ……………………….KCL equation 1
V = I1R1 + I2 R2 ..........…………....KVL equation 2
V = I1R1 + I3 (R3 + R4) ….…………KVL equation 3
Example
Consider four gadgets in a house connected in series across battery sources, namely a
washing machine, lamp, fan, and radio. Given that the washing machine has a voltage
drop of 6V, the lamp has a voltage drop of 3V, the fan has a voltage drop of 2V, and the
radio has a voltage drop of 1V. Find the voltage of the battery source.
Solution
Using the KVL,
Vtotal = Vwashing machine + Vlamp + Vfan + Vradio
Vtotal = 6A + 3A + 2A + 1A = 12A

Series and Parallel Circuits

In series circuits, resistors are connected one after another, creating a single path for
current flow. The equivalent resistance (RT) of series resistors is the sum of individual
resistances.

Figure 4.11: Three resistors in Series

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SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

Characteristics of a Series circuit

a. The same current flows through all resistors
b. Total potential difference is equal to the sum of individual potential differences
c. Individual potential difference is directly proportional to individual resistance
d. Total resistance is equal to the sum of individual resistances
e. Total power in a series circuit is equal to the sum of the individual values of
power in the circuit.
Since the same current flows through each resistor, the supply voltage is equal to the
sum of the potential differences across each resistor:
V = V1 + V2 + V3
V = IRT, V1 = IR1, V2 = IR2, V3 = IR3
IRT = IR1 + IR2 + IR3

Dividing through by I
Total Resistance, RT = R1 + R2 + R3

Question:
You have a 12V battery and three resistors with values R1 = 2 Ω, R2 = 3 Ω, and R3 = 5 Ω
connected in series.
a. Calculate the total resistance:
Rtotal = 2 + 3 + 5 = 10 Ω
b. Calculate the current
I = V / Rtotal = 12 V / 10 Ω = 1.2 A
c. Calculate the voltage drop across each resistor:
V1 = I × R1 = 1.2 A × 2 Ω = 2.4 V
V2 = I × R2 = 1.2 A × 3 Ω = 3.6 V
V3 = I × R3 = 1.2 A × 5 Ω =6.0 V
d. Verify the total voltage:
V = V1 + V2 + V3 = 2.4 + 3.6 + 6.0 = 12 V

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SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

Resistors connected in parallel

When resistors are connected in parallel in the same circuit, they can work as if each
resistor were connected in a separate circuit.

Figure 4.12: Three resistors in Parallel

Characteristics of a parallel circuit

a. The same potential difference is across each resistor.
b. Total current is equal to the sum of individual currents.
c. Individual currents are inversely proportional to the individual resistances.
d. Total power in a parallel circuit is equal to the sum of the individual values of
power in each branch.
When two (2) Resistors are connected in parallel
I = I1 + I2

I= V = V + V
RT R1 R2

Where V is the applied voltage

RT is the total resistance of the parallel combination
V= V + V
RT R1 R2

Dividing through by V
1 = 1 + 1
RT R1 R2

Find the LCM

1 = R2 + R1
RT R1 × R2

Hence, total resistance for the parallel combination,

RT = R1 × R2
R1 + R2

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SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

When three (3) Resistors are connected in parallel,

I = I1 + I2 + I3

IT = V = V + V + V
RT R1 R2 R3

Where V is the applied voltage

RT is the total resistance of the parallel combination
V= V + V + V
RT R1 R2 R3

Dividing through by V

I = 1 = 1 + 1 + 1
RT R1 R2 R3

Find the LCM

1 = R2R3 + R1R3 + R1R2
RT R1 R2 R3

Hence, total resistance for the parallel combination, RT = R1.R2.R3

R2.R3 + R1.R3 + R1.R2
Question:
Consider a parallel circuit with a 12 V battery and three resistors R1 =2 Ω, R2 =3 Ω, and
R3 = 6 Ω.
a. Total Resistance:
1 = 1 + 1 + 1
RTotal R1 R2 R3
1 = 1 + 1 + 1
RT 2 3 6

= 1+2+1
6
= 6
6
=1

RT = 1 Ω
b. Current through each Resistor:

