Electrical and Electronic Principles and Technology

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Date:	Sunday, 24 August 2025, 10:49 AM

1. Basic Electrical Principles
- 1.1. Electrical Physics
- 1.2. Electrical Power
2. DC and AC Supplies
- 2.1. DC Supplies
- 2.2. AC Supplies
3. Transformers
- 3.1. Introduction to Transformers
- 3.2. Principle Operation of Transformers

1. Basic Electrical Principles

At the end of this section you will have an understanding of:

· basic electrical quantities

· electrical power

· conductors and insulators

· simple circuit theory

· Ohms Law

1.1. Electrical Physics

1. Electric Charge

Symbol:
$q$
q
Unit: Coulomb (C)
Types of Charge: Positive (+), Negative (−)
Like charges repel, unlike charges attract.
Elementary charge:
$e = 1.6 \times 10^{-19}$
$e = 1.6 \times 1 0 -19$ C

2. Coulomb’s Law

Describes the force between two point charges:

F = k \frac{|q_1 q_2|}{r^2}

$F = k r 2 ∣ q 1 q 2 ∣$

$k = 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2$
$k = 8.99 \times 109 Nm 2 / C 2$
$r$
r = distance between charges

3. Electric Field (E)

Electric field due to a point charge:

E = \frac{F}{q} = \frac{kQ}{r^2}

$E = q F = r 2 k Q$

Unit: N/C or V/m
Direction: Away from positive, toward negative

4. Electric Potential (V)

Work done per unit charge:

V = \frac{W}{q} = \frac{kQ}{r}

$V = q W = r k Q$

Unit: Volt (V)

5. Potential Difference (Voltage)

$V = IR$
$V = I R$
Energy per unit charge between two points

6. Capacitance

Ability to store charge:

C = \frac{Q}{V}

$C = V Q$

Unit: Farad (F)
Capacitance of parallel plate capacitor:

C = \varepsilon \frac{A}{d}

$C = ε d A$

$\varepsilon$
ε: Permittivity of the medium

7. Current (I)

Flow of charge:

I = \frac{Q}{t}

$I = t Q$

Unit: Ampere (A)

8. Ohm’s Law

Relation between Voltage, Current, Resistance:

V = IR

$V = I R$

Resistance
$R$
R unit: Ohm (Ω)

9. Electrical Power (P)

Energy used per second:

P = VI = I^2R = \frac{V^2}{R}

$P = V I = I 2 R = R V 2$

Unit: Watt (W)

10. Resistors in Circuits

Series:
- $R_{eq} = R_1 + R_2 + \dots$
  $R e q = R 1 + R 2 + \dots$
- Same current through all
Parallel:
- $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$
  $R e q 1 = R 1 1 + R 2 1 + \dots$
- Same voltage across each

11. Kirchhoff’s Laws

KCL (Current Law): Total current into a junction = total current out
KVL (Voltage Law): Sum of voltage changes around a loop = 0

12. DC vs AC

DC (Direct Current): Flows in one direction (batteries)
AC (Alternating Current): Changes direction periodically (mains power)

1.2. Electrical Power

1. What is an Electrical Circuit?

An electrical circuit is a closed loop that allows current to flow through a path consisting of components like resistors, capacitors, power sources, switches, etc.

2. Basic Circuit Components

Component	Symbol	Function
Battery / Cell	🔋	Provides voltage (electrical energy source)
Resistor	▭▭	Limits current, provides resistance
Switch	🔘	Opens/closes the circuit
Wire	—	Connects components (assumed to have no R)
Lamp / Bulb	💡	Emits light when current passes
Capacitor
Ammeter	(A)	Measures current (in series)
Voltmeter	(V)	Measures voltage (in parallel)

3. Electric Current (I)

Flow of electric charge (electrons)
Measured in Amperes (A)

I = \frac{Q}{t}

$I = t Q$

4. Voltage (V) / Potential Difference

Energy per unit charge
Measured in Volts (V)

V = \frac{W}{Q}

$V = Q W$

5. Resistance (R)

Opposition to the flow of current
Measured in Ohms (Ω)

R = \frac{V}{I}

$R = I V$

6. Ohm’s Law

V = IR

$V = I R$

7. Types of Circuits

➤ Series Circuit:

