Master Curriculum & Topic Map: ECE 2107 / ECE 2207 (Electrical Machines-I)

Purpose for AI & Researchers: This master map indexes every topic, mathematical derivation, equivalent circuit model, experimental test, and textbook problem across Lectures L-01 to L-11. Consult this index to pinpoint the exact file, slide number, and line reference without loading all slide markdowns into the context window.

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1. Executive Curriculum Directory

Lecture Tag	Machine Domain	File Link	Primary Lecture Theme	Slides	Key Highlights
L-01	Foundations	L-01_ECE-2207.md	Magnetic Fields & Machine Principles	11	Field generation, Biot-Savart, Transformer/Motor/Generator action, Fleming's rules
L-02	Induction Motor	L-02_ECE-2207.md	Rotating Magnetic Field (RMF)	14	AC vs DC motors, 2-$\varphi$ RMF ($F_m$), 3-$\varphi$ RMF ($1.5F_m$), flux revolving theory
L-03	Induction Motor	L-03_ECE-2107.md	Slip, Vector Diagram & Equivalent Circuit	20	Synchronous speed $N_s$, slip $s$, rotor frequency $f_r$, transformer model, exact circuit
L-04	Induction Motor	L-04_ECE-2107.md	Torque Equations & Characteristics	17	Starting torque, running torque, max torque condition ($s_{max}=R_2/X_2$), torque-speed curve
L-05	Induction Motor	L-05_ECE-2107.md	Parameter Determination & Tests	15	No-load test, Blocked-rotor test, DC stator test, loss separation, worked 40-hp problem
L-06	Induction Motor	L-06_ECE-2107.md	Power Flow & Starting Methods	20	Power stages ($P_g:P_{cu}:P_{dev}=1:s:1-s$), synchronous watt, DOL, Auto-transformer, Star-Delta, Rotor rheostat
L-07	Induction Motor	L-07_ECE-2107.md	Speed Control, Braking, 1-$\varphi$ IM & Circle Diagram	24	Speed control methods, dynamic/DC/capacitor braking, plugging, induction generator, 1-$\varphi$ split-phase/capacitor motors, circle diagram
L-08	Transformer	L-08_ECE-2107.md	Fundamentals & Principle of Action	14	Transformer action, efficiency, DC transient behavior, AC sinusoidal derivation ($E=4.44fN{\Phi }_m$)
L-09	Transformer	L-09_ECE-2107.md	Construction & Phasor Diagrams	13	Core vs Shell type, no-load phasor ($I_0,I_{\mu },I_w$), loaded phasor (unity, lagging, leading pf)
L-10	Transformer	L-10_ECE-2107.md	Equivalent Circuit, Regulation & Tests	19	Leakage reactance, impedance referring ($K^2$), exact/approximate circuits, voltage regulation, OC test, SC test
L-11	Transformer	L-11_ECE-2107.md	3-$\varphi$ Transformers, Scott-T & Vector Groups	29	3-$\varphi$ connections (Y-Y, Y-$\Delta$, $\Delta$-Y, $\Delta$-$\Delta$), 3rd harmonic issues, Open-$\Delta$ (57.7%), Scott-T 3-$\varphi$ to 2-$\varphi$, Vector groups (Dyn11)

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2. Granular Slide-by-Slide Syllabus & Topic Mapping

[L-01] Fundamentals of Electrical Machines & Magnetic Fields

• Primary File: L-01_ECE-2207.md
• Core Machine Family: Electromechanical Foundations
• Total Slides: 11
• Slide Breakdown:
  • Slide 01: Course Title & Course Code (ECE-2207).
  • Slide 02: Quranic Inscription (Surah Al-’Alaq 96:1).
  • Slide 03: Prescribed Study Materials:
    • Basic Knowledge: B.L. Theraja (Vol-II), Stephen J. Chapman (Electric Machinery Fundamentals), A.E. Fitzgerald.
    • Competitive / Govt Job Exams: V.K. Mehta, J.B. Gupta.
  • Slide 04: Magnetic Field as the medium of electromechanical energy conversion.
  • Slide 05: Generation of Magnetic Field: Permanent magnets (magnetic dipole, magnetic lines of force).
  • Slide 06: Generation of Magnetic Field: Current-carrying straight conductor (Biot-Savart Law, Right-Hand Grip Rule).
  • Slide 07: Generation of Magnetic Field: Current-carrying coil / solenoid (Ampere's Circuital Law, polarity rule).
  • Slide 08: Fundamental Electromechanical Mechanisms: Overview of physical laws linking fields and mechanical systems.
  • Slide 09: Basis of Transformer Action: Faraday's Law of Electromagnetic Induction ($e=-N\frac{d\Phi }{dt}$); time-varying magnetic field inducing voltage in stationary coil.
  • Slide 10: Basis of Motor Action: Lorentz force on current-carrying conductor in a magnetic field ($F=BIl\sin \theta$); Fleming's Left-Hand Rule (Thumb: Force/Motion, Index: Field, Middle: Current).
  • Slide 11: Basis of Generator Action: Motional EMF induced in conductor moving through magnetic field ($e=Blv\sin \theta$); Fleming's Right-Hand Rule (Thumb: Motion, Index: Field, Middle: Induced Current).

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[L-02] Induction Motor Fundamentals & Rotating Magnetic Field (RMF)

• Primary File: L-02_ECE-2207.md
• Core Machine Family: 3-Phase Induction Motors (Part 1)
• Total Slides: 14
• Slide Breakdown:
  • Slide 01: Title slide (Induction Motor-SL1).
  • Slide 02: Quranic Inscription (Surah Ta-Ha 20:114).
  • Slide 03: Terminology & Physical Construction: Stator (stationary outer frame) vs. Rotor (rotating inner cylinder); Field vs. Armature windings.
  • Slide 04: AC Motors Overview: Synchronous motors (runs at $N_s$) vs. Asynchronous / Induction motors (runs at $N<N_s$).
  • Slide 05: Induction Motor vs. DC Motor: Conduction via commutator/brushes (DC) vs. Inductive contactless energy transfer (AC).
  • Slide 06: Induction Motor Rotor Types: Squirrel-cage rotor vs. Wound/Slip-ring rotor (Ref: Video V-01).
  • Slide 07: Operational Pros & Cons:
    • Advantages: Simple and rugged construction, low cost, high reliability, self-starting, minimal maintenance.
    • Disadvantages: Essentially constant speed with speed drop on load, starting torque lower than DC motor, low lagging power factor at light loads.
  • Slide 08: Flux Revolving Theory: How multi-phase stator currents produce a revolving magnetic field of constant magnitude.
  • Slide 09: Production of RMF by 2-$\varphi$ Supply: Two stator coils spaced $90^{\circ }$ electrically fed by currents in phase quadrature ($i_A=I_m\cos \omega t$, $i_B=I_m\sin \omega t$).
  • Slide 10: Mathematical Proof for 2-$\varphi$ RMF across Angles:
    • $\theta =0^{\circ }⟹{\Phi }_r={\Phi }_m\angle 0^{\circ }$
    • $\theta =45^{\circ }⟹{\Phi }_r={\Phi }_m\angle 45^{\circ }$
    • $\theta =90^{\circ }⟹{\Phi }_r={\Phi }_m\angle 90^{\circ }$
    • $\theta =135^{\circ }⟹{\Phi }_r={\Phi }_m\angle 135^{\circ }$
  • Slide 11: Proof continued ($\theta =180^{\circ }$); Conclusion: Constant resultant amplitude $F_R=F_m$ rotating at angular speed $\omega =2\pi f$.
  • Slide 12: Production of RMF by 3-$\varphi$ Supply: Three windings displaced $120^{\circ }$ in space carrying balanced currents displaced $120^{\circ }$ in time ($i_R,i_Y,i_B$).
  • Slide 13: Mathematical Proof for 3-$\varphi$ RMF:
    • $\theta =0^{\circ }⟹{\Phi }_R=\frac{3}{2}{\Phi }_m\angle 0^{\circ }$
    • $\theta =60^{\circ }⟹{\Phi }_R=\frac{3}{2}{\Phi }_m\angle 60^{\circ }$
  • Slide 14: Proof continued for $\theta =120^{\circ },180^{\circ }$; Core Conclusion: Resultant field has constant magnitude ${\Phi }_R=1.5{\Phi }_m=\frac{3}{2}{\Phi }_m$ and rotates synchronously at $N_s=120f/P$.