I1 = V = 12 = 6A
R1 2

I2 = V = 12 = 4A
R2 3

I2 = V = 12 = 2A
R2 6

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SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

c. Total Current: Using KCL,

IT = I1 + I2 + I3
IT = 6A + 4A + 2A
IT = 12A

USING KIRCHHOFF’S LAWS TO FIND CURRENTS

AND VOLTAGES IN DC CIRCUITS
Analysing DC circuits using Kirchhoff’s laws is an essential skill for anyone studying
electrical engineering or related fields. Kirchhoff’s laws are two fundamental principles
that govern the behaviour of electrical circuits. Sample problems solved using Kirchoff’s
Laws are presented below:

Question 1:
Using figure 4.13 below,

Figure 4.13

Calculate:
a. the total resistance RT;
b. current, Is;
c. voltage, Vs.
d. the voltage across the 9Ω resistor
Solution:
a. The 9Ω resistor is in parallel with the 7Ω resistor. Using the concept of series
and parallel resistors above,
1 = 1 + 1
RP 9 7
1 = 7+9
RP 7×9
RP = 9 × 7
9+7
= 3.9375 Ω

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SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

The combination of the 9Ω resistor and the 7Ω is in series with the 12Ω, therefore
RT = Rp + 12
= 3.9375 + 12
= 15.9375 Ω
⸫ The total resistance of the circuit, RT = 15.94Ω

b. Using the Ohms law, the voltage drop across the total resistance is (which is
equal to the source voltage), Vs = IsRT,

hence Is = VS
RT
The voltage drop across the 12Ω has been given as V = 15V, using ohms law,

Is = 15
22
= 1.25A
c. Applying the KVL to the loop that contains the 9Ω resistance, the 12Ω resistor
and the source voltage,
Vs = Vp + 15V
Vp = IsRp
Is = 1.25A and Rp = 3.9375Ω
Vp = 1.25 × 3.9375
= 4.921875V

Vs = 4.921875 + 15
= 19.921875V

d. Voltage across 9Ω Resistor, Vp = 4.9218V

Question 2:
Using Kirchhoff’s laws in figure 4.14,

Figure 4.14

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SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

Calculate the
a. I1
b. I2
c. the voltage across the 3Ω resistor
Solution
The 2.5Ω and the 1.5Ω resistors are in series hence,
Rs = 2.5Ω + 1.5Ω
= 4.0Ω
The Total Voltage, Vs = 12V + 6V
= 18V
From the circuit diagram
I2 = I – I1 --------- Equation 1
18 = 4I + 5I1 -------- Equation 2
18 = 4I + 3I2 ------- Equation 3

Substituting equation 1 into equation 3

18 = 4I + 3(I – I1)
18 = 4I + 3I – 3I1

18 = 7I – 3I1--------------- Equation 4
Equation 2 × 3
54 = 12I + 15I1----------- Equation 5
Equation 4 × 5
90 = 35I – 15I1----------- Equation 6

Equation 5 + Equation 6
144 = 47I

I = 144
47
= 3.0638A

a. Substituting I = 3.0638 into equation 2

18 = 4I + 5I1
18 = 4(3.0638) + 5I1
18 = 12.2552 + 5I1
5I1 = 18 – 12.2552

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SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

5I1 = 5.7448

I1 = 5.7448
5
⸫ I1 = 1.14896A

b. Substituting I = 3.0638 into equation 3

18 = 4I + 3I2
18 = 4(3.0638) + 3I2
18 = 12.2552 + 3I2
3I2 = 18 – 12.2552
3I2 = 5.7448

I2 = 5.7448
3
I2 = 1.9149A

c. The voltage across the 3Ω resistor,

V = 3I2
= 3 × 1.9149
= 5.7447V

Question 3:
Figure 4.15 is a resistive network. If the power dissipated in the 12Ω resistor is 48W,
calculate the:
a. current flowing in the 12Ω resistor
b. the total current (I) in the circuit
c. value of the resistor, R.