Components connected end-to-end
Same current through all components
Voltage divides across components

Formulas:

R_{\text{eq}} = R_1 + R_2 + \dots

$R eq = R 1 + R 2 + \dots$

V_{\text{total}} = V_1 + V_2 + \dots

$V total = V 1 + V 2 + \dots$

I = \text{same for all}

$I = same for all$

➤ Parallel Circuit:

Components connected across the same two points
Same voltage across each component
Current divides between branches

Formulas:

\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots

$R eq 1 = R 1 1 + R 2 1 + \dots$

V = \text{same for all}

$V = same for all$

I_{\text{total}} = I_1 + I_2 + \dots

$I total = I 1 + I 2 + \dots$

8. Kirchhoff’s Laws

Kirchhoff’s Current Law (KCL):

Total current entering a junction = total current leaving

\sum I_{\text{in}} = \sum I_{\text{out}}

$\sum I in = \sum I out$

Kirchhoff’s Voltage Law (KVL):

Sum of voltage changes around any closed loop = 0

\sum V = 0

$\sum V = 0$

9. Power in Circuits

P = VI = I^2R = \frac{V^2}{R}

$P = V I = I 2 R = R V 2$

10. Measuring Instruments

Instrument	Connected in	Measures
Ammeter	Series	Current (A)
Voltmeter	Parallel	Voltage (V)
Multimeter	Both	V, A, Ω
Galvanometer	Series (low I)	Small currents

11. Capacitors in Circuits

In Series:

\frac{1}{C_{\text{eq}}} = \frac{1}{C_1} + \frac{1}{C_2} + \dots

$C eq 1 = C 1 1 + C 2 1 + \dots$

In Parallel:

C_{\text{eq}} = C_1 + C_2 + \dots

$C eq = C 1 + C 2 + \dots$

12. Time-Dependent Circuits (RC Circuits)

Charge/discharge of a capacitor over time

V(t) = V_0 e^{-t/RC}

$V (t) = V 0 e - t / RC$

Q(t) = Q_0 (1 - e^{-t/RC})

$Q (t) = Q 0 (1 - e - t / RC)$

$RC$
RC is the time constant (in seconds)

13. Important Circuit Symbols (in ASCII)

Symbol	Representation
Battery	---
Resistor	—▭— or —//—
Capacitor	—
Switch	—o/ o—
Ground	⏚
Wire Junction	●

14. Common Mistakes to Avoid

Confusing series vs parallel voltage/current rules
Incorrect instrument placement (ammeter in parallel = 🔥!)
Ignoring internal resistance of batteries
Forgetting unit conversions (e.g., mA → A, kΩ → Ω)

Summary Sheet

Quantity	Formula	Units
Current	$I = \frac{Q}{t}$ $I = t Q$	Amperes (A)
Voltage	$V = IR$ $V = I R$	Volts (V)
Resistance	$R = \frac{V}{I}$ $R = I V$	Ohms (Ω)
Power	$P = VI$ $P = V I$	Watts (W)
Energy	$E = Pt$ $E = Pt$	Joules (J)

2. DC and AC Supplies

Leaning Outcome:

At the end of this section you will have an understanding of;

· Dry and wet cell

· Electronic DC power supply units

· how AC is generated

· how ac is measured

· phase and phase difference

· inductance

· capacitance

2.1. DC Supplies

Introduction

In electrical engineering, power supplies are essential for providing the energy required to operate various devices and circuits. A DC (Direct Current) supply delivers a constant voltage or current in a single direction, making it ideal for powering most electronic components and systems. Unlike AC (Alternating Current), which periodically reverses direction, DC flows uniformly, offering stable and predictable performance. DC supplies are commonly used in batteries, electronic devices, automotive systems, and renewable energy technologies such as solar power.

Understanding how DC supplies work, the types available, and their characteristics is fundamental for anyone studying electricity or working with electronic systems.

1. Definition

DC Supply (Direct Current Supply) provides a constant voltage or current in one direction.

2. Types of DC Sources

Type	Description	Example
Battery	Electrochemical source	AA battery, car battery
DC Power Supply Unit	Converts AC to DC using rectifiers	Lab power supply
Solar Cell	Converts sunlight into DC electricity	Solar panels
DC Generator	Converts mechanical energy into DC	Dynamo

3. Characteristics of DC Supply

Voltage remains constant over time (ideal case).
Current flows in only one direction.
Represented as a straight line in a V vs. t graph.