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[L-03] Induction Motor Principles, Slip, Vector Diagram & Equivalent Circuit

• Primary File: L-03_ECE-2107.md
• Core Machine Family: 3-Phase Induction Motors (Part 2)
• Total Slides: 20
• Slide Breakdown:
  • Slide 01: Title slide (Induction Motor-SL2).
  • Slide 02: Quranic Inscription (Surah Ash-Sharh 94:5-6).
  • Slide 03: Synchronous Speed Equation: $N_s=\frac{120f}{P}$. Mechanical rotor speed $N_r\le N_s$.
  • Slide 04: Why Does the Rotor Rotate?: Relative velocity cuts rotor bars $\to$ Induced EMF $\to$ Rotor circulating current.
  • Slide 05: Lenz's Law & Torque Production: Mechanical force $F=BIl$ exerts torque in the direction of field rotation to reduce relative speed; why rotor can never reach $N_s$ (no relative speed $⟹$ no induced EMF $⟹$ zero torque).
  • Slide 06: Slip Definitions: Slip Speed $=N_s-N$.
  • Slide 07: Fractional & Percentage Slip: $s=\frac{N_s-N}{N_s}$, $N=N_s(1-s)$.
  • Slide 08: Frequency of Rotor Current: $f_r=s\cdot f$. Standstill ($s=1⟹f_r=f$); running ($s\approx 0.02-0.05⟹f_r\approx 1-3\text{ Hz}$).
  • Slide 09: Textbook Practice Problems: B.L. Theraja Examples 34.3, 34.4, 34.5 (Poles, slip speed, rotor speed, rotor current frequency).
  • Slide 10: Induction Motor as a Generalized Transformer: Stator as primary, short-circuited rotating rotor as secondary.
  • Slide 11: Stator vs Rotor Quantities: Stator per-phase voltage $V_1=-E_1+I_1{Z}_1$; Standstill rotor EMF $E_2$; Running rotor EMF $E_r=s{E}_2$; Running rotor reactance $X_r=s{X}_2$.
  • Slide 12: No-Load Stator Current $I_0$: Core-loss component $I_w$ and Magnetizing component $I_{\mu }$ ($I_0=\sqrt{I_{\mu }^2+I_w^2}$).
  • Slide 13: Induction Motor Equivalent Circuit: Ideal transformer model coupling stator and rotor.
  • Slide 14: Internal EMF & Flux Relationship: Core flux linked to internal voltage $E_1$.
  • Slide 15: Effective Turns Ratio $a_{\text{eff}}$ between stator and rotor windings.
  • Slide 16: Rotor Circuit Model Transformation: Rotor current $I_2=\frac{s{E}_2}{\sqrt{R_2^2+(s{X}_2{)}^2}}=\frac{E_2}{\sqrt{(R_2/s{)}^2+X_2^2}}$.
  • Slide 17: Standstill Voltage Reference: $E_{R0}$ under locked-rotor conditions.
  • Slide 18: Variable Equivalent Resistance Decomposition: $$\frac{R_2}{s}=R_2+R_2\left(\frac{1-s}{s}\right)$$
    • $R_2$: Actual rotor winding ohmic copper loss.
    • $R_2\left(\frac{1-s}{s}\right)$: Fictitious load resistance representing electromechanical power developed.
  • Slide 19: Transformation to Stator Reference: Referring rotor parameters using turns ratio ($R_2^{\prime }=a_{\text{eff}}^2{R}_2,X_2^{\prime }=a_{\text{eff}}^2{X}_2$).
  • Slide 20: Complete Per-Phase Equivalent Circuit Diagram: Features stator branch ($R_1,X_1$), shunt core branch ($R_c,X_M$), and referred rotor branch ($R_2^{\prime }/s,X_2^{\prime }$).

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[L-04] Induction Motor Torque Equations, Maximum Torque & Characteristics