Figure 4.15

32
SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

Answers
a. Current flowing in the 12Ω resistor, I1 = 2.0A
b. The total current I = 3.5A
c. The value of Resistor R = 10.2Ω

Question 4:

Figure 4.16

Figure 4.16 is a circuit diagram. Using the diagram, calculate the:

a. current (I1) flowing through resistor R1
b. current (I) flowing through the circuit
c. current (I2) flowing through resistor R2
Answers
a. The current, I1= 0.3A
b. The Total current, I = 0.9A
c. The current, I2 = 0.6A

Question 5:

Figure 4.17
Using Kirchhoff’s law in Figure 4.17, calculate
a. the value of current I1
b. the value of current I2
Answers
a. Current I1 = 5A
b. Current I2 = 10A

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SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

Activity 4.10

1. Using the circuit diagram in Figure 4.18 below, Calculate

a. the total resistance in the circuit
b. the currents I1, I2 and I3 in the circuit
c. the voltage drops across R1

Figure 4.18

Answers:
a. RT = 5Ω
b. I1 = 5A, I2 = 2.5A and I3 = 2.5A
c. VR1 = 15V

Figure 4.19

2. Using Kirchhoff’s law in Figure 4.19, calculate

a. the total resistance in the circuit
b. the value of current I1
c. the value of current I2
d. the value of current I3
e. the voltage drops across R2
Answers:
a. RT = 0.588Ω
b. I1 = 5.333A
c. I2 = - 0.667A
d. I3 = 4.667A
e. VR2 = 2.224V

34
SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

3.

Figure 4.20

Using Figure 4.20, Calculate:

a. the current, I1 through the resistor R1
b. the total voltage across the circuit, ES
c. the resistance of the resistor, R1
Answers:
a. I1 = 2.5A
b. ES = 50V
c. R1 = 20Ω

COMPUTING POWER IN DC AND SINGLE-PHASE

AC CIRCUITS
Power is the rate at which work is done or the rate of energy transfer. It measures
how quickly energy is converted or used in a system. The SI unit of power is the watt,
represented by the symbol “W.”

Power (P) = Energy (E) or P = E

Time (t) t
Where: P = Power in watts (W)
E = Energy in joules (J)
t = Time in seconds (s)

Relationship between Power, Voltage, and Current:

P = VI for resistive circuits
Where: P = Power in watts (W),
V = Voltage in volts (V)
I = Current in amperes (A)

35
SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

Power in DC Circuits
P = VI
P = I2R

P=V
2

Question 1:
If a resistor connected to a 12V DC supply has current of 1.2A flowing through it,
calculate the power dissipated by the resistor.
Solution:
P = IV
P = 1.2 × 12
P = 14.4 W

Question 2:
An electrical circuit consists of a 24 V DC power source and a resistor of resistance 6Ω
connected across it. Calculate the power dissipated.
Solution:
P= V
2

R
P = 24
2

6
P = 576
6
P = 96 W

Question 3:
Two resistors of resistances 4Ω and 8Ω are connected in series. If a current flowing
through them is 1.67A, determine the total power dissipated in the circuit.
Solution:
Total Resistance, R = 4 + 8
= 12 Ω
Current, I = 1.67A
P = I2R
P = 1.672 × 12
P = 33.4668 W

36
SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

Activity 4.11

1. In a DC circuit, a 12 V battery is connected to a resistor with a resistance

of 8ᘯ. Calculate the power dissipated in the resistor. Also, explain how the
power value changes if the resistance is doubled while keeping the voltage
constant.
2. A DC motor consumes 10 A of current from a 24 V battery while operating.
The motor has an output shaft power of 180W. Calculate the efficiency of
the motor. If the efficiency is found to be low, suggest some possible ways to
improve it.
3. Solve for terminal quantities such as voltage and current in the DC circuit
and then compute the power.

SOFTWARE TOOL TO SIMULATE SIMPLE

CIRCUITS TO DERIVE CURRENT, VOLTAGE, AND
POWER IN DC CIRCUITS
Circuit Simulation Software
In the field of electronics, circuit simulation software plays a crucial role in
understanding, designing, and testing electrical circuits without the need for physical
components. These tools allow users to create and simulate circuits virtually, making
them an essential learning aid in education. Three commonly used user-friendly circuit
simulation software tools are Proteus, LTspice and CircuitLab.

Proteus
Proteus is a popular circuit simulation tool that is widely used in education and hobbyist
projects. It offers a simple and intuitive interface that makes it suitable for beginners.
Proteus circuit builder allows learners to drag and drop components onto the canvas,
making it easy to assemble circuits.

Figure 4.21: A picture of Proteus interface

37
SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

Here are steps to simulate a simple circuit to derive current, voltage, and power in DC
circuit using Proteus.