4. AC vs DC Comparison

Feature	DC	AC
Flow Direction	One direction (unidirectional)	Alternating direction
Voltage Level	Constant	Varies sinusoidally
Source Examples	Battery, solar cell	Mains electricity
Transmission Losses	Higher	Lower (can use transformers)

5. Basic DC Circuit Components

Resistors: Limit current.
Capacitors: Store charge temporarily.
Inductors: Resist change in current (less common in pure DC).
Switches: Control circuit connection.
Diodes: Allow current in one direction only.

6. Applications of DC Supply

Electronic circuits (Arduino, Raspberry Pi)
Portable devices (phones, laptops)
Automotive systems (DC motors)
Solar power systems

7. Formulas (DC Circuits)

Ohm's Law:
$V = IR$
$V = I R$
(Voltage = Current × Resistance)
Power:
$P = VI = I^2R = \frac{V^2}{R}$
$P = V I = I 2 R = R V 2$
Energy:
$E = Pt$
$E = Pt$
(Energy = Power × Time)

8. Regulated vs Unregulated DC Supply

Type	Description
Unregulated	Output voltage varies with load
Regulated	Constant output voltage, regardless of load

2.2. AC Supplies

Introduction to AC Supplies

Alternating Current (AC) is the most common form of electrical power used for residential, commercial, and industrial purposes. Unlike Direct Current (DC), which flows in one direction, AC reverses direction periodically, typically in the form of a sine wave. This reversing nature makes AC more efficient for transmitting electricity over long distances, which is why it is used in national power grids.

AC supplies are generated using alternators in power stations and can be easily stepped up or down in voltage using transformers. Understanding AC characteristics, waveform properties, and its behavior in circuits is essential for grasping how electrical systems operate on a large scale.

AC Supplies – Notes

1. Definition

AC Supply (Alternating Current Supply) is a type of electrical current that changes direction periodically and varies in magnitude with time.

2. Waveform

The most common AC waveform is the sine wave.
Other types: Square wave, Triangular wave (used in some electronic systems).
In a sine wave:
$V(t) = V_{max} \sin(\omega t)$
$V (t) = V ma x sin (ω t)$

3. Characteristics of AC Supply

Parameter	Symbol	Description
Frequency	f	Number of cycles per second (Hz)
Period	T	Time taken for one complete cycle (T = 1/f)
Amplitude	$V_{max}$ Vmax	Peak voltage
RMS Value	$V_{rms}$ Vrms	Effective value = $\frac{V_{max}}{\sqrt{2}}$ 2Vmax
Phase	θ	Describes the shift between waveforms

4. Comparison: AC vs DC

Feature	AC	DC
Flow Direction	Reverses periodically	Constant in one direction
Transmission	Efficient over long distances	Less efficient
Generation	Alternator	Battery, DC generator
Voltage Change	Easy with transformer	Difficult
Common Use	Power grids, appliances	Electronics, vehicles

5. Sources of AC Supply

Alternators (in power plants)
AC generators
Inverters (convert DC to AC)
Mains electricity (e.g., 230V, 50Hz in India)

6. Applications of AC Supply

Powering homes and industries
Running electric motors and appliances
Lighting systems
HVAC systems
Transmission and distribution systems

7. Important Formulas

Instantaneous Voltage:
$V(t) = V_{max} \sin(\omega t + \phi)$
$V (t) = V ma x sin (ω t + ϕ)$
RMS Value:
$V_{rms} = \frac{V_{max}}{\sqrt{2}}$
$V r m s = 2$

$V ma x$
Power in AC Circuits:
$P = V_{rms} I_{rms} \cos(\phi)$
$P = V r m s I r m s cos (ϕ)$
(Where
$\cos(\phi)$
cos(ϕ) is the power factor)

8. Types of AC Loads

Resistive: Heaters, incandescent bulbs
Inductive: Motors, transformers
Capacitive: Capacitor banks

3. Transformers

Learning outcome

At the end of this section you will have an understanding of:

· the principle of operation of a transformer

· how the output voltage relates to the secondary

· how transformers are connected

· centre tapped transformers

3.1. Introduction to Transformers

Introduction

A transformer is a static electrical device used to transfer electrical energy between two or more circuits through electromagnetic induction. It is mainly used to increase (step-up) or decrease (step-down) AC voltages. Transformers play a critical role in electrical power distribution, allowing high-voltage transmission for efficiency and low-voltage delivery for safety.