• Primary File: L-04_ECE-2107.md
• Core Machine Family: 3-Phase Induction Motors (Part 3)
• Total Slides: 17
• Slide Breakdown:
  • Slide 01: Title slide (Induction Motor-SL3).
  • Slide 02: Quranic Inscription (Surah Al-Baqarah 2:286).
  • Slide 03: Rotor Torque Principles: $T\propto \Phi I_2\cos {\phi }_2\propto E_2{I}_2\cos {\phi }_2$.
  • Slide 04: Starting Torque Derivation: Standstill condition ($s=1$), rotor current $I_2=\frac{E_2}{\sqrt{R_2^2+X_2^2}}$, rotor power factor $\cos {\phi }_2=\frac{R_2}{\sqrt{R_2^2+X_2^2}}$.
  • Slide 05: Starting Torque Formula: $$T_{st}=\frac{K_1{E}_2^2{R}_2}{R_2^2+X_2^2}\text{where }{K}_1=\frac{3}{2\pi N_s}$$
  • Slide 06: Condition for Maximum Starting Torque: $$\frac{d{T}_{st}}{d{R}_2}=0⟹R_2=X_2$$ Starting torque is maximized when standstill rotor resistance per phase equals standstill rotor reactance per phase.
  • Slide 07: Textbook Practice Problems: B.L. Theraja Examples 34.6, 34.7, 34.8, 34.9, 34.11 (Calculating $T_{st}$, effect of extra rotor resistance, determining full-load torque).
  • Slide 08: Rotor Quantities Under Running Condition (at slip $s$): $E_{2r}=s{E}_2$, $X_{2r}=s{X}_2$, $Z_{2r}=\sqrt{R_2^2+(s{X}_2{)}^2}$.
  • Slide 09: Running Torque Proportionality: $T_r\propto E_{2r}{I}_{2r}\cos {\phi }_{2r}$.
  • Slide 10: General Running Torque Equation: $$T_r=\frac{K_{1}s{E}_2^2{R}_2}{R_2^2+(s{X}_2{)}^2}$$
  • Slide 11: Torque Constant Evaluation: $K_1=\frac{3}{2\pi N_s}$ (yielding torque in Newton-meters $\text{N}\cdot \text{m}$).
  • Slide 12: Condition for Maximum Torque Under Running Conditions: Differentiating $T_r$ with respect to slip $s$: $$\frac{d{T}_r}{ds}=0⟹s=s_{max}=s_b=\frac{R_2}{X_2}$$
  • Slide 13: Running Condition for Max Torque: Maximum torque occurs at the slip where rotor reactance equals rotor resistance ($s{X}_2=R_2$).
  • Slide 14: Breakdown / Pull-Out Torque Formula: $$T_{max}=T_b=\frac{K_1{E}_2^2}{2X_2}$$ Crucial Conclusion: Maximum torque is independent of rotor resistance $R_2$; however, the slip $s_b$ at which $T_{max}$ occurs is directly proportional to $R_2$.
  • Slide 15: Torque-Slip Characteristics Analysis:
    • Low Slip Region ($s\approx 0$): $s{X}_2\ll R_2⟹T\propto s$ (linear curve).
    • High Slip Region ($s$ near 1): $s{X}_2\gg R_2⟹T\propto \frac{1}{s}$ (hyperbolic curve).
  • Slide 16: Pull-Out Torque & Operating Stability: Stable motor operation occurs between $s=0$ and $s=s_{max}$; operation beyond pull-out causes motor stalling.
  • Slide 17: Torque-Speed Characteristics Curves: Family of torque-speed curves for varying rotor resistance ($R,4R,6R$) demonstrating starting torque enhancement without altering peak pull-out torque.

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[L-05] Induction Motor Parameter Determination & Testing

• Primary File: L-05_ECE-2107.md
• Core Machine Family: 3-Phase Induction Motors (Part 4)
• Total Slides: 15
• Slide Breakdown:
  • Slide 01: Title slide (Induction Motor-SL4).
  • Slide 02: Quranic Inscription.
  • Slide 03: Purpose of Parameter Determination: Finding $R_1,R_2,X_1,X_2,X_M$, and rotational/core losses.
  • Slide 04: No-Load Test Concept: Uncoupled motor running at rated voltage and rated frequency ($s\approx 0$).
  • Slide 05: No-Load Equivalent Circuit: Rotor branch acts as open circuit ($R_2/s\to \infty$); input impedance $Z_{NL}\approx R_1+j(X_1+X_M)$.
  • Slide 06: No-Load Test Equations: $$S_{NL}=\sqrt{3}{V}_{NL}{I}_{NL},Q_{NL}=\sqrt{S_{NL}^2-P_{NL}^2},X_{NL}=\frac{Q_{NL}}{3I_{NL,ph}^2}=X_1+X_M$$
  • Slide 07: Separation of Losses from No-Load Test: $$P_{rot}=P_{core}+P_{f\&w}=P_{NL}-3I_{NL}^2{R}_1$$
  • Slide 08: Separation of Core Loss from Friction & Windage: Plotting $P_{NL}-3I_1^2{R}_1$ against $V^2$ and extrapolating to $V=0$ (intercept gives $P_{f\&w}$).
  • Slide 09: Blocked-Rotor Test Concept: Rotor clamped stationary ($N=0,s=1$); low voltage applied at reduced frequency (e.g., 15 Hz) to limit current to rated value.
  • Slide 10: Blocked-Rotor Equivalent Circuit: Magnetizing branch $X_M$ neglected ($X_M\gg X_2$); series impedance $Z_{BR}\approx R_{BR}+j{X}_{BR}^{\prime }$.
  • Slide 11: Blocked-Rotor Equations & Reactance Splitting: $$Z_{BR}=\frac{V_{BR,ph}}{I_{BR,ph}},R_{BR}=\frac{P_{BR,ph}}{I_{BR,ph}^2}=R_1+R_2,X_{BR}^{\prime }=\sqrt{Z_{BR}^2-R_{BR}^2}$$ Frequency correction: $X_{BR,60}=\frac{60}{f_{test}}{X}_{BR,test}$. Splitting per NEMA Design B: $X_1=0.4X_{BR,60}$, $X_2=0.6X_{BR,60}$.
  • Slide 12: DC Test for Stator Resistance: DC current injected into stator terminals to isolate pure ohmic resistance without inductive reactance.
  • Slide 13: DC Test Formulations:
    • Wye (Y) Connected: $R_1=\frac{R_{DC}}{2}$
    • Delta ($\Delta$) Connected: $R_1=\frac{3}{2}{R}_{DC}$
  • Slide 14: Skin Effect & Temperature AC Correction: $R_{1,AC}\approx 1.15-1.25R_{1,DC}$.
  • Slide 15: Comprehensive Worked-Out Numerical Problem:
    • Problem Statement: 3-$\varphi$, Y-connected, 40-hp, 60-Hz, 460-V, Design B motor ($I_{rated}=57.8\text{ A}$, Blocked rotor at 15 Hz: $V_{line}=36.2\text{V},I=58.0\text{A},P=2573.4\text{W}$; No-load: $V_{line}=460\text{V},I=32.7\text{A},P=4664.4\text{W}$; DC test: $V_{DC}=12\text{V},I_{DC}=59\text{A}$).
    • Step-by-step Solution:
      • $R_1=\frac{12/59}{2}=0.102\Omega /\text{phase}$
      • $R_2=R_{BR}-R_1=0.2550-0.102=0.153\Omega /\text{phase}$
      • $X_1=0.4073\Omega ,X_2=0.6109\Omega$
      • $X_M=X_{NL}-X_1=7.99-0.4073=7.58\Omega /\text{phase}$
      • Combined Core, Friction & Windage Loss $=4337.3\text{ W}$
      • $I_{NL}\text{ as \% of rated}=\frac{32.7}{57.8}\times 100\%=56.6\%$.

