K Mean Black

• Name: B.Tech 1st Year
• Branch: B.Tech Printing Technology 1st Sem
• Published: Dec. 18, 2025

Basic Electrical Engineering

UNIT–I: DC Circuits

1. Electrical Circuit Elements

(a) Resistor (R)

• Opposes current flow
• Obeys Ohm’s Law:

V=IR

• Unit: ohm (Ω)

(b) Inductor (L)

• Opposes change in current
• Voltage across inductor:

V=Ldidt

• Unit: henry (H)

(c) Capacitor (C)

• Stores electrical energy
• Voltage across capacitor:

i=CdVdt

• Unit: farad (F)

2. Voltage and Current Sources

Voltage Source

• Maintains constant voltage
• Ideal: zero internal resistance

Current Source

• Maintains constant current
• Ideal: infinite internal resistance

3. Kirchhoff’s Laws

(a) Kirchhoff’s Current Law (KCL)

At any junction, sum of currents entering equals sum leaving:

∑I=0

(b) Kirchhoff’s Voltage Law (KVL)

In any closed loop, algebraic sum of voltages is zero:

∑V=0

4. Mesh Analysis (Loop Current Method)

• Applicable to planar circuits
• Assign a loop current to each mesh
• Apply KVL to each loop
• Solve simultaneous equations

5. Nodal Analysis

• Based on KCL
• Choose a reference (ground) node
• Write equations for remaining node voltages
• Preferred when current sources are present

6. Superposition Theorem

Statement

In a linear circuit with multiple sources, the response is the sum of responses due to each source acting alone.

Procedure

1. Consider one source at a time
2. Replace:
   • Voltage source → short circuit
   • Current source → open circuit
3. Add individual responses

7. Thevenin’s Theorem

Statement

Any linear two-terminal network can be replaced by:

• A single voltage source Vth
• A series resistance Rth

Steps

1. Remove load
2. Find open-circuit voltage → Vth
3. Deactivate sources and find resistance → Rth

8. Norton’s Theorem

Statement

Any two-terminal network can be replaced by:

• A current source IN
• A parallel resistance RN

Relation

RN=Rth,IN=VthRth

9. Maximum Power Transfer Theorem

Statement

Maximum power is delivered to the load when:

RL=Rth

Maximum Power

Pmax=Vth24Rth

10. Star–Delta (Y–Δ) Conversion

Star to Delta

RAB=RARB+RBRC+RCRARC

(similar expressions for other sides)

Delta to Star

RA=RABRCARAB+RBC+RCA

Used to simplify complex resistor networks.

11. Time-Domain Analysis of First-Order Circuits

(a) RL Circuit

Time Constant

τ=LR

Current Growth

i(t)=I(1-e-t/τ)

Current Decay

i(t)=Ie-t/τ

(b) RC Circuit

Time Constant

τ=RC

Capacitor Charging

V(t)=V(1-e-t/RC)

Capacitor Discharging

V(t)=Ve-t/RC

12. Applications of DC Circuit Analysis

• Power supplies
• Signal conditioning circuits
• Battery-operated systems
• Transient analysis

13. Summary Table

Concept	Key Formula
Ohm’s Law	V=IR
KCL	∑I=0
KVL	∑V=0
Time constant (RL)	L/R
Time constant (RC)	RC
Max power condition	RL=Rth

 

 

UNIT–II: AC Circuits

1. Sinusoidal Waveforms

An alternating quantity varies periodically with time and changes direction.

General Equation

v(t)=Vmsin⁡(ωt+ϕ)

where

• Vm= peak (maximum) value
• ω=2πf= angular frequency
• ϕ= phase angle

2. Peak, Average and RMS Values

Peak Value

• Maximum value of voltage or current
• Vm,Im

Average Value

• For a sinusoidal wave over one half cycle:

Vavg=2Vmπ

RMS Value

Equivalent DC value producing same heating effect.

Vrms=Vm2,Irms=Im2

3. Phasor Representation

A phasor is a rotating vector representing a sinusoidal quantity.

