Books/Theraja/Ch-34/Ch-34_Index.md
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| title | Chapter 34: Induction Motor — Master Navigation & Comprehensive Study Guide |
|---|---|
| author | B.L. Theraja & A.K. Theraja |
| book | A Textbook of Electrical Technology — Volume II (AC & DC Machines) |
| chapter | 34 |
| total_pages | 70 |
| source_file | Ch-34.pdf |
| subject | ECE 2207: Electrical Machines |
Chapter 34: Induction Motor
Master Navigation & Comprehensive Study Guide
Textbook: A Textbook of Electrical Technology (Vol. II — AC & DC Machines) by B.L. Theraja & A.K. Theraja
Chapter Scope: Pages 1243–1312 (70 PDF pages, complete 100% word-for-word digitization with vector-extracted diagrams)
📚 Vault Module Structure
To ensure lightning-fast rendering, seamless Obsidian mobile & desktop navigation, and focused topic study, this 70-page chapter has been organized into four modular study units:
Ch-34/
├── Ch-34_Index.md <-- Master Curriculum & Navigation Hub (You are here)
├── Ch-34_01_Construction_and_RMF.md <-- Part 1: Construction & Rotating Magnetic Field
├── Ch-34_02_Torque_and_Characteristics.md <-- Part 2: Torque Equations & Motor Characteristics
├── Ch-34_03_Power_Stages_and_Torque.md <-- Part 3: Power Stages & Torque Relations
└── Ch-34_04_Linear_Motors_and_Equivalent_Circuit.md <-- Part 4: Linear Motors & Equivalent Circuit
📑 Detailed Table of Contents
Part 1: Construction & Rotating Magnetic Field
- Pages: 1243–1256 (PDF pp. 1–14)
- Core Articles:
- 34.1: Classification of A.C. Motors (Induction, Synchronous, Commutator)
- 34.2: Induction Motor: General Principle
- 34.3: Construction (Stator core, windings, frame)
- 34.4: Squirrel-cage Rotor (End-rings, uninsulated copper/aluminum bars, skewing)
- 34.5: Phase-wound Rotor (Slip-ring rotor, 3-phase star-connected distributed winding)
- 34.6: Production of Rotating Field (Physical concepts of revolving stator flux)
- 34.7: Mathematical Proof for 2-Phase Supply (Φr=Φm constant magnitude)
- 34.8: Mathematical Proof for 3-Phase Supply (Φr=1.5Φm constant magnitude revolving at ω rad/s)
- 34.9: Why Does the Rotor Rotate? (Lenz's Law, force F=BIl)
- 34.10: Slip (Definition, fractional slip s, percentage slip, slip speed)
- 34.11: Frequency of Rotor Current (fr=sf)
- Worked Examples: 34.1 to 34.5 (Speed, slip, rotor frequency, poles)
- Diagrams: Figures 34.1 to 34.16 + cutaway stator/rotor photographs.
Part 2: Torque Equations & Motor Characteristics
- Pages: 1256–1280 (PDF pp. 14–38)
- Core Articles:
- 34.12: Relation between Torque and Rotor Power Factor (T∝ΦI2cosϕ2)
- 34.13: Starting Torque (Tst) derivation
- 34.14: Starting Torque of a Squirrel-cage Motor
- 34.15: Starting Torque of a Slip-ring Motor (Addition of external resistance)
- 34.16: Condition for Maximum Starting Torque (R2=X2)
- 34.17: Effect of Change in Supply Voltage on Starting Torque (Tst∝V2)
- 34.18: Rotor E.M.F. and Reactance Under Running Conditions (Er=sE2, Xr=sX2)
- 34.19: Torque Under Running Conditions (T∝R22+(sX2)2sE22R2)
- 34.20: Condition for Maximum Torque Under Running Conditions (R2=sX2 or sm=R2/X2)
- 34.21: Maximum Torque (Tmax∝2X2E22, independent of R2)
- 34.22: Full-load Torque and Maximum Torque Ratio (TmaxTf=a2+sf22asf)
- 34.23: Starting Torque and Maximum Torque Ratio (TmaxTst=1+a22a)
- 34.24: Effect of Change in Supply Voltage on Torque and Speed
- 34.25: Effect of Change in Supply Frequency on Torque and Speed
- 34.26: Full-load Torque and Starting Torque Ratio
- 34.27: Torque-Speed and Torque-Slip Curves (Stable and unstable operating regions)
- 34.28: Current-Torque Curve of an Induction Motor
- 34.29: Current-Speed Curve of an Induction Motor
- 34.30: Operating Modes (Motoring mode 0<s<1, Generating mode s<0, Braking/Plugging mode s>1)
- 34.31: Complete Torque-Speed Characteristic (−∞<N<+∞)
- 34.32: Crawling (Harmonic torques, 7th harmonic forward crawl at ≈Ns/7)
- 34.33: Cogging or Magnetic Locking (Harmonic teeth alignment, remedies)
- Worked Examples: 34.6 to 34.26 (Extensive numerical analysis of torques, slips, and external resistors)
- Practice Sets:
- Tutorial Problem No. 34.1: Starting & Maximum Torque Ratios (8 Problems)
- Tutorial Problem No. 34.2: Slip, Running Torque & Resistance Variation (15 Problems)
- Diagrams: Figures 34.17 to 34.32.