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[L-06] Power Stages, Torque & Starting Methods of Induction Motors

• Primary File: L-06_ECE-2107.md
• Core Machine Family: 3-Phase Induction Motors (Part 5)
• Total Slides: 20
• Slide Breakdown:
  • Slide 01: Title slide (Induction Motor-SL5).
  • Slide 02: Quranic Inscription.
  • Slide 03: Power Stages in an Induction Motor: Complete power flow chain overview.
  • Slide 04: Power Flow Diagram:
    • Stator Electrical Input: $P_{in}=\sqrt{3}{V}_L{I}_L\cos \theta$.
    • Stator Losses: Stator Copper Loss ($3I_1^2{R}_1$) + Stator Iron / Core Loss.
    • Air-gap Power (Rotor Input Power $P_g$ or $P_2$): $P_g=P_{in}-\text{Stator Losses}$.
  • Slide 05: Fundamental Power Division:
    • Rotor Copper Loss: $P_{cu,rotor}=3I_2^2{R}_2=s{P}_g$.
    • Gross Mechanical Power Developed ($P_{dev}$ or $P_{md}$): $P_{dev}=(1-s)P_g$.
    • Golden Power Ratio: $$P_g:P_{cu,rotor}:P_{dev}=1:s:(1-s)$$
  • Slide 06: Torque Developed by Motor: $T_d=\frac{P_g}{{\omega }_s}=\frac{P_{dev}}{{\omega }_m}=\frac{P_g}{2\pi N_s/60}$.
  • Slide 07: Rotor Output Power (Shaft Power $P_{out}$): $P_{out}=P_{dev}-\text{Rotational Losses }(P_{f\&w}+P_{stray})$.
  • Slide 08: Machine Efficiency: $\eta =\frac{P_{out}}{P_{in}}\times 100\%=\frac{P_{out}}{P_{out}+\text{Total Losses}}\times 100\%$.
  • Slide 09: Summary of Energy Transformations across stator air gap and rotor shaft.
  • Slide 10: Synchronous Watt Concept: $$\text{Torque in Synchronous Watts}=\text{Rotor Input Power }{P}_g\text{ in Watts}$$ Defined as the torque which, at synchronous speed, develops 1 Watt of mechanical power.
  • Slide 11: Starting Problem of Induction Motors: Severe starting current ($5-8\times I_{FL}$) at low lagging power factor causes severe line voltage dips.
  • Slide 12: Direct Switching / Line Starting (DOL): $I_{st}\approx 7I_{fl}$, but $T_{st}$ is only $\approx 1.96T_{fl}$; limited to small motors ($<5\text{ kW}$).
  • Slide 13: Classification of Starting Methods:
    • Squirrel-cage: Primary resistor/reactor, Auto-transformer, Star-Delta ($\text{Y}$-$\Delta$).
    • Slip-ring: Rotor rheostat starter.
  • Slide 14: Primary Resistor / Reactor Starting: Applied voltage reduced to $xV$; Starting current $I_{st}=x{I}_{sc}$; Starting torque $T_{st}=x^2{T}_{sc}$.
  • Slide 15: Auto-Transformer Starting: Transformer tapping ratio $x$:
    • Voltage across motor $=x{V}_1$.
    • Motor starting current $=x{I}_{sc}$.
    • Line starting current drawn from supply $=x^2{I}_{sc}$.
    • Starting torque $T_{st}=x^2{T}_{sc}$.
  • Slide 16: Starting to Full-Load Torque Ratio for Auto-Transformer: $$\frac{T_{st}}{T_{fl}}=x^2{\left(\frac{I_{sc}}{I_{fl}}\right)}^2{s}_{fl}$$
  • Slide 17: Schematic Circuit Diagram of Auto-Transformer Starter (Start vs Run positions).
  • Slide 18: Star-Delta ($\text{Y}$-$\Delta$) Starting:
    • In Star (Start): $V_{ph}=\frac{V_L}{\sqrt{3}}⟹I_{st,\text{line}}=\frac{1}{3}{I}_{sc,\Delta }$.
    • Starting torque: $T_{st}=\frac{1}{3}{T}_{sc,\Delta }$.
    • Torque Ratio: $\frac{T_{st}}{T_{fl}}=\frac{1}{3}{\left(\frac{I_{sc}}{I_{fl}}\right)}^2{s}_{fl}$.
  • Slide 19: Slip-Ring Motor Starting via Rotor Rheostat: External resistance $R_{ext}$ added to rotor via slip rings; reduces starting current while simultaneously increasing starting torque ($R_2+R_{ext}\approx X_2$).
  • Slide 20: Rotor Rheostat Operation Sequence: Gradual cut-out of external resistance as motor reaches rated speed; textbook practice example B.L. Theraja 34.10.

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[L-07] Speed Control, Electric Braking, Induction Generator, 1-$\varphi$ Motors & Circle Diagram

• Primary File: L-07_ECE-2107.md
• Core Machine Family: 3-Phase & 1-Phase Induction Machines (Part 6)
• Total Slides: 24
• Slide Breakdown:
  • Slide 01: Title slide (Induction Motor-SL6).
  • Slide 02: Quranic Inscription (Surah Al-Baqarah 2:269).
  • Slide 03: Speed Control Classifications:
    • Stator Side: (1) Stator voltage control, (2) Supply frequency control ($V/f$ control), (3) Changing stator poles, (4) Adding external stator impedance.
    • Rotor Side: (1) Adding external rotor resistance (slip-ring only), (2) Cascade control, (3) Injecting slip-frequency EMF (Scherbius/Kramer drives).
  • Slide 04: Textbook Reference: B.L. Theraja Article 35.18.
  • Slide 05: Practice Problems on Speed Control: B.L. Theraja Examples 35.29, 35.30.
  • Slide 06: Dynamic Electric Braking: Converting stored mechanical kinetic energy into heat by running the motor as a loaded generator.
  • Slide 07: DC Injection Braking: Stator disconnected from AC line and energized with DC current; creates stationary magnetic field inducing eddy currents and copper losses in spinning rotor.
  • Slide 08: Capacitor Braking: Motor disconnected from line and connected to 3-$\varphi$ capacitor bank; operates as self-excited generator dissipating energy in windings and discharge resistors.
  • Slide 09: Plugging (Reverse Voltage Braking): Interchanging any two stator leads; reverses direction of RMF, producing massive counter-torque ($s\approx 2$ at initiation of braking); high rotor $I^{2}R$ dissipation.
  • Slide 10: Induction Generator Operation: Motor driven by prime mover above synchronous speed ($N>N_s⟹s<0$); mechanical input converted to electrical active power delivered to AC system while absorbing reactive VARs from grid for excitation.
  • Slide 11: Grid-Connected Induction Generator schematic (driven by engine/turbine).
  • Slide 12: Self-Excited Induction Generator (SEIG): Standalone generator using shunt capacitors to provide excitation reactive power.
  • Slide 13: Complete Torque-Speed Operating Curve of 3-Phase Induction Machine:
    • Motoring Region: $0<N<N_s$ ($0<s<1$).
    • Generating Region: $N>N_s$ ($s<0$).
    • Braking / Plugging Region: Reverse rotation $N<0$ ($s>1$).
  • Slide 14: Textbook Practice Problem: B.L. Theraja Example 34.26.
  • Slide 15: Single-Phase Induction Motor (1-$\varphi$ IM): Pulsating single-phase stator field alternates along one space axis; inherently non-self-starting ($T_{st}=0$).
  • Slide 16: Double Revolving Field Theory: Alternating flux $\Phi ={\Phi }_m\cos \omega t$ resolved into two oppositely rotating fluxes of magnitude $\frac{{\Phi }_m}{2}$. Standstill slip $s_f=1,s_b=2-1=1⟹T_f=T_b⟹T_{resultant}=0$.
  • Slide 17: Making 1-$\varphi$ IM Self-Starting: Conversion into temporary 2-phase machine during start via auxiliary/starting winding spaced $90^{\circ }$ electrically.
  • Slide 18: Split-Phase Induction Motor: Main winding has low $R$, high $X$; Auxiliary winding has high $R$, low $X$; Phase angle split $\alpha \approx 30^{\circ }$; Centrifugal switch disconnects auxiliary winding at $70-80\%$ speed.
  • Slide 19: Capacitor-Start Induction-Run Motor: Capacitor in series with auxiliary winding produces $\approx 80^{\circ }$ phase split between $I_m$ and $I_s$; develops very high starting torque ($3-4\times T_{fl}$); Centrifugal switch cuts out capacitor.
  • Slide 20: Phasor diagram and torque comparison of Split-phase vs Capacitor-start motors.
  • Slide 21: Capacitor-Start Capacitor-Run & Permanent Split Capacitor (PSC) Motors: Uses two capacitors (large starting electrolytic capacitor + small continuous running paper/oil capacitor) for optimal start and high running efficiency/power factor.
  • Slide 22: Circle Diagram Fundamentals: Graphical locus of AC circuits; series $R$-$L$ circuit locus is a semicircle as reactance or resistance varies.
  • Slide 23: Construction of Induction Motor Circle Diagram: Using No-Load test ($V_{NL},I_0,\cos {\phi }_0$) and Blocked-Rotor test ($V_{BR},I_{BR},\cos {\phi }_{BR}$) to construct the circle diameter, torque line, and output line.
  • Slide 24: Parameter Extraction from Circle Diagram: Finding max output power, max torque, slip, efficiency, and power factor graphically; Practice problems: B.L. Theraja Examples 35.3, 35.5, 35.6, 35.8, 35.9.