Advantages

• Simplifies AC analysis
• Converts differential equations into algebraic equations

4. Power in AC Circuits

(a) Real (True) Power

P=VrmsIrmscos⁡ϕ(Watts)

(b) Reactive Power

Q=VrmsIrmssin⁡ϕ(VAR)

(c) Apparent Power

S=VrmsIrms(VA)

Power Triangle

S2=P2+Q2

5. Power Factor

Definition

Power Factor=cos⁡ϕ

Significance

• Indicates efficiency of power usage
• Low power factor → higher losses

6. AC Circuits with Basic Elements

(a) Pure Resistive Circuit

• Voltage and current in phase

Z=R,I=VR

(b) Pure Inductive Circuit

• Current lags voltage by 90°

XL=ωL,Z=XL

(c) Pure Capacitive Circuit

• Current leads voltage by 90°

XC=1ωC,Z=XC

7. RL, RC and RLC Series Circuits

(a) RL Series Circuit

Z=R2+XL2

Phase angle:

ϕ=tan⁡-1(XLR)

(b) RC Series Circuit

Z=R2+XC2

Phase angle:

ϕ=tan⁡-1(-XCR)

(c) RLC Series Circuit

Z=R2+(XL-XC)2

8. Parallel AC Circuits

• Current divides among branches
• Total current is phasor sum of branch currents

Admittance

Y=1Z

9. Resonance in AC Circuits

(a) Series Resonance

Occurs when:

XL=XC

Resonant Frequency

fr=12πLC

Characteristics

• Impedance minimum
• Current maximum
• Power factor = 1

(b) Parallel Resonance

Characteristics

• Impedance maximum
• Line current minimum
• Acts as rejector circuit

10. Quality Factor (Q)

Series RLC

Q=ωrLR

Indicates sharpness of resonance.

11. Bandwidth

Bandwidth=f2-f1=frQ

12. Applications of AC Circuits

• Power systems
• Radio and TV receivers
• Filters and tuning circuits

13. Summary Table

Circuit	Phase Relation
R	V and I in phase
L	I lags V
C	I leads V
RL	Lagging
RC	Leading
RLC	Depends on XL & XC

 

14. Three-Phase System

A three-phase system consists of three sinusoidal voltages or currents:

• Equal magnitude
• Same frequency
• Phase difference of 120° electrical between each phase

Advantages

• Higher efficiency
• Constant power output
• Less conductor material
• Smooth motor operation

15. Balanced Three-Phase Circuits

Definition

A three-phase circuit is balanced when:

• All phase impedances are equal
• Phase voltages and currents are equal in magnitude
• Phase angle difference is 120°

Result

• Line currents are equal
• Neutral current is zero (in star connection)

16. Star (Y) Connection

Configuration

• One end of each phase is connected to a common point (neutral)
• Other ends connected to line conductors

Voltage Relations (Star)

VL=3 Vph

where

• VL= line voltage
• Vph= phase voltage

Current Relations (Star)

IL=Iph

Power in Star Connection

P=3 VLILcos⁡ϕ

17. Delta (Δ) Connection

Configuration

• End of one phase connected to start of next
• Forms a closed loop

Voltage Relations (Delta)

VL=Vph

Current Relations (Delta)

IL=3 Iph

Power in Delta Connection

P=3 VLILcos⁡ϕ

18. Comparison of Star and Delta Connections

Quantity	Star (Y)	Delta (Δ)
Line Voltage	3Vph	Vph
Line Current	Iph	3Iph
Neutral Wire	Required	Not required
Application	High voltage	High current

19. Measurement of Three-Phase Power

Two Wattmeter Method

Purpose

• Measure total power
• Measure power factor
• Applicable to balanced and unbalanced loads

Connection

• Two wattmeters connected in two lines
• Pressure coils connected to the third line

Total Power

P=W1+W2

20. Power Factor Measurement Using Two Wattmeters

Let:

• W1and W2be wattmeter readings

Power Factor Formula

tan⁡ϕ=3(W1-W2)W1+W2
cos⁡ϕ=Power Factor

21. Special Cases in Two Wattmeter Method

Power Factor	Wattmeter Readings
Unity (cos⁡ϕ=1)	W1=W2
0.5	One wattmeter reads zero
< 0.5	One wattmeter reads negative
Zero	W1=-W2

