JSSC (Chapter – 3) Electrical Engineering Part B

(Chapter – 3) Electrical Engineering Part B – Basic concepts, Circuit law, Magnetic circuit, AC fundamentals, Measurement and Measuring Instruments, Electrical Machines, Fractional Kilowatt Motors and single phase induction Motors, Synchronous Machines, Generation, Transmission and Distribution, Estimation and Costing, Utilization and Electrical Energy, Basic Electronics

1.1 Fundamental Quantities

Quantity	Symbol	Unit	Key Relation
Charge	Q	Coulomb (C)	Q = It
Current	I	Ampere (A)	I = Q/t
Voltage	V	Volt (V)	V = W/Q
Resistance	R	Ohm (Ω)	R = ρL/A
Conductance	G	Siemens (S)	G = 1/R
Power	P	Watt (W)	P = VI
Energy	E	Joule (J)	E = Pt
Frequency	f	Hz	f = 1/T

1.2 Electrical Laws and Definitions

Ohm’s Law: V = IR, provided physical conditions remain constant.
EMF: Energy supplied per unit charge by a source.
Potential difference: Energy transferred per unit charge between two points.
Resistance: Opposition to current flow.
Resistivity: Resistance of a material specimen of unit length and unit cross-sectional area.
Conductivity: σ = 1/ρ.
Temperature coefficient: Indicates change in resistance with temperature.

1.3 Resistors

Series: R_eq = R₁ + R₂ + …
Parallel: 1/R_eq = 1/R₁ + 1/R₂ + …
For two parallel resistors: R_eq = R₁R₂/(R₁+R₂)
Series → same current.
Parallel → same voltage.

1.4 Electrical Power

DC: P = VI = I²R = V²/R
Electrical energy = power × time.
1 kWh = 3.6 MJ.

2. CIRCUIT LAWS

2.1 Kirchhoff’s Laws

KCL: Algebraic sum of currents at a node = 0.
Current entering a node = current leaving the node.
KVL: Algebraic sum of voltages around a closed loop = 0.
Used extensively in network analysis.

2.2 Network Theorems

Theorem	Key Fact
Superposition	Response in a linear circuit = algebraic sum of responses due to individual independent sources.
Thevenin	Linear two-terminal network → V_th in series with R_th.
Norton	Linear two-terminal network → I_N in parallel with R_N.
Maximum Power Transfer	For resistive DC network, R_L = R_th.
Reciprocity	Applicable to suitable linear bilateral networks.

2.3 Star-Delta Conversion

Used to simplify networks that cannot be reduced by simple series/parallel combinations.
For balanced star resistors R: equivalent delta branch = 3R.
For balanced delta resistors R: equivalent star branch = R/3.

2.4 Capacitor

C = Q/V
Energy stored: W = ½CV²
DC steady state: ideal capacitor behaves as an open circuit.
Capacitive reactance: X_C = 1/(2πfC)
Higher frequency → lower X_C.

2.5 Inductor

Voltage: v = L(di/dt)
Energy: W = ½LI²
DC steady state: ideal inductor behaves approximately as a short circuit.
Inductive reactance: X_L = 2πfL

3. MAGNETIC CIRCUITS

3.1 Basic Quantities

Quantity	Symbol	Relation/Unit
Magnetic flux	Φ	Weber (Wb)
Flux density	B	B = Φ/A, Tesla
MMF	F	F = NI, ampere-turn
Magnetic field intensity	H	H = NI/l, A/m
Permeability	μ	μ = B/H
Reluctance	ℜ	ℜ = l/(μA)

3.2 Magnetic Circuit

Hopkinson’s Law: Φ = MMF/Reluctance = NI/ℜ.
Electrical analogy: EMF ↔ MMF; current ↔ flux; resistance ↔ reluctance.
Air gap has high reluctance compared with iron.
Magnetic leakage → actual useful flux is less than total produced flux.

3.3 Hysteresis

Hysteresis = lag of magnetic flux density B behind magnetizing force H.
Area of B-H loop ∝ hysteresis energy loss per unit volume per cycle.
Soft magnetic material: narrow hysteresis loop; low loss.
Hard magnetic material: wide loop; high coercivity; permanent magnets.