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[L-08] Transformer Fundamentals, Energy Transfer & Principles of Action

• Primary File: L-08_ECE-2107.md
• Core Machine Family: Transformers (Part 1)
• Total Slides: 14
• Slide Breakdown:
  • Slide 01: Title slide (Transformer-SL1).
  • Slide 02: Quranic Inscription (Surah Ibrahim).
  • Slide 03: Prescribed Study Materials: Rosenblatt (Ch 14), B.L. Theraja (Ch 32).
  • Slide 04: Transformer Definition & Nature: Static electromagnetic machine; transfers AC power between circuits at constant frequency via mutual magnetic induction.
  • Slide 05: Industrial Uses of Transformers: Voltage stepping for bulk transmission, distribution stepping for consumer utilization, galvanic DC isolation, impedance matching, instrument measurement (CT/PT).
  • Slide 06: Power Transformers: High-voltage transmission and substation step-up/step-down ratings.
  • Slide 07: Physical Construction & Visuals: Silicon steel core, laminated limbs, high/low voltage bushings, oil conservator tank, cooling radiators.
  • Slide 08: Transformer Efficiency: Why efficiency is exceptionally high ($95-99\%$): absence of moving parts eliminates friction, windage, and mechanical wear losses.
  • Slide 09: Principle of Transformer Action with Transient DC Input:
    • Switch closing: DC current rises $\to \frac{d\Phi }{dt}>0\to$ Induced secondary EMF opposing flux build-up (Lenz's law).
    • Steady DC state: $\frac{d\Phi }{dt}=0\to$ Induced EMF drops to zero (transformers do not operate on steady DC).
  • Slide 10: Direction Finding: Right-hand grip rule for flux direction, Lenz's law for secondary induced polarity, dot convention.
  • Slide 11: Transient DC Input - Switch Opening: Magnetic flux collapses rapidly ($\frac{d\Phi }{dt}<0$) inducing reverse EMF pulse.
  • Slide 12: Core Insight of DC Transient Operation: Inductive energy transfer requires changing flux linkage.
  • Slide 13: Principle of Transformer Action with Sinusoidal AC Input: Sinusoidal supply voltage produces alternating flux $\Phi ={\Phi }_m\sin \omega t$.
  • Slide 14: Derivation of Fundamental EMF Equation: $$e_1=-N_1\frac{d\Phi }{dt}=-N_1\frac{d}{dt}({\Phi }_m\sin \omega t)=-N_1\omega {\Phi }_m\cos \omega t=2\pi f{N}_1{\Phi }_m\sin (\omega t-90^{\circ })$$ $$\text{RMS Primary EMF: }{E}_1=\frac{2\pi }{\sqrt{2}}f{N}_1{\Phi }_m=4.44f{N}_1{\Phi }_m$$ $$\text{RMS Secondary EMF: }{E}_2=4.44f{N}_2{\Phi }_m$$ Transformation Ratio $K=\frac{E_2}{E_1}=\frac{N_2}{N_1}$.

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[L-09] Transformer Construction & Phasor Diagrams

• Primary File: L-09_ECE-2107.md
• Core Machine Family: Transformers (Part 2)
• Total Slides: 13
• Slide Breakdown:
  • Slide 01: Title slide (Transformer-SL2).
  • Slide 02: Quranic Inscription (Surah An-Nahl).
  • Slide 03: Transformer Construction Types:
    • Core Type: Windings encircle the two vertical magnetic limbs; simple insulation, suited for high-voltage applications.
    • Shell Type: Magnetic core surrounds and encloses the windings; three limbs (central limb has twice the cross-sectional area of outer limbs); high mechanical bracing, suited for low-voltage, high-current applications.
    • Laminated silicon steel sheets ($0.35-0.5\text{ mm}$) insulated by varnish to minimize eddy current loss.
  • Slide 04: Transformer Phasor Diagram Overview: Modeling ideal vs real transformer under varying loads.
  • Slide 05: Phasor Diagram Under No-Load Condition: Secondary open ($I_2=0$); primary draws small no-load current $I_0$ ($3-5\%$ of full-load current).
  • Slide 06: Components of No-Load Current $I_0$:
    • Magnetizing Component ($I_{\mu }$ or $I_m$): $I_{\mu }=I_0\sin {\phi }_0$ (in phase with mutual flux ${\Phi }_m$, wattless/reactive, sets up core flux).
    • Working / Core-Loss Component ($I_w$ or $I_c$): $I_w=I_0\cos {\phi }_0$ (in phase with applied voltage $V_1$, active/wattful, supplies hysteresis and eddy current losses).
    • Magnitude: $I_0=\sqrt{I_{\mu }^2+I_w^2}$.
  • Slide 07: No-Load Phasor Diagram Construction: Mutual flux $\Phi$ on horizontal reference; induced EMFs $E_1$ and $E_2$ lag $\Phi$ by $90^{\circ }$; applied voltage $V_1=-E_1$ leads $\Phi$ by $90^{\circ }$; $I_0$ lags $V_1$ by no-load angle ${\phi }_0$.
  • Slide 08: No-Load Power Factor & Iron Loss: No-load power factor $\cos {\phi }_0\approx 0.1-0.2$ lagging; No-load power $W_0=V_1{I}_0\cos {\phi }_0=\text{Iron Loss }{P}_i$.
  • Slide 09: Textbook Practice Problems: Rosenblatt Example 14.4, B.L. Theraja Example 32.9 (Calculating $I_0,I_{\mu },I_w,\cos {\phi }_0$).
  • Slide 10: Phasor Diagram Under Loaded Condition:
    • Secondary supplies load current $I_2$ at power factor $\cos {\phi }_2$.
    • Secondary MMF $N_2{I}_2$ demagnetizes the core.
    • Primary draws reflected load current $I_2^{\prime }$ to neutralize secondary MMF ($N_1{I}_2^{\prime }=N_2{I}_2⟹I_2^{\prime }=K{I}_2$).
    • Total Primary Current: $I_1=I_0+I_2^{\prime }$.
  • Slide 11: Phasor Diagram for Non-Inductive Load (Unity Power Factor, $\cos {\phi }_2=1$): Secondary current $I_2$ in phase with $V_2$.
  • Slide 12: Phasor Diagram for Reactive Loads:
    • Inductive Load (Lagging pf): $I_2$ lags $V_2$ by angle ${\phi }_2$.
    • Capacitive Load (Leading pf): $I_2$ leads $V_2$ by angle ${\phi }_2$.
  • Slide 13: Textbook Practice Problems: B.L. Theraja Examples 32.12, 32.13, 32.14 (Determining primary current $I_1$ and primary power factor $\cos {\phi }_1$).