Working Principle

Transformers operate based on Faraday’s Law of Electromagnetic Induction:

When an alternating current (AC) flows through the primary coil, it creates a changing magnetic field, which induces a voltage in the secondary coil.

Only works with AC (not DC).
No direct electrical connection between primary and secondary windings – energy is transferred via magnetic field.

Basic Structure

Primary Winding – Connected to the input AC supply.
Secondary Winding – Delivers the transformed voltage.
Core – Soft iron material that links magnetic flux between the windings.

Key Formulas

Turns Ratio:
VpVs=NpNs\frac{V_p}{V_s} = \frac{N_p}{N_s}VsVp=NsNp
Where:
- $V_p$
  Vp,
  $V_s$
  Vs: Primary and secondary voltages
- $N_p$
  Np,
  $N_s$
  Ns: Primary and secondary turns
Current Ratio:
$\frac{I_p}{I_s} = \frac{N_s}{N_p}$ $I s I p = N p N s$
Power Conservation (Ideal Transformer):
$V_p I_p = V_s I_s$ $V p I p = V s I s$

Types of Transformers

Type	Function	Example Use
Step-Up	Increases voltage	Power stations
Step-Down	Decreases voltage	Home adapters
Isolation Transformer	Voltage remains same, provides safety	Medical equipment
Auto-Transformer	Single winding acts as both primary & secondary	Voltage regulation
Instrument Transformer	For measurement & protection	CTs and PTs in substations

AC vs DC with Transformer

Feature	AC	DC
Transformer Use	✅ Yes (essential)	❌ No (doesn't work)
Reason	Changing current induces EMF	No changing flux in DC

Applications

Power transmission & distribution
Mobile phone chargers
UPS and inverters
Audio systems
Instrumentation and measurement

Core Types

Core Type	Description
Laminated Core	Reduces eddy current losses
Toroidal Core	Ring-shaped, high efficiency
Shell Type	Windings enclosed by core on both sides

Losses in Transformers

Iron Losses – Hysteresis + Eddy current loss (in the core)
Copper Losses –
$I^2R$
I2R losses in windings
Flux Leakage – Not all flux links both windings
Dielectric Loss – In insulation

Efficiency:

\text{Efficiency} = \frac{\text{Output Power}}{\text{Input Power}} \times 100\%

$Efficiency = Input Power Output Power \times 100%$

Simple Diagram Explanation

Magnetic flux links the two windings through the iron core.
Voltage depends on the turns ratio between coils.

3.2. Principle Operation of Transformers

By the End of This Section, You Will Understand:

✅ The principle of operation of a transformer
✅ How the output voltage relates to the secondary winding
✅ How transformers are connected in circuits
✅ What a centre-tapped transformer is and how it works

⚙️ 1. Principle of Operation of a Transformer

A transformer works on the principle of electromagnetic induction — specifically Faraday’s Law — which states:

A changing magnetic field in a coil of wire induces a voltage in another nearby coil.

Key points:

Only works with AC supply.
Primary winding receives AC input and generates a changing magnetic field.
This magnetic field passes through a magnetic core and cuts the secondary winding, inducing a voltage in it.
No electrical connection between the primary and secondary coils – power is transferred magnetically.

Faraday’s Law Formula:

e = -N \frac{d\phi}{dt}

$e = - N d t d ϕ$

Where:

$e$
e: Induced EMF
$N$
N: Number of turns
$\frac{d\phi}{dt}$
dtdϕ: Rate of change of magnetic flux

2. How Output Voltage Relates to the Secondary

The voltage induced in the secondary coil depends on:

The number of turns in both primary (
$N_p$
Np) and secondary (
$N_s$
Ns) windings.
The AC voltage applied to the primary coil.