Step 1: Configure and Simulate the Circuit

a. Set Component Values:
i. Draw the circuit diagram you want to simulate.
ii. Open the proteus schematic editor window.
iii. Select the components from the component list and place them on the
simulation interface.
iv. Perform all the necessary connections.
v. Double-click on each component to set its properties, such as the resistance
value for resistors or voltage for the DC source.
b. Place Measurement Instruments: Add virtual instruments like voltmeters and
ammeters to measure voltage and current at various points in the circuit.
c. Run the Simulation:
i. Click the “Play” button (triangle icon) to run the simulation.
ii. Observe the behaviour of the circuit and the readings from the virtual
instruments

Step 2: Measure and Record Values

a. Measure Voltage: Place a voltmeter across the components where you want to
measure the voltage.
b. Measure Current: Place an ammeter in series with the components where you
want to measure the current.
c. Calculate Power:
i. Use the formula P = V × I to calculate power, where P is power, V is voltage,
and I is current.
ii. Alternatively, you can place a wattmeter to directly measure the power if
available.
Example Circuit: Series and Parallel Resistor Network
Series Circuit:
• Place a DC voltage source.
• Connect two or more resistors in series with the voltage source.
• Place voltmeters across each resistor and an ammeter in series with the
circuit to measure the total current.
• Run your simulation and record the values for the current and the
voltages.
Parallel Circuit:
• Place a DC voltage source.
• Connect two or more resistors in parallel with the voltage source.

38
SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

• Place voltmeters across each resistor and an ammeter in series with each
branch to measure the individual currents.
• Run your simulation and record the values for the currents and the
voltage.

Step 3: Analyse and Interpret Results

a. Analyse Measurements: Compare the measured values of voltage, current, and
power with theoretical calculations using Ohm’s Law, Kirchhoff’s Current Law
and Kirchhoff’s Voltage Law.
b. Interpret Results: Discuss any discrepancies between the measured and
theoretical values, considering possible sources of error or limitations of the
simulation.

Step 4: Report Findings

a. Document the Process: Write a report detailing the circuit design, simulation
setup, measurements taken, and the results obtained.
b. Include Screenshots: Take screenshots of your Proteus circuit design and
measurement readings.
c. Present Results: Prepare a presentation or a report to share your findings with
the class, explaining how Proteus helped in understanding the principles of DC
circuits.

LTspice
LTspice is a powerful circuit simulation software widely used in engineering and
educational settings. It offers more advanced features than Tinkercad but may have
a steeper learning curve. It provides a schematic editor where students can design
circuits by placing components and connecting them with wires.

Figure 4.22: A picture of LTspice interface

Here are steps to simulate a simple circuit to derive current, voltage, and power in DC
circuit using LTspice.

39
SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

Step 1: Run the Simulation

a. Set Up Simulation:
i. Click on the Simulate menu and select Edit Simulation Command.
ii. In the simulation command window, choose the type of analysis you want
to run (e.g., DC operating point, Transient, or AC Analysis). For DC circuits,
choose DC operating point.
iii. Click OK and place the simulation command on the schematic.
b. Run the Simulation: Click on the Run icon (a running man symbol) or press
F9 to run the simulation.

Step 2: Measure and Record Values

a. Measure Voltage:
i. Click on the Voltage probe (red probe icon) and then click on the node where
you want to measure the voltage.
ii. LTspice will display the voltage at that node.
b. Measure Current:
i. Click on the Current probe (current meter icon) and then click on the
component that you want to measure the current flowing through.
ii. LTspice will display the current through that component.
c. Calculate Power:
i. Use the formula P = V × I to calculate power, where P is power, V is voltage,
and I is current.
ii. Alternatively, you can right-click on a component and select Power to display
the power directly.
Example Circuit: Series and Parallel Resistor Network
Series Circuit:
• Place a DC voltage source.
• Connect two or more resistors in series with the voltage source.
• Measure the voltage across each resistor and the total current in the
circuit.
Parallel Circuit:
• Place a DC voltage source.
• Connect two or more resistors in parallel with the voltage source.
• Measure the voltage across each resistor and the current through each
branch.

Step 3: Analyse and Interpret Results

a. Analyse Measurements: Compare the measured values of voltage, current, and
power with theoretical calculated values.

40
SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

b. Interpret Results: Discuss any discrepancies between the measured and

theoretical values, considering possible sources of error or limitations of the
simulation.