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[L-10] Transformer Leakage Reactance, Equivalent Circuit, Voltage Regulation & Testing

• Primary File: L-10_ECE-2107.md
• Core Machine Family: Transformers (Part 3)
• Total Slides: 19
• Slide Breakdown:
  • Slide 01: Title slide (Transformer-SL3).
  • Slide 02: Quranic Inscription (Surah Al-Hadid 57:25).
  • Slide 03: Leakage Reactance Concept: Primary leakage flux ${\Phi }_{L1}$ and secondary leakage flux ${\Phi }_{L2}$ completing paths through air rather than linking both windings.
  • Slide 04: Effect of Leakage Flux: Induces self-reactance EMFs that cause internal inductive voltage drops.
  • Slide 05: Fictitious Reactance Representation: $X_1=2\pi f{L}_1$, $X_2=2\pi f{L}_2$.
  • Slide 06: Total Winding Impedances: Primary $Z_1=R_1+j{X}_1$; Secondary $Z_2=R_2+j{X}_2$.
  • Slide 07: Transformer Terminal Voltage Equations: $$V_1=-E_1+I_1{R}_1+j{I}_1{X}_1,E_2=V_2+I_2{R}_2+j{I}_2{X}_2$$
  • Slide 08: Transformation Ratio $K$: $K=\frac{E_2}{E_1}=\frac{N_2}{N_1}\approx \frac{V_2}{V_1}=\frac{I_1}{I_2}$.
  • Slide 09: Equivalent Resistance Referring:
    • Secondary referred to Primary: $R_2^{\prime }=\frac{R_2}{K^2}⟹R_{01}=R_1+\frac{R_2}{K^2}$.
    • Primary referred to Secondary: $R_1^{\prime }=K^2{R}_1⟹R_{02}=R_2+K^2{R}_1$.
  • Slide 10: Equivalent Reactance Referring:
    • Secondary referred to Primary: $X_2^{\prime }=\frac{X_2}{K^2}⟹X_{01}=X_1+\frac{X_2}{K^2}$.
    • Primary referred to Secondary: $X_1^{\prime }=K^2{X}_1⟹X_{02}=X_2+K^2{X}_1$.
    • Equivalent Impedances: $Z_{01}=\sqrt{R_{01}^2+X_{01}^2}$, $Z_{02}=\sqrt{R_{02}^2+X_{02}^2}$.
  • Slide 11: Transformed Voltage & Current References: $E_2^{\prime }=E_2/K=E_1$, $V_2^{\prime }=V_2/K$, $I_2^{\prime }=K{I}_2$.
  • Slide 12: Complete Exact Equivalent Circuit Diagram: Complete circuit schematic showing $R_1,X_1,R_0,X_0,R_2^{\prime },X_2^{\prime }$ and ideal transformer block.
  • Slide 13: Approximate Equivalent Circuits: Shunt magnetizing branch ($R_0,X_0$) shifted to input terminals; combines series parameters into $R_{01}$ and $X_{01}$.
  • Slide 14: Complete Phasor Diagram with Winding Resistances and Leakage Reactances (Lagging Power Factor Load).
  • Slide 15: Complete Phasor Diagram for Leading & Unity Power Factor Loads.
  • Slide 16: Voltage Regulation (VR): $$VR=\frac{V_{S,nl}-V_{S,fl}}{V_{S,fl}}\times 100\%$$ $$\text{Approximate Expression: }VR\approx \frac{I_2(R_{02}\cos {\phi }_2\pm X_{02}\sin {\phi }_2)}{V_{2,fl}}\times 100\%$$ (+ for lagging power factor, - for leading power factor).
  • Slide 17: Open-Circuit (No-Load) Test:
    • Performed on Low-Voltage (LV) side with High-Voltage (HV) open.
    • Rated voltage applied; instruments measure $V_1,I_0,W_0$.
    • Wattmeter measures Core/Iron Loss $P_i=W_0$.
    • Parameter extractions: $$\cos {\phi }_0=\frac{W_0}{V_1{I}_0},I_w=I_0\cos {\phi }_0,I_{\mu }=I_0\sin {\phi }_0,R_0=\frac{V_1}{I_w},X_0=\frac{V_1}{I_{\mu }}$$
  • Slide 18: Short-Circuit (Impedance) Test:
    • Performed on High-Voltage (HV) side with Low-Voltage (LV) dead short-circuited.
    • Reduced voltage ($5-10\%$ of rated) applied to circulate full-load rated current $I_{sc}$.
    • Wattmeter measures Full-Load Copper Loss $W_{sc}=P_{cu}$.
    • Parameter extractions: $$R_{01}=\frac{W_{sc}}{I_{sc}^2},Z_{01}=\frac{V_{sc}}{I_{sc}},X_{01}=\sqrt{Z_{01}^2-R_{01}^2}$$
  • Slide 19: Textbook Practice Problems: Rosenblatt Examples 14.7, 14.8, 14.9, 14.10, B.L. Theraja Examples 32.27, 32.35, 32.36, 32.40 (Equivalent circuit parameters, OC/SC tests, voltage regulation, efficiency).