Turns Ratio Formula:

\frac{V_s}{V_p} = \frac{N_s}{N_p}

$V p V s = N p N s$

Where:

$V_s$
Vs: Secondary voltage
$V_p$
Vp: Primary voltage
$N_s$
Ns: Number of turns in secondary
$N_p$
Np: Number of turns in primary

Results:

If
$N_s > N_p$
$N s > N p$ : It’s a Step-Up Transformer
If
$N_s < N_p$
$N s < N p$ : It’s a Step-Down Transformer
If
$N_s = N_p$
$N s = N p$ : Same voltage (isolation transformer)

3. How Transformers Are Connected

Transformers can be connected in different ways depending on the application:

a) Single-Phase Transformer Connection

Most basic type
Used in small electronics, domestic applications

b) Three-Phase Transformer Connections

Used in industrial and power systems:

Star-Star (Y-Y)
Delta-Delta (Δ-Δ)
Delta-Star (Δ-Y) – Common for transmission
Star-Delta (Y-Δ) – Common for motor starting

Why use different connections?

To manage phase shifts, load balancing, voltage levels, and fault handling.

4. Centre-Tapped Transformer

A centre-tapped transformer has a secondary winding with a tap in the middle, which divides the winding into two equal halves.

Structure:

The center tap (CT) is usually connected to ground or 0V reference.
Provides two equal and opposite voltages (e.g., +12V and −12V).
Common in dual power supplies for op-amps and analog circuits.

Example:

If the total secondary voltage is 24V (AC), then:

From A to CT: +12V
From B to CT: −12V
From A to B: 24V total

Summary Table

Topic	Key Points
Principle of Operation	Based on electromagnetic induction using AC
Voltage Relationship	$\frac{V_s}{V_p} = \frac{N_s}{N_p}$ $V p V s = N p N s$
Transformer Connections	Single-phase or Three-phase (Star, Delta)
Centre-Tapped Transformer	Gives dual voltages from one secondary winding

Let me know if you'd like:

A labeled diagram of a centre-tapped transformer
A worksheet or quiz for practice
A PDF version of these notes for printing or sharing

Electrical and Electronic Principles and Technology

Table of contents

1. Basic Electrical Principles

At the end of this section you will have an understanding of:

1.1. Electrical Physics

1. Electric Charge

2. Coulomb’s Law

3. Electric Field (E)

4. Electric Potential (V)

5. Potential Difference (Voltage)

6. Capacitance

7. Current (I)

8. Ohm’s Law

9. Electrical Power (P)

10. Resistors in Circuits

11. Kirchhoff’s Laws

12. DC vs AC

1.2. Electrical Power

1. What is an Electrical Circuit?

2. Basic Circuit Components

3. Electric Current (I)

4. Voltage (V) / Potential Difference

5. Resistance (R)

6. Ohm’s Law

7. Types of Circuits

➤ Series Circuit:

Formulas:

➤ Parallel Circuit:

Formulas:

8. Kirchhoff’s Laws

Kirchhoff’s Current Law (KCL):

Kirchhoff’s Voltage Law (KVL):

9. Power in Circuits

10. Measuring Instruments

11. Capacitors in Circuits

In Series:

In Parallel:

12. Time-Dependent Circuits (RC Circuits)

13. Important Circuit Symbols (in ASCII)

14. Common Mistakes to Avoid

Summary Sheet

2. DC and AC Supplies

Leaning Outcome:

2.1. DC Supplies

Introduction

1. Definition

2. Types of DC Sources

3. Characteristics of DC Supply

4. AC vs DC Comparison

5. Basic DC Circuit Components

6. Applications of DC Supply

7. Formulas (DC Circuits)

8. Regulated vs Unregulated DC Supply

2.2. AC Supplies

Introduction to AC Supplies

AC Supplies – Notes

1. Definition

2. Waveform

3. Characteristics of AC Supply

4. Comparison: AC vs DC

5. Sources of AC Supply

6. Applications of AC Supply

7. Important Formulas

8. Types of AC Loads

3. Transformers

Learning outcome

3.1. Introduction to Transformers

Introduction

Working Principle

Basic Structure

Key Formulas

Types of Transformers

AC vs DC with Transformer

Applications

Core Types

Losses in Transformers

Simple Diagram Explanation

3.2. Principle Operation of Transformers

By the End of This Section, You Will Understand:

⚙️ 1. Principle of Operation of a Transformer