Step 4: Report Findings

a. Document the Process: Write a report detailing the circuit design, simulation
setup, measurements taken, and the results obtained.
b. Include Screenshots: Take screenshots of your LTspice circuit design and
measurement readings.
c. Present Results: Prepare a presentation or a report to share your findings with
the class, explaining how LTspice helped in understanding the principles of DC
circuits.

CircuitLab
CircuitLab is another user-friendly online circuit simulator with a focus on simplicity
and ease of use. It features a schematic editor that enables learners to create circuits
quickly and efficiently. It also includes a wide range of components and supports
various simulation types.

Figure 4.23: A picture of Circuitlab interface

Here are steps to simulate a simple circuit to derive current, voltage, and power in DC
circuit using Circuitlab.

Step 1: Run the Simulation

a. Set Up Simulation:
i. Click on the Simulate button in the top toolbar.
ii. In the simulation settings window, choose the type of analysis you want to
run (e.g., DC, Transient, or AC Analysis). For DC circuits, choose DC.
b. Configure Analysis:
i. Set the parameters for the DC analysis, such as the range of values to be
swept if needed.
ii. Click Run DC Solver to start the simulation.

41
SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

Step 2: Measure and Record Values

a. Measure Voltage:
i. Click on the Voltage probe tool and then click on the node where you want
to measure the voltage.
ii. CircuitLab will display the voltage at that node.
b. Measure Current:
i. Click on the Current probe tool and then click on the component through
which you want to measure the current.
ii. CircuitLab will display the current through that component.
c. Calculate Power:
i. Use the formula P = V × I to calculate power, where P is power, V is voltage,
and I is current.
ii. Alternatively, you can use CircuitLab’s built-in measurement tools to directly
display power if available.
Example Circuit: Series and Parallel Resistor Network
Series Circuit:
• Place a DC voltage source.
• Connect two or more resistors in series with the voltage source.
• Measure the voltage across each resistor and the total current in the
circuit.
Parallel Circuit:
• Place a DC voltage source.
• Connect two or more resistors in parallel with the voltage source.
• Measure the voltage across each resistor and the current through each
branch.

Step 3: Analyse and Interpret Results

a. Analyse Measurements: Compare the measured values of voltage, current, and
power with theoretical calculations.
b. Interpret Results: Discuss any discrepancies between the measured and
theoretical values, considering possible sources of error or limitations of the
simulation.

Step 4: Report Findings

a. Document the Process: Write a report detailing the circuit design, simulation
setup, measurements taken, and the results obtained.
b. Include Screenshots: Take screenshots of your CircuitLab circuit design and
measurement readings.

42
SECTION 4 ELECTRICAL AND ELECTRONIC CIRCUIT

c. Present Results: Prepare a presentation or a report to share your findings with

the class, explaining how CircuitLab helped in understanding the principles of
DC circuits.
Example of Detailed Steps for a Series Circuit:
a. Start a New Schematic: Click New Document.
b. Add Components:
i. From the left toolbar, click DC Voltage Source and place it on the workspace.
ii. Click Resistor and place two resistors in series with the voltage source.
iii. Click Ground and place it at the bottom of the voltage source.
c. Connect Components:
i. Use the Wire tool to connect the positive terminal of the voltage source to
one end of the first resistor.
ii. Connect the other end of the first resistor to one end of the second resistor.
iii. Connect the other end of the second resistor to the ground.
d. Set Values:
i. Double-click the voltage source and set its value (e.g., 10V).
ii. Double-click each resistor and set their values (e.g., 1kΩ each).
e. Run Simulation:
i. Click Simulate.
ii. In the simulation settings, select DC.
iii. Click Run DC Solver.
f. Measure and Record:
i. Use the Voltage probe to measure the voltage across each resistor.
ii. Use the Current probe to measure the current through the series circuit.

Running Simulations
After setting up the circuit parameters, it’s time to run the simulation. Most software
tools have a “simulate” or “run” button that initiates the analysis. The software will
calculate the behaviour of the circuit based on the specified parameters and generate
simulation results, such as voltage and current waveforms, which can be displayed on
the screen.

Introduction to DC Circuits Simulation

1. Open the circuit simulation software (e.g., SPICE, LTspice, or any other tool you
prefer) and create a new project.
2. Design your DC circuit on the simulation interface by placing components like
resistors, capacitors, and voltage/current sources.
3. Once the circuit is ready, you can begin the simulation setup.