22. Advantages of Two Wattmeter Method

• Simple and economical
• No neutral required
• Measures power in both star and delta systems

23. Applications

• Power plants
• Industrial loads
• Three-phase motors
• Electrical substations

24. Key Formula Summary

Quantity	Formula
Three-phase power	P=3VLILcos⁡ϕ
Star voltage relation	VL=3Vph
Delta current relation	IL=3Iph
Power factor (2-W method)	tan⁡ϕ=3(W1-W2)W1+W2

 

 

UNIT–III: Electrical Machines – Transformers

1. Transformer: Definition and Principle

Definition

A transformer is a static electrical device that transfers AC electrical power from one circuit to another at the same frequency but usually at different voltage levels, by mutual induction.

Working Principle

A transformer works on Faraday’s law of electromagnetic induction.

E=-Ndϕdt

2. Construction of Transformer

Main Parts

(a) Magnetic Core

• Made of laminated silicon steel
• Reduces eddy current losses
• Provides low reluctance path for flux

(b) Windings

• Primary winding: connected to AC supply
• Secondary winding: connected to load
• Made of copper/aluminium

Types of Construction

1. Core type
2. Shell type

3. Working of Transformer

1. AC supply applied to primary
2. Alternating current produces alternating magnetic flux
3. Flux links both windings
4. EMF induced in secondary
5. Power transferred magnetically

4. EMF Equation of Transformer

E=4.44fNϕm

where

• f= frequency
• N= number of turns
• ϕm= maximum flux

5. Ideal Transformer

Assumptions

• No copper losses
• No core losses
• No leakage flux
• Infinite permeability

Voltage Ratio

V1V2=N1N2

Current Ratio

I1I2=N2N1

Efficiency

η=100%

6. Practical Transformer

Differences from Ideal

• Copper losses present
• Core losses present
• Leakage flux exists
• Finite permeability

7. Phasor Diagram of Transformer

No-Load Condition

• Primary current lags voltage by ~90°
• Flux in phase with magnetizing current

On-Load Condition

• Secondary current produces opposing flux
• Primary draws additional current to maintain flux

8. Equivalent Circuit of Transformer

Components

• R1,R2: winding resistances
• X1,X2: leakage reactances
• Rc: core loss resistance
• Xm: magnetizing reactance

Equivalent circuit simplifies performance analysis.

9. Losses in Transformer

(a) Core (Iron) Losses

• Hysteresis loss
• Eddy current loss
• Constant at rated voltage

(b) Copper Losses

Pcu=I2R

• Vary with load

10. Voltage Regulation

Definition

Change in secondary voltage from no-load to full-load.

%Regulation=VNL-VFLVFL×100

Significance

• Indicates ability to maintain constant voltage

11. Efficiency of Transformer

Definition

η=Output PowerInput Power×100

Condition for Maximum Efficiency

Copper loss=Core loss

12. Auto-Transformer

Definition

A transformer with single winding, part of which acts as both primary and secondary.

Advantages

• Higher efficiency
• Smaller size
• Less copper used

Disadvantages

• No electrical isolation
• Safety issues

Applications

• Voltage regulators
• Induction motor starters
• Power transmission

13. Comparison: Two-Winding Transformer vs Auto-Transformer

Feature	Two-Winding	Auto-Transformer
Windings	Two	One
Isolation	Yes	No
Efficiency	Lower	Higher
Cost	Higher	Lower

14. Summary Table

Concept	Key Formula
EMF equation	E=4.44fNϕm
Voltage ratio	V1/V2=N1/N2
Regulation	(VNL-VFL)/VFL
Max efficiency	Copper loss = Core loss

 

15. Generation of Rotating Magnetic Field (RMF)

Principle

When a three-phase AC supply is applied to a three-phase stator winding placed 120° apart, the currents produce a magnetic field that rotates in space.

Key Points

• Magnitude of magnetic field remains constant
• Speed of rotation is called synchronous speed

Ns=120fP

where

• f= supply frequency
• P= number of poles

16. Three-Phase Induction Motor

Definition

An induction motor is an AC motor in which current is induced in the rotor by the rotating magnetic field of the stator.