3.4 Eddy Current

Circulating currents induced in magnetic cores by changing flux.
Cause power loss and heating.
Reduced by using thin insulated laminations.

4. AC FUNDAMENTALS

4.1 Sinusoidal AC

v = V_m sin(ωt + φ)
ω = 2πf
RMS value of sine wave: V_rms = V_m/√2
Average value over a half cycle: V_avg = 2V_m/π
Form factor of sine wave ≈ 1.11.
Crest factor of sine wave = √2 ≈ 1.414.

4.2 Phase Relations

Element	Relation
Pure Resistance	V and I in phase
Pure Inductance	Current lags voltage by 90°
Pure Capacitance	Current leads voltage by 90°

4.3 AC Impedance

Series R-L: Z = √(R² + X_L²)
Series R-C: Z = √(R² + X_C²)
Series R-L-C: Z = √[R² + (X_L − X_C)²]
Power factor: cosφ = R/Z for a series R-L-C circuit.

4.4 AC Power

Active power: P = VI cosφ → W
Reactive power: Q = VI sinφ → VAR
Apparent power: S = VI → VA
S² = P² + Q²
Power factor = kW/kVA.
Inductive loads → lagging PF.
Capacitive loads → leading PF.

4.5 Resonance

Series resonance occurs when X_L = X_C.
Resonant frequency: f_r = 1/(2π√LC)
At series resonance: impedance minimum and current maximum.
At ideal parallel resonance: input impedance maximum and source current minimum.

4.6 Three-Phase AC

Three voltages have equal magnitude and are separated by 120° electrical.
Star connection: V_L = √3 V_ph, I_L = I_ph.
Delta connection: V_L = V_ph, I_L = √3 I_ph.
Three-phase power: P = √3 V_LI_Lcosφ.
Balanced three-phase systems can transmit power efficiently using three conductors.

5. MEASUREMENT & MEASURING INSTRUMENTS

5.1 Basic Terms

Accuracy: Closeness to true value.
Precision: Closeness among repeated measurements.
Sensitivity: Output change per unit input change.
Resolution: Smallest distinguishable change.
Calibration: Comparison/adjustment against a known standard.
Error: Difference between measured and true/reference value.

5.2 Analog Instruments

Instrument	Principle/Use
PMMC	Permanent magnet; mainly DC
Moving Iron	Attraction/repulsion; AC and DC
Electrodynamometer	Current interaction; AC/DC; wattmeter use
Induction type	Electromagnetic induction; AC only
Electrostatic	Electrostatic force; high voltage measurement

5.3 Ammeter and Voltmeter

Ammeter is connected in series.
Ideal ammeter resistance → zero.
Voltmeter is connected in parallel.
Ideal voltmeter resistance → infinite.
Shunt is used to extend ammeter range.
Series multiplier is used to extend voltmeter range.

5.4 Power and Energy Measurement

Wattmeter: Measures electrical power.
Energy meter: Measures electrical energy, commonly in kWh.
Single-phase power can be measured using a wattmeter.
Two-wattmeter method is widely used for balanced/unbalanced three-phase three-wire systems.

5.5 Instrument Transformers

CT: Current Transformer → measures/isolates high current.
PT/VT: Potential/Voltage Transformer → measures/isolates high voltage.
Important: CT secondary should not be left open-circuited while primary is energized.

5.6 Bridges

Wheatstone bridge: Medium resistance measurement.
Kelvin double bridge: Low resistance measurement.
Maxwell bridge: Inductance measurement.
Schering bridge: Capacitance and dielectric loss measurement.
Wien bridge: Frequency measurement.

6. ELECTRICAL MACHINES

6.1 Transformer

Static AC device transferring electrical energy between circuits through electromagnetic induction.
Operates on mutual induction.
Ideal transformer: V₁/V₂ = N₁/N₂ = I₂/I₁
Step-up transformer → increases voltage.
Step-down transformer → decreases voltage.
Transformer does not operate normally on steady DC.