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Setting Simulation Time and Analysing Transient or Steady-State

Behaviour:
a. Before running the simulation, determine the time span you want to observe. For
transient analysis, set the simulation time long enough to capture the behaviour
of interest. For steady-state analysis, you can set a shorter simulation time.
b. Configure the simulation settings, selecting either transient or steady-state
analysis.
c. Run the simulation and observe the behaviour of the circuit over time (transient
analysis) or once it reaches a stable state (steady-state analysis).

Measuring Current, Voltage, and Power:

a. To measure current and voltage at specific locations in the circuit, place
measurement probes accordingly. Probes are typically voltage probes (for
voltage measurement) and current probes (for current measurement).
b. After running the simulation, examine the waveforms displayed on the
oscilloscope or plotter. You can use the cursors or markers to measure specific
values.
c. Analyse the measured values to understand how voltage and current change
over time or at specific points in the circuit.

Analysing Power in DC Circuits:

a. To calculate power dissipation in resistive elements (e.g., resistors), use the
formula: Power (P) = Voltage (V) × Current (I). This is valid for resistive
elements in both DC circuits.
b. Sum up the power dissipated across all resistors in the circuit and verify power
conservation, which states that the total power supplied by voltage sources must
equal the total power consumed by resistive elements.

Activity 4.12

The teacher will draw and explain the power relations of Apparent Power, Real
Power and Reactive Power, including power factor and provide all relevant
equations.
Interactive Simulation
Objective: Use an online simulation tool to explore the behaviour of passive and
active circuit elements.
Materials Needed:
• Computer or tablet with internet access
• Circuit simulation software (e.g., CircuitLab, Falstad Circuit Simulator)

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Instructions:
a. The teacher will introduce you to the basics of circuit simulation software
and how to use it.
b. You will be assigned specific circuits or circuit elements to simulate,
including both passive and active components.
c. Observe and analyse the behaviour of each component as they vary circuit
parameters (e.g., resistance, voltage, frequency).
d. You are encouraged to compare the behaviour of passive and active elements
and identify any differences.
e. Join a discussion based on your observations, focusing on the roles and
characteristics of passive and active components in circuits.

Activity 4.13: Simulating Simple DC Circuits Using Circuit

Simulation Software

Objectives:
• Understand the basic principles of DC circuits.
• Learn how to use circuit simulation software.
• Derive current, voltage, and power in simple DC circuits.
Materials:
• Computer with internet access
• Circuit simulation software (e.g., Proteus, Circuit Lab, or LTspice)
• Worksheet for recording observations and calculations
Instructions:
Part 1: Introduction to Circuit Simulation Software
a. Introduction to the Software:
i. The teacher will provide a brief tutorial on how to use the selected
circuit simulation software.
ii. The teacher will show you how to create a new circuit, add components
(resistors, batteries, wires, etc.), and connect them.
b. Exploration: Explore the software and familiarise yourself with its interface
and tools.

Part 2: Simulating a Simple Series Circuit

a. Build a Series Circuit:
i. Build a simple series circuit with one battery (DC power source) and
two resistors.
ii. Example: Connect a 9V battery in series with a 10Ω resistor and a 20Ω
resistor.

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b. Simulate and Observe:

i. Run the simulation and observe the current and voltage across each
resistor.
ii. Use the software’s measurement tools to measure the current through
the circuit and the voltage across each resistor.
c. Record Observations:
i. Record the current and voltage values in a worksheet.
ii. Calculate the total resistance, total current, and power dissipated in
each resistor using Ohm’s Law and the power formula.
d. Analysis:
i. Compare the simulated results with theoretical calculations.
ii. Discuss any discrepancies and possible reasons (e.g., measurement
errors, ideal vs. real components).

Part 3: Simulating a Simple Parallel Circuit

a. Build a Parallel Circuit:
i. Build a simple parallel circuit with one battery (DC power source) and
two resistors.
ii. Example: Connect a 9V battery in parallel with a 10Ω resistor and a 20Ω
resistor.
b. Simulate and Observe:
i. Run the simulation and observe the current and voltage across each
resistor.
ii. Use the software’s measurement tools to measure the current through
each branch of the circuit and the voltage across each resistor.
c. Record Observations:
i. Record the current and voltage values in a worksheet.
ii. Calculate the total resistance, total current, and power dissipated in
each resistor using Ohm’s Law and the power formula.
d. Analysis:
i. Compare the simulated results with theoretical calculations.
ii. Discuss any discrepancies and possible reasons.