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[L-11] 3-Phase Transformers, Connections, Two-Transformer Schemes, Scott-T & Vector Groups

• Primary File: L-11_ECE-2107.md
• Core Machine Family: 3-Phase Transformers (Part 4)
• Total Slides: 29
• Slide Breakdown:
  • Slide 01: Title slide (Transformer-SL4).
  • Slide 02: Quranic Inscription (Surah Al-Mulk 67:30).
  • Slide 03: Necessity of 3-Phase Transformers: Generation, transmission, and heavy industrial distribution.
  • Slide 04: Construction Options: Bank of three separate single-phase transformers vs Single 3-phase unit (3-legged / 5-legged core).
  • Slide 05: Comparison: 3-$\varphi$ single unit is lighter, smaller, cheaper, and $\approx 15\%$ more efficient; Bank offers replacement of single faulted phase.
  • Slide 06: Standard 3-Phase Connections: Four standard topologies ($\text{Y}$-$\text{Y}$, $\text{Y}$-$\Delta$, $\Delta$-$\text{Y}$, $\Delta$-$\Delta$).
  • Slide 07: Wye-Wye ($\text{Y}$-$\text{Y}$) Connection: $$V_{\phi P}=\frac{V_{LP}}{\sqrt{3}},V_{LS}=\sqrt{3}{V}_{\phi S},\text{Line Voltage Ratio }\frac{V_{LP}}{V_{LS}}=a$$
  • Slide 08: Severe Problems with $\text{Y}$-$\text{Y}$ Connection:
    1. Unbalanced Load Problem: In ungrounded Y-Y, unbalanced loads shift the neutral voltage (floating neutral), causing severe line-to-neutral overvoltages.
    2. Third-Harmonic Voltage Distortion: Magnetizing current contains prominent 3rd harmonics; in ungrounded wye, 3rd harmonic currents cannot flow, distorting phase voltage into peaked waves with $3rd$ harmonic voltages up to $50\%$ of fundamental.
  • Slide 09: Solutions to $\text{Y}$-$\text{Y}$ Defects: Solidly ground neutrals, or include a closed tertiary delta ($\Delta$) winding to circulate 3rd harmonic currents.
  • Slide 10: Summary of $\text{Y}$-$\text{Y}$ connection.
  • Slide 11: Wye-Delta ($\text{Y}$-$\Delta$) Connection: $$V_{LP}=\sqrt{3}{V}_{\phi P},V_{LS}=V_{\phi S},\text{Line Voltage Ratio }\frac{V_{LP}}{V_{LS}}=\sqrt{3}a$$ Commonly used for step-down transmission substations.
  • Slide 12: $\text{Y}$-$\Delta$ Characteristics: Third-harmonic currents freely circulate in closed delta (no voltage distortion); introduces a $30^{\circ }$ phase shift between primary and secondary line voltages.
  • Slide 13: Delta-Wye ($\Delta$-$\text{Y}$) Connection: $$V_{LP}=V_{\phi P},V_{LS}=\sqrt{3}{V}_{\phi S},\text{Line Voltage Ratio }\frac{V_{LP}}{V_{LS}}=\frac{a}{\sqrt{3}}$$ Commonly used for generator step-up stations (low voltage to transmission EHV); provides neutral on secondary for 4-wire commercial distribution; introduces a $30^{\circ }$ phase shift.
  • Slide 14: Delta-Delta ($\Delta$-$\Delta$) Connection: $$V_{LP}=V_{\phi P},V_{LS}=V_{\phi S},\text{Line Voltage Ratio }\frac{V_{LP}}{V_{LS}}=a$$ No phase shift; handles unbalanced loads cleanly; third harmonics circulate in delta; permits Open-$\Delta$ operation if one unit fails.
  • Slide 15: 3-Phase Transformation Using Only Two Transformers: Emergency and economic schemes.
  • Slide 16: Open-$\Delta$ (or V-V) Connection: Formed when one transformer of a $\Delta$-$\Delta$ bank is removed for maintenance. Balanced 3-phase voltages maintained: $$V_C=-V_A-V_B=-V\angle 0^{\circ }-V\angle -120^{\circ }=V\angle 120^{\circ }$$
  • Slide 17: Power Handling Capability of Open-$\Delta$: $$\text{Closed-}\Delta \text{ Rating}=3V_{ph}{I}_{ph}=\sqrt{3}{V}_L(\sqrt{3}{I}_S)=3V_L{I}_S$$ $$\text{Open-}\Delta \text{ Rating}=\sqrt{3}{V}_L{I}_S$$
  • Slide 18: Open-$\Delta$ Capacity Ratios Derivation: $$\frac{\text{Open-}\Delta \text{ kVA}}{\text{Closed-}\Delta \text{ kVA}}=\frac{\sqrt{3}{V}_L{I}_S}{3V_L{I}_S}=\frac{1}{\sqrt{3}}\approx 0.577⟹57.7\%$$ $$\text{Utilization of 2 Installed Units}=\frac{\sqrt{3}{V}_L{I}_S}{2V_L{I}_S}=\frac{\sqrt{3}}{2}\approx 0.866⟹86.6\%$$
  • Slide 19: Practice Problems on Open-$\Delta$: Rosenblatt Examples 14.4, 14.5.
  • Slide 20: Open-Wye Open-Delta Connection: Derived from two phases and neutral of 4-wire wye system for rural 3-phase loads; disadvantage: large neutral return current.
  • Slide 21: Scott-T Connection: Converts 3-phase power to 2-phase power (at $90^{\circ }$) or vice versa.
  • Slide 22: Scott-T Hardware Topology:
    • Main Transformer ($T_1$): Connected between lines B and C; center-tapped at $50\%$ point $D$.
    • Teaser Transformer ($T_2$): Connected between line A and center tap $D$; tapped at $86.6\%$ ($\frac{\sqrt{3}}{2}$) of full primary winding.
  • Slide 23: Scott-T Mathematical & Phasor Proof: $$V_{ad}=V_{ab}+V_{bd}=V_L\angle -120^{\circ }+0.5V_L\angle 0^{\circ }=\frac{\sqrt{3}}{2}{V}_L\angle -90^{\circ }$$ Proves teaser voltage is strictly in quadrature ($90^{\circ }$) with main transformer voltage.
  • Slide 24: Three-Phase T-Connection: Two transformers connected in T configuration on both primary and secondary to convert 3-$\varphi$ to 3-$\varphi$ power.
  • Slide 25: Vector Groups of Transformers: Defines the phase angle displacement between primary (HV) and secondary (LV) voltage vectors introduced by winding configurations.
  • Slide 26: Clock Representation System:
    • HV reference phasor set at 12 o'clock ($0^{\circ }$).
    • Anti-clockwise phasor rotation: each clock hour corresponds to $30^{\circ }$ phase displacement.
    • $1\text{ o’clock}=-30^{\circ }$ (LV lags HV by $30^{\circ }$).
    • $6\text{ o’clock}=180^{\circ }$ phase inversion.
    • $11\text{ o’clock}=+30^{\circ }$ (LV leads HV by $30^{\circ }$).
  • Slide 27: Vector Group Nomenclature:
    • Capital Letter: HV winding connection ($\text{Y}$ = Star, $\text{D}$ = Delta).
    • Small Letter: LV winding connection ($\text{y}$ = star, $\text{d}$ = delta, $\text{z}$ = zigzag).
    • Letter 'n' or 'N': Neutral brought out.
    • Four Standard Groups: Group 1 ($0^{\circ }$: Yy0, Dd0, Dz0), Group 2 ($180^{\circ }$: Yy6, Dd6, Dz6), Group 3 ($-30^{\circ }$: Yd1, Dy1, Yz1), Group 4 ($+30^{\circ }$: Yd11, Dy11, Yz11).
  • Slide 28: Dyn1 Vector Group Detailed Connection & Clock Diagram.
  • Slide 29: Dyn11 Vector Group Detailed Example: Delta HV, Wye LV with neutral brought out; secondary line voltage leads primary line voltage by $30^{\circ }$ (11 o'clock).

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3. Essential Equations & Mathematical Cheat-Sheet

3.1 Foundations & Magnetic Circuits (L-01)

• Faraday's Law of Induction: $e=-N\frac{d\Phi }{dt}$
• Lorentz Force on Conductor: $F=BIl\sin \theta$
• Motional Induced EMF: $e=Blv\sin \theta$

3.2 Induction Motor Kinematics & Rotor Quantities (L-02, L-03)

• Resultant RMF (2-Phase): $F_R=F_m$
• Resultant RMF (3-Phase): $F_R=1.5F_m=\frac{3}{2}{F}_m$
• Synchronous Speed: $N_s=\frac{120f}{P}$
• Slip: $s=\frac{N_s-N}{N_s}$
• Rotor Frequency: $f_r=s\cdot f$
• Rotor Running Voltage: $E_{2r}=s{E}_2$
• Rotor Running Reactance: $X_{2r}=s{X}_2$
• Rotor Current: $I_{2r}=\frac{s{E}_2}{\sqrt{R_2^2+(s{X}_2{)}^2}}=\frac{E_2}{\sqrt{(R_2/s{)}^2+X_2^2}}$

3.3 Induction Motor Torque & Power Flow (L-04, L-06)

• Starting Torque: $T_{st}=\frac{3}{2\pi N_s}\frac{E_2^2{R}_2}{R_2^2+X_2^2}$
• Max Starting Torque Condition: $R_2=X_2$
• Running Torque: $T_r=\frac{3}{2\pi N_s}\frac{s{E}_2^2{R}_2}{R_2^2+(s{X}_2{)}^2}$
• Max Running Torque Slip: $s_{max}=s_b=\frac{R_2}{X_2}$
• Breakdown / Pull-Out Torque: $T_{max}=\frac{3}{2\pi N_s}\frac{E_2^2}{2X_2}$ (independent of $R_2$)
• Power Ratio: $P_g:P_{cu,rotor}:P_{dev}=1:s:(1-s)$
• Developed Torque: $T_d=\frac{P_g}{{\omega }_s}=\frac{P_{dev}}{{\omega }_m}$

3.4 Induction Motor Starting & Starters (L-06)

• Auto-Transformer Starter: $I_{st}=x^2{I}_{sc},\frac{T_{st}}{T_{fl}}=x^2{\left(\frac{I_{sc}}{I_{fl}}\right)}^2{s}_{fl}$
• Star-Delta Starter: $I_{st}=\frac{1}{3}{I}_{sc,\Delta },\frac{T_{st}}{T_{fl}}=\frac{1}{3}{\left(\frac{I_{sc}}{I_{fl}}\right)}^2{s}_{fl}$

3.5 Single-Phase Induction Motors (L-07)

• Double Revolving Slips: $s_f=s,s_b=2-s$
• Standstill Condition: $s_f=1,s_b=1⟹T_f=T_b⟹T_{st}=0$

3.6 Transformers: EMF, Impedance & Regulation (L-08, L-10)

• EMF Equation: $E=4.44fN{\Phi }_m$
• Transformation Ratio: $K=\frac{E_2}{E_1}=\frac{N_2}{N_1}\approx \frac{V_2}{V_1}=\frac{I_1}{I_2}$
• Referred Resistance to Primary: $R_{01}=R_1+\frac{R_2}{K^2}$
• Referred Reactance to Primary: $X_{01}=X_1+\frac{X_2}{K^2}$
• Referred Resistance to Secondary: $R_{02}=R_2+K^2{R}_1$
• Referred Reactance to Secondary: $X_{02}=X_2+K^2{X}_1$
• Voltage Regulation: $VR\approx \frac{I_2(R_{02}\cos {\phi }_2\pm X_{02}\sin {\phi }_2)}{V_{2,fl}}\times 100\%$

3.7 3-Phase Transformers & Scott-T (L-11)

• Open-$\Delta$ vs Closed-$\Delta$ Capacity: $\frac{S_{V-V}}{S_{\Delta }}=\frac{1}{\sqrt{3}}\approx 0.577(57.7\%)$
• Open-$\Delta$ Utilization Factor: $\frac{\sqrt{3}{V}_L{I}_S}{2V_L{I}_S}=\frac{\sqrt{3}}{2}\approx 0.866(86.6\%)$
• Scott-T Teaser Winding Tap: $86.6\%=\frac{\sqrt{3}}{2}\approx 0.866$
• Scott-T Main Winding Tap: $50\%$ center tap
• Vector Group Clock Angle: Each hour $=30^{\circ }$ phase lag (anti-clockwise phasor rotation)

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4. Experimental Tests & Laboratory Procedures

Machine	Test Name	Purpose / Parameters Determined	Slides
Induction Motor	No-Load Test	Determines magnetizing reactance $X_M$, core loss resistance $R_c$, and separates friction & windage losses $P_{f\&w}$.	L-05: S04–S08
Induction Motor	Blocked-Rotor Test	Determines total equivalent resistance $R_{BR}=R_1+R_2$ and equivalent leakage reactance $X_{BR}^{\prime }=X_1+X_2$.	L-05: S09–S11
Induction Motor	DC Stator Resistance Test	Measures ohmic stator resistance $R_1$ for Wye ($R_{DC}/2$) and Delta ($1.5R_{DC}$) connections.	L-05: S12–S14
Induction Motor	Circle Diagram Test	Uses No-load and Blocked-rotor test points to plot circle diagram for graphical determination of slip, torque, power, and losses.	L-07: S22–S24
Transformer	Open-Circuit (OC) Test	Conducted on LV side with HV open. Determines core/iron loss $P_i$, magnetizing reactance $X_0$, and core-loss resistance $R_0$.	L-10: S17
Transformer	Short-Circuit (SC) Test	Conducted on HV side with LV shorted. Determines full-load copper loss $P_{cu}$, equivalent resistance $R_{01}$, and leakage reactance $X_{01}$.	L-10: S18

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5. Textbook Numerical Problems Index

Lecture	Prescribed Textbook	Example / Problem Reference	Core