6.2 Transformer Losses

Loss	Cause
Copper loss	I²R in windings
Hysteresis loss	Repeated magnetization of core
Eddy-current loss	Induced currents in core
Stray loss	Leakage-flux induced losses

Transformer efficiency = Output/Input × 100.
Maximum efficiency occurs approximately when copper loss = iron/core loss.
Open-circuit test: Mainly determines core loss and shunt parameters.
Short-circuit test: Determines equivalent series impedance and copper loss at rated current.

6.3 DC Generator

Converts mechanical energy → electrical energy.
Principle: electromagnetic induction.
Generated EMF: E_g = PΦZN/(60A)
Commutator converts internally generated alternating emf into unidirectional output.

6.4 DC Motor

Converts electrical energy → mechanical energy.
Back EMF opposes applied voltage.
Motor equation: V = E_b + I_aR_a (neglecting brush drop).
Torque is approximately proportional to ΦI_a.
DC series motor has high starting torque.
DC series motor should not be operated at no load because speed can rise dangerously.

6.5 Induction Motor

Works on electromagnetic induction.
Rotor current is induced; external rotor electrical supply is not normally required for a squirrel-cage motor.
Synchronous speed: N_s = 120f/P
Slip: s = (N_s − N)/N_s
Rotor frequency: f_r = sf
Rotor speed is always less than synchronous speed in motoring operation.

6.6 Induction Motor Types

Motor	Feature
Squirrel Cage	Simple, rugged, low maintenance
Slip Ring/Wound Rotor	External rotor resistance possible; improved starting control
Three Phase IM	Self-starting
Single Phase IM	Not inherently self-starting

7. FRACTIONAL KILOWATT & SINGLE-PHASE INDUCTION MOTORS

7.1 Fractional kW Motors

Used where power requirement is small.
Applications: fans, blowers, pumps, refrigerators, washing machines, small machines and domestic appliances.

7.2 Single-Phase Induction Motor

Single-phase induction motor produces a pulsating magnetic field.
According to double-revolving-field theory, the pulsating field can be resolved into two oppositely rotating fields.
At standstill, starting torque is ideally zero for a basic single-phase induction motor.

7.3 Types

Motor	Key Feature/Application
Split Phase	Auxiliary starting winding; moderate starting torque
Capacitor Start	High starting torque
Capacitor Run	Good running PF and efficiency
Capacitor Start-Capacitor Run	High starting torque + good running performance
Shaded Pole	Very simple; low starting torque
Universal Motor	Operates on AC or DC; high speed

7.4 Universal Motor

Series-connected field and armature.
Can operate on AC as well as DC.
High starting torque and high speed.
Used in portable tools, mixers, vacuum cleaners, etc.

8. SYNCHRONOUS MACHINES

8.1 Synchronous Generator

Also called alternator.
Converts mechanical energy → three-phase AC electrical energy.
Rotor rotates at synchronous speed.
N_s = 120f/P
Frequency: f = PN/120

8.2 Alternator Construction

Salient-pole rotor: Low/medium-speed machines; large diameter and short axial length.
Cylindrical rotor: High-speed turbo-alternators; small diameter and long axial length.
In large alternators, armature winding is generally placed on the stator.

8.3 Synchronous Motor

Runs at synchronous speed under steady operation.
Speed is essentially independent of load until synchronism is lost.
Not inherently self-starting.
Can operate at lagging, unity or leading power factor by changing field excitation.
Over-excited synchronous motor → leading power factor.
Used for power-factor improvement as a synchronous condenser.

8.4 Power Factor

Low PF → higher current for the same real power.
Higher current → higher I²R loss and voltage drop.
PF improvement methods: capacitor banks, synchronous condensers and suitable power-electronic compensators.

9. GENERATION, TRANSMISSION & DISTRIBUTION

9.1 Power Generation

Plant	Prime Mover/Source
Thermal	Steam turbine
Hydroelectric	Hydraulic turbine
Nuclear	Steam turbine using nuclear heat source
Diesel	IC engine
Gas Turbine	Gas turbine
Solar PV	Photovoltaic conversion
Wind	Wind turbine

9.2 Transmission

Electrical power is transmitted at high voltage to reduce current for a given power.
For fixed transmitted power, lower current reduces I²R losses.
Transmission system includes conductors, insulators, towers/poles, transformers and protection equipment.
Common overhead conductors: AAC, AAAC, ACSR.