Part 4: Reflection and Discussion

a. Summary of Findings:
i. Summarise your findings from the series and parallel circuit simulations.
ii. Discuss the differences between series and parallel circuits in terms of
current, voltage, and power distribution.
b. Applications:
i. Discuss real-world applications of series and parallel circuits.
ii. Explore how understanding these circuits is important in designing
electronic devices and electrical systems.

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Activity 4.14

Build the same circuits (in series and in parallel) using components from the lab
on a breadboard and measure the current, voltage and power using instruments
like ammeter and voltmeter.
1. Assess the accuracy and limitations of the simulation software in replicating
real-world circuit behaviour. Compare the software’s predictions with
actual measurements from a physical circuit and identify areas where the
simulation may not accurately represent reality.
2. Critique the effectiveness of the software tool in helping you understand the
fundamental concepts of current, voltage, and power in DC circuits. Identify
any areas where the software may have helped or hindered.

47
Review Questions

1. How would you explain the function of a resistor in a DC circuit? Provide an

example of where resistors are commonly used.
2. Describe the role of a capacitor in DC circuits. What are the different types of
capacitors and where are they typically used?
3. Discuss the function of an inductor in DC circuits. Where are inductors
commonly found in electronic devices?
4. Explain how a diode works in a DC circuit. What is the purpose of using diodes
in electronic circuits?
5. Compare and contrast an LED with a regular diode. How does an LED emit
light, and where are LEDs commonly used in modern electronics?
6. Discuss the importance of understanding circuit symbols in electronics. Why
are standardised symbols used across electronic circuits?
7. Define passive and active elements in electrical circuits. Provide examples of
each.
8. Classify the following circuit elements as passive or active:
a. Resistor
b. Capacitor
c. Transistor
d. Inductor
e. Operational Amplifier (Op-amp)
9. Explain why resistors, capacitors, and inductors are classified as passive
elements in electrical circuits.
10.Discuss the role of active elements such as transistors and op-amps in electronic
circuits. Provide an example of where each is commonly used.
11.Describe a scenario where understanding the classification of circuit elements
into passive and active is crucial in circuit design.
12.Compare the characteristics of passive and active elements in terms of energy
consumption and signal handling capabilities.
13.Discuss the importance of identifying and correctly classifying circuit elements
in troubleshooting and repairing electronic devices.
14.How do Kirchhoff’s laws differ from Ohm’s law? Explain with examples.
15.In a DC circuit with a voltage of 12V and a current of 2A, find the power
consumed.

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Answers to Review Questions

1.
• Function: A resistor limits the flow of current in a circuit, thereby controlling
the amount of current that flows through other components.
• Example: Resistors are commonly used in voltage dividers, LED current
limiting circuits, and as pull-up or pull-down resistors in digital electronics.
2.
• Role: Capacitors store electrical energy and release it when needed,
smoothing voltage fluctuations and filtering signals in DC circuits.
• Types: Electrolytic capacitors (polarised, used for larger capacitance values)
and ceramic capacitors (non-polarised, used for smaller values and higher
frequencies).
• Applications: Capacitors are used in power supply filtering, timing circuits,
and noise suppression.
3.
• Function: An inductor stores energy in a magnetic field when current flows
through it, resisting changes in current.
• Applications: Inductors are used in DC-DC converters, filters, oscillators,
and as energy storage devices in power supplies.
4.
• Function: A diode allows current to flow in one direction only (forward-
biased) while blocking current in the opposite direction (reverse-biased).
• Purpose: Diodes are used in rectifiers to convert AC to DC, voltage regulation
circuits, and to protect sensitive components from reverse polarity.
5.
• Comparison: LEDs (Light Emitting Diodes) emit light when current flows
through them in the forward direction, whereas regular diodes do not emit
light.
• Usage: LEDs are commonly used in indicators, displays, lighting (both
decorative and functional), and as status indicators in electronic devices.
6.
• Importance: Understanding circuit symbols allows engineers and techni-
cians to easily interpret and communicate circuit designs and schematics.
• Standardisation: Standard symbols ensure clarity and consistency in circuit
diagrams, facilitating accurate design, troubleshooting, and maintenance of
electronic systems.
7.
• Passive Elements: Passive elements do not supply energy to the circuit and
cannot amplify signals. Examples: Resistors, capacitors, inductors.