Part 3: Power Stages & Torque Relations
- Pages: 1278–1296 & 1298–1300 (PDF pp. 36–54 & pp. 56–58)
- Core Articles:
- 34.34: Power Stages in an Induction Motor: Stator Input (P1)−Stator LossesRotor Input (P2)−Rotor Cu Loss (Pcr)Gross Mechanical Power (Pm)−Friction & WindageShaft Output (Pout)
- 34.35: Fundamental Power Ratio: P2:Pcr:Pm=1:s:(1−s)
- 34.36: Torque Developed in Synchronous Watts (Tg=P2 synchronous watts)
- 34.37: Induction Motor Efficiency and Slip Relations (Rotor efficiency=1−s=N/Ns)
- 34.38: Shaft Torque and Gross Mechanical Torque Relations
- 34.39: Condition for Maximum Mechanical Power Output
- 34.40: Calculation of Stator Current and Power Factor
- 34.41: Measurement of Slip (Stroboscopic method, Galvanometer method, Tachometer method)
- 34.42: Determination of Rotor Resistance and Reactance by Blocked-Rotor Test
- Worked Examples: 34.27 to 34.51 (Complete numerical problem coverage)
- Practice Set:
- Tutorial Problem No. 34.3: Power Balance, Slip, Losses & Efficiency (19 Problems)
- Diagrams: Figures 34.33 to 34.40 + Power Stage block diagrams.
Part 4: Linear Induction Motors & Equivalent Circuit
- Pages: 1296–1311 (PDF pp. 54–69)
- Core Articles:
- 34.43: Sector Induction Motor (Construction, flux travel, power rating reduction)
- 34.44: Linear Induction Motor (LIM) (vs=2wf, reaction plates)
- 34.45: Properties of Linear Induction Motor (Synchronous speed, slip, thrust F=P2/vs, power flow)
- 34.46: Magnetic Levitation (Physics of tractive vs levitation forces, high-speed space shift Δt, M-Bahn transit)
- 34.47: Induction Motor as a Generalized Transformer (Phasor diagram, why stator and rotor fields are stationary relative to each other in space)
- 34.48: Rotor Output Derivation via Transformer Model
- 34.49: Equivalent Circuit of the Rotor (R2/s=R2+RL, where RL=R2(1/s−1))
- 34.50: Complete & Approximate Equivalent Circuit of Induction Motor (Transformation to stator)
- 34.51: Power Balance Equations from Equivalent Circuit
- 34.52: Maximum Power Output Theorem (RL=Z01)
- 34.53: Corresponding Slip for Maximum Power Output (s=R2+Z01R2) and Pg max=2(R01+Z01)3V12
- Worked Examples: 34.52 to 34.60 (LIM calculations, equivalent circuit solving, exact & approximate methods)
- Practice Sets:
- Tutorial Problem No. 34.4: Equivalent Circuit & Maximum Power Output (3 Problems)
- Objective Tests – 34: Complete 28 Multiple-Choice & Fill-in-the-Blank examination questions with worked explanations and master answer key.
- Diagrams: Figures 34.41 to 34.59 + Maglev color photo.
⚡ Key Formula Cheatsheet
| Parameter / Relation | Formula | Unit / Notes |
|---|---|---|
| Synchronous Speed | Ns=P120f | rpm |
| Fractional Slip | s=NsNs−N | Dimensionless (0≤s≤1) |
| Rotor Speed | N=Ns(1−s) | rpm |
| Rotor Frequency | fr=sf | Hz |
| Rotor EMF per phase | Er=sE2 | V |
| Rotor Standstill Impedance | Z2=R22+X22 | Ω |
| Rotor Running Impedance | Zr=R22+(sX2)2 | Ω |
| Starting Torque | Tst=R22+X22kE22R2 | N-m |
| Condition for Max Starting Torque | R2=X2 | Standstill condition |
| Running Torque | T=R22+(sX2)2ksE22R2 | N-m |
| Slip at Maximum Torque | sm=X2R2 | Fractional slip |
| Maximum Torque (Pull-out) | Tmax=2X2kE22 | Independent of R2 |
| Full Load to Max Torque Ratio | TmaxTf=a2+sf22asf | where a=R2/X2 |
| Starting to Max Torque Ratio | TmaxTst=1+a22a | where a=R2/X2 |
| Power Ratio Triangle | P2:Pcr:Pm=1:s:(1−s) | Fundamental relation |
| Rotor Copper Loss | Pcr=sP2=3I22R2 | Watts |
| Gross Mechanical Power | Pm=(1−s)P2=3I22R2(s1−s) | Watts |
| Gross Torque in Sync. Watts | Tg=P2=1−sPm | synchronous watts |
| Gross Torque in N-m | Tg=Ns9.55P2=N9.55Pm | N-m |
| Electrical Load Resistance | RL=R2(s1−1) | Ω/phase |
| Max Power Output Condition | RL=Z01=R012+X012 | Equivalent circuit |
| Slip at Max Power Output | s=R2+Z01R2 | Output power condition |
| Maximum Gross Power Output | Pg max=2(R01+Z01)3V12 | Watts |
| LIM Synchronous Speed | vs=2wf | m/s (w=pole pitch) |
| LIM Thrust | F=vsP2 | Newtons (N) |
🖼️ Diagram Directory Reference
All diagrams are cropped from vector elements at high resolution (150 DPI) and stored locally under diagrams/:
- Part 1:
Ch-34_p01_maglev.jpg,Ch-34_p02_motor.jpg,Ch-34_p02_fig01.jpgtoCh-34_p12_fig16.jpg(20 images) - Part 2:
Ch-34_p14_fig17.jpgtoCh-34_p34_fig32.jpg(15 images) - Part 3:
Ch-34_p36_slip_curve.jpg,Ch-34_p36_fig33_34.jpgtoCh-34_p47_fig40.jpg(9 images) - Part 4:
Ch-34_p54_fig41.jpgtoCh-34_p66_fig59.jpg+Ch-34_p55_maglev_photo.jpg(20 images)
Total Visual Artifacts Digitized: 64 high-fidelity diagrams & figures.