17. Construction of Three-Phase Induction Motor

Main Parts

(a) Stator

• Laminated silicon steel core
• Three-phase distributed winding
• Produces rotating magnetic field

(b) Rotor

Two types:

1. Squirrel cage rotor
   • Aluminium or copper bars
   • Short-circuited by end rings
2. Slip ring (wound rotor)
   • External resistance through slip rings

18. Working Principle of Induction Motor

1. Three-phase supply → rotating magnetic field
2. RMF cuts rotor conductors → induced EMF
3. Rotor current flows → Lorentz force
4. Rotor starts rotating in same direction as RMF

Slip

s=Ns-NrNs

where Nr= rotor speed

19. Advantages of Three-Phase Induction Motor

• Simple and rugged construction
• Low maintenance
• High efficiency
• Good speed regulation

20. Applications of Three-Phase Induction Motor

• Pumps and compressors
• Conveyors
• Lifts and cranes
• Machine tools
• Fans and blowers

21. DC Machine

A DC machine can work as:

• DC generator
• DC motor

22. Construction of DC Machine

Main Parts

(a) Field System

• Poles and field windings
• Produces magnetic field

(b) Armature

• Laminated core with conductors
• Rotates in magnetic field

(c) Commutator

• Converts AC in armature to DC at terminals

(d) Brushes

• Carbon brushes
• Collect current from commutator

23. Working Principle of DC Machine

Generator Action

Based on Faraday’s law of electromagnetic induction.

Motor Action

Based on Lorentz force law:

F=BIl

Current-carrying conductor in magnetic field experiences force.

24. Speed Equation of DC Motor

N∝V-IaRaϕ

where

• V= supply voltage
• Ia= armature current
• Ra= armature resistance
• ϕ= flux per pole

25. Speed Control of DC Motor

(a) Flux Control Method

• Vary field current
• Speed inversely proportional to flux
• Used above rated speed

(b) Armature Voltage Control

• Vary armature voltage
• Most efficient method
• Used below rated speed

(c) Armature Resistance Control

• Add external resistance in armature
• Simple but inefficient (power loss)

26. Applications of DC Motors

Type	Application
Shunt motor	Lathes, fans
Series motor	Cranes, traction
Compound motor	Elevators

27. Comparison: Induction Motor vs DC Motor

Feature	Induction Motor	DC Motor
Supply	AC	DC
Maintenance	Low	High
Speed control	Difficult	Easy
Cost	Low	Higher

28. Summary Table

Topic	Key Formula
Synchronous speed	Ns=120f/P
Slip	(Ns-Nr)/Ns
DC motor speed	N∝(V-IaRa)/ϕ

 

 

UNIT–IV: Electrical Instruments and LT Installations

1. Electrical Instruments

Electrical instruments are used to measure electrical quantities such as voltage, current, and power.

1.1 Permanent Magnet Moving Coil (PMMC) Instruments

Principle

• Operates on Lorentz force law: A current-carrying conductor in a magnetic field experiences a torque.
• Torque proportional to current.

Construction

• Moving coil suspended between permanent magnets
• Pointer attached to coil
• Spring provides control torque

Characteristics

• Measures DC current and voltage only
• High accuracy
• Linear scale

Applications

• DC ammeters
• DC voltmeters
• Multimeters

1.2 Electrodynamometer Instruments

Principle

• Torque produced due to interaction between two coils carrying current.

T∝I1×I2

Construction

• Fixed coil (stator)
• Moving coil (rotor)
• Pointer attached to moving coil

Characteristics

• Can measure AC and DC
• Measures current, voltage, and power
• Scale approximately linear

Applications

• AC & DC ammeters and voltmeters
• Wattmeters (static type)

1.3 Moving Iron Instruments

Principle

• Iron piece moves in a magnetic field produced by current-carrying coil.
• Deflection proportional to square of current.