49
 • Active Elements: Active elements supply energy to the circuit and can
amplify signals. Examples: Transistors, operational amplifiers (op-amps),
integrated circuits (ICs).
8.
a. Resistor: Passive
b. Capacitor: Passive
c. Transistor: Active
d. Inductor: Passive
e. Operational Amplifier (Op-amp): Active
9. Reasoning: Resistors, capacitors, and inductors do not require an external
power source to operate. They absorb or store energy rather than amplify or
generate power.
10.
• Transistors: Transistors amplify and switch electronic signals. They are
used in amplifiers, digital logic circuits, and as switches in electronic
devices.
• Operational Amplifiers (Op-amps): Op-amps amplify small electrical
signals. They are used in audio amplifiers, signal conditioning circuits, and
as comparators in voltage sensing applications.
11. Scenario: In designing a low-power electronic device, choosing passive
elements like resistors and capacitors minimises energy consumption, whereas
active elements like transistors are used for signal amplification or switching,
enhancing the device’s performance.
12.
• Passive Elements: Passive elements have low energy consumption as
they do not generate or amplify signals. They handle signals by resisting,
storing, or filtering without additional power input.
• Active Elements: Active elements consume energy to amplify, switch,
or generate signals. They have higher signal-handling capabilities and can
control or modify signals to meet specific circuit requirements.
13. Importance: Proper classification helps in identifying faulty components,
understanding circuit behaviour, and ensuring compatibility in circuit
replacements or upgrades during troubleshooting and repair processes.
14. Difference: Ohm’s law relates voltage (V), current (I), and resistance (R) in a
single component, V = IR, while Kirchhoff’s laws apply to entire circuits.
Example: For a resistor R connected to a voltage source V:
• Ohm’s law gives the current I = V/R flowing through the resistor.
• Kirchhoff’s laws analyse the currents and voltages in the entire circuit,
considering how multiple components interact.
15. P = 12 V × 2 A = 24 W
Therefore, the power consumed in the circuit is 24 watts.

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Extended Reading
1. Hiley, J., Brown, K. E., & Hughes, E. (2001). Hughes Electrical & Electronic Technology-
either edition.

References
Name of Image Reference (link)

A picture of resistors https://www.istockphoto.com/photo/colored-resistors-in-a-

mounted on a circuit board row-gm1026481050-275266904,

A picture of Capacitors https://www.istockphoto.com/photo/capacitors-various-

kinds-gm485813632-73621583?searchscope=image%2Cfilm

A picture of Inductors https://stock.adobe.com/search?k=inductor&asset_

id=144467511

A picture of Diodes https://education.ni.com/teach/resources/926/diodes

A picture of a transistor https://www.shutterstock.com/image-vector/transistor-

electronic-component-symbol-diagram-vector-2169223279

A picture of an Integrated https://www.indiamart.com/proddetail/integrated-

circuit (IC) circuit-15619107491.html

A picture of a Transformer https://www.shutterstock.com/image-photo/small-

transformers-audio-573684904

A picture of some switches https://www.alamy.com/stock-photo-various-electrical-

switches-35091447.html?imageid=64F111E3-4E51-4B54-
BC73-9461F2AC64A9&p=33979&pn=1&searchId=3e3f87cf7
257ca5452f937978778f91b&searchtype=0

A picture illustrating KCL https://www.shutterstock.com/image-vector/illustration-first-

law-current-2297629107

A picture illustrating KVL https://www.pinterest.com/pin/689473024184809854/

Circuit diagrams No source

A picture of Proteus https://images.app.goo.gl/M24yajruTLYgJuvH7,

interphase

A picture of LTspice https://images.app.goo.gl/eodaM4uoggKNXcq26,

interphase

A picture of Circuitlab https://images.app.goo.gl/mmZ1YVEApAncuo9F9

interphase

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Acknowledgements

List of Contributors
Name Institution

Ing. Timothy Alhassan Kumasi Technical University

Ing. Dr. Daniel Opoku Kwame Nkrumah University of Science and Technology

Daniel K. Agbogbo Kwabeng Anglican SHTS

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