9.3 Transmission Line Parameters

Resistance: Causes I²R loss.
Inductance: Causes reactive voltage drop.
Capacitance: Important especially for long/high-voltage lines.
Corona may occur around high-voltage conductors when electric field exceeds the critical level.

9.4 Distribution

Feeder: Carries power from substation toward distribution areas; normally designed mainly for current capacity.
Distributor: Has multiple consumer tapping points; voltage drop is an important design consideration.
Service mains: Connect distributor to consumer premises.
Distribution systems may be radial, ring-main or interconnected.

9.5 Substation

Main functions: voltage transformation, switching, protection, isolation, control and metering.
Main equipment: transformer, circuit breaker, isolator, CT, PT/VT, busbar, relay, lightning arrester and earthing system.

9.6 Protection

Fuse: Melts under excessive current.
Circuit breaker: Opens circuit under fault/abnormal conditions and can be reset/operated according to type.
Relay: Detects abnormal electrical conditions and initiates breaker operation.
Earthing: Provides a low-impedance path for fault current and helps maintain safe touch voltages.

10. ELECTRICAL ESTIMATION & COSTING

10.1 Basic Concepts

Estimation: Determining quantities and approximate cost of electrical work.
Costing: Determining monetary cost of materials, labour, overheads and other expenses.
BOQ: Bill of Quantities lists items, quantities and units.
Schedule of Rates: Standard rates used for estimating works.

10.2 Electrical Wiring Systems

System	Feature
Cleat Wiring	Temporary/simple installations
Casing-Capping	Conductors enclosed in casing and covered
Batten Wiring	Cables fixed on wooden/PVC battens
Conduit Wiring	Conductors protected inside conduits

10.3 Estimation Steps

Study drawing/specification.
Prepare circuit/wiring layout.
Determine connected load.
Calculate maximum demand where required.
Select conductor size and protective devices.
Calculate quantities of cables, conduits, switches, sockets, DBs, fittings, etc.
Apply rates → material cost + labour + other applicable costs.

10.4 Important Terms

Connected load: Sum of rated loads of connected equipment.
Maximum demand: Highest demand occurring during a specified period.
Demand factor = Maximum demand / Connected load
Load factor = Average load / Maximum demand
Diversity factor = Sum of individual maximum demands / Maximum demand of the combined system
Diversity factor is generally greater than or equal to 1.

11. UTILIZATION OF ELECTRICAL ENERGY

11.1 Electric Heating

Electrical heating converts electrical energy into heat.
Joule heating: H = I²Rt.
Applications: electric furnace, oven, heater, welding, water heating.
Heating methods: resistance, induction, dielectric and arc heating.

11.2 Electric Welding

Uses electrical energy to generate heat for joining metals.
Important methods: resistance welding and arc welding.
Resistance welding heat: H = I²Rt.

11.3 Electric Lighting

Quantity	Meaning/Unit
Luminous flux	Light output; lumen (lm)
Luminous intensity	cd
Illuminance	Light falling on surface; lux (lm/m²)
Luminance	Brightness-related photometric quantity; cd/m²

11.4 Lighting Laws

Inverse square law: E ∝ 1/r² for a point source when incidence is normal.
Lambert’s cosine law: E ∝ cosθ/r² for an inclined surface.

11.5 Electric Drives

Electric drive = motor + power converter/controller + control system + mechanical load.
Advantages: easy control, clean operation, high efficiency and automation.
Speed control methods depend on motor type.

11.6 Electric Traction

Electric traction uses electric motors for transportation.
Important requirements: high starting torque, acceleration, regenerative braking where applicable and reliable control.
Regenerative braking returns part of kinetic energy to the electrical system.

12. BASIC ELECTRONICS

12.1 Semiconductor

Conductivity lies between conductor and insulator.
Common semiconductor materials: Silicon and Germanium.
Intrinsic: Pure semiconductor.
Extrinsic: Doped semiconductor.
N-type: Electrons are majority carriers.
P-type: Holes are majority carriers.

12.2 PN Junction Diode

Allows current mainly in one direction.
Forward bias → reduces depletion barrier and allows substantial conduction.
Reverse bias → very small reverse current until breakdown.
Applications: rectification, switching, clipping, clamping and protection.

12.3 Rectifiers

Rectifier	Key Point
Half Wave	Uses one half-cycle
Full Wave Centre-Tapped	Uses both half-cycles; centre-tapped transformer
Bridge	Four diodes; no centre-tapped transformer required

12.4 Zener Diode

Designed to operate in reverse breakdown region.
Used mainly for voltage regulation/reference.

12.5 Transistor

BJT terminals: Emitter, Base, Collector.
Types: NPN and PNP.
Used for amplification and switching.
In active region, a BJT can provide amplification.
Common configurations: CB, CE, CC.
CE configuration is widely used for voltage amplification.

12.6 FET

Field Effect Transistor is a voltage-controlled device.
High input impedance is a major feature.
Types include JFET and MOSFET.
MOSFET is widely used in switching and digital circuits.

12.7 Operational Amplifier

Ideal op-amp: very high open-loop gain, very high input impedance and very low output impedance.
Inverting amplifier: A_v = −R_f/R_in
Non-inverting amplifier: A_v = 1 + R_f/R₁
Applications: amplification, addition, subtraction, integration, differentiation, filtering and comparison.

12.8 Digital Electronics

Gate	Function
AND	Output 1 only when all inputs are 1
OR	Output 1 when any input is 1
NOT	Inverts input
NAND	NOT + AND
NOR	NOT + OR
XOR	Output 1 when inputs are different
XNOR	Output 1 when inputs are same

12.9 Number Systems

Binary → base 2.
Octal → base 8.
Decimal → base 10.
Hexadecimal → base 16.
1 hexadecimal digit represents 4 binary bits.
1 octal digit represents 3 binary bits.

12.10 Power Electronics – Basic Devices

Device	Key Feature
SCR	Thyristor; controlled turn-on
TRIAC	Bidirectional AC power control
DIAC	Bidirectional trigger device
MOSFET	Fast switching; voltage-controlled
IGBT	High-power switching; MOS gate + bipolar conduction characteristics

IMPORTANT FORMULA SHEET

Topic	Formula
Ohm’s law	V = IR
Resistance	R = ρL/A
DC power	P = VI = I²R = V²/R
Energy	E = Pt
Capacitive reactance	X_C = 1/(2πfC)
Inductive reactance	X_L = 2πfL
AC impedance	Z = √[R² + (X_L−X_C)²]
AC active power	P = VI cosφ
3-phase power	P = √3 V_LI_Lcosφ
Resonance	f_r = 1/(2π√LC)
Magnetic flux	Φ = NI/ℜ
Transformer ratio	V₁/V₂ = N₁/N₂
DC generator EMF	E_g = PΦZN/(60A)
Synchronous speed	N_s = 120f/P
Induction motor slip	s = (N_s−N)/N_s
Rotor frequency	f_r = sf
Demand factor	Maximum demand/Connected load
Load factor	Average load/Maximum demand
Joule heating	H = I²Rt
Op-amp inverting gain	A_v = −R_f/R_in

1-MINUTE REVISION

Basic: V = IR → P = VI → E = Pt.
Circuit: KCL at node + KVL around loop + network theorems.
Magnetic: Φ = NI/ℜ; hysteresis + eddy-current losses.
AC: X_L = 2πfL; X_C = 1/(2πfC); P = VIcosφ.
3-phase: P = √3V_LI_Lcosφ.
Measurement: PMMC → DC; MI → AC/DC; wattmeter → power; CT/PT → high current/voltage measurement.
Transformer: Mutual induction; no normal DC operation; maximum efficiency near copper loss = core loss.
DC machine: Generator → mechanical to electrical; Motor → electrical to mechanical.
Induction motor: N_s = 120f/P; slip is necessary for torque.
Single-phase motor: Not inherently self-starting; auxiliary starting method required.
Synchronous machine: Runs at synchronous speed; alternator generates AC.
Transmission: High voltage → lower current for same power → lower I²R loss.
Distribution: Feeder → Distributor → Service mains.
Utilization: Heating, lighting, drives and traction.
Electronics: Diode → rectification; Zener → regulation; BJT/FET → amplification/switching; SCR/IGBT → power control.