Construction

• Fixed coil or coils
• Soft iron vane or cylinder moves
• Spring provides control torque

Characteristics

• Can measure AC and DC
• Non-linear scale
• Rugged construction

Applications

• AC & DC ammeters and voltmeters
• Low-cost instruments for industrial use

1.4 Induction Type Energy Meter

Principle

• Uses electromagnetic induction
• Deflection of aluminum disc proportional to power consumed

Energy=V⋅I⋅cos⁡ϕ⋅t

Construction

• Fixed coils: Voltage coil (series) and Current coil (shunt)
• Aluminium disc rotates between magnetic fields
• Braking magnet provides damping

Characteristics

• Measures AC energy (kWh)
• Works only for AC supply
• Induction type ensures accuracy

Applications

• Domestic energy meters
• Industrial energy measurement

2. Low Tension (LT) Installations

• Supply voltage ≤ 1 kV
• Used for domestic, commercial, and small industrial loads

Components

1. Service mains – Supply from utility
2. Distribution board – Fuses, MCBs, meters
3. Wiring system – Copper/aluminium wires
4. Outlets – Sockets and switches
5. Protective devices – Fuses, MCBs, ELCB

Types of Wiring

• Concealed wiring – Pipes/casings hidden in walls
• Surface wiring – Wires fixed on wall surface

3. Summary Table of Instruments

Instrument	Principle	AC/DC	Applications
PMMC	Lorentz force	DC	DC ammeter/voltmeter
Electrodynamometer	Torque between coils	AC/DC	Ammeters, voltmeters, wattmeters
Moving Iron	Iron movement in magnetic field	AC/DC	Industrial meters
Induction Energy Meter	Electromagnetic induction	AC	kWh measurement

 

 

4. Components of LT Switchgear

Low Tension (LT) switchgear is used for protection, control, and isolation of low voltage electrical circuits (≤1 kV).

4.1 Switch Fuse Unit (SFU)

• Combination of switch and fuse in a single unit
• Function:
  • Switch → ON/OFF control
  • Fuse → Overcurrent protection
• Applications: Domestic and small industrial circuits

4.2 Miniature Circuit Breaker (MCB)

• Automatically switches OFF circuit during overload or short-circuit
• Advantages:
  • Can be reset
  • Quick operation
• Rated for: 6–100 A, 230/400 V

4.3 Earth Leakage Circuit Breaker (ELCB)

• Detects leakage current to earth
• Protects human life from electric shock
• Rated in milliamperes (mA)

4.4 Moulded Case Circuit Breaker (MCCB)

• Provides overload and short-circuit protection
• Higher capacity than MCB (up to 1000 A)
• Can be manually or automatically operated

5. Types of Wires and Cables

5.1 Types of Wires

• PVC insulated – Residential use, 1.1 kV rating
• Flexible copper wire – Appliances

5.2 Types of Cables

• Single-core – For high voltage lines
• Multi-core – Domestic and industrial circuits
• Armoured cable – Mechanical protection

6. Earthing

Purpose

• Protects human life and equipment
• Provides low resistance path for fault currents

Types of Earthing

1. Plate earthing – Copper/galvanized iron plate in soil
2. Pipe earthing – Copper pipe buried in moist soil
3. Rod earthing – Copper/steel rod in soil

Earth Resistance

Re≤1 Ω (for safety)

7. Energy Consumption Calculation

Energy consumed in electrical devices:

E=P⋅t

where

• E= energy (kWh)
• P= power (kW)
• t= time (hours)

Example

• 1 kW heater for 5 hours → E=1×5=5 kWh

8. Power Factor Improvement

• Power factor (pf) = cosϕ
• Low pf → higher losses and voltage drop
• Improve by connecting capacitors in parallel

Capacitance Required

Qc=P(tan⁡ϕ1-tan⁡ϕ2)

where

• Qc= reactive power of capacitor
• ϕ1= initial phase angle
• ϕ2= desired phase angle

9. Summary Table

Component	Function	Notes
SFU	ON/OFF + fuse protection	Domestic
MCB	Overload/short-circuit protection	Resettable
ELCB	Earth leakage protection	Human safety
MCCB	High capacity protection	Industrial
PVC Wire	Domestic wiring	Low cost
Armoured Cable	Mechanical protection	Outdoor use
Earthing	Safety	Earth resistance < 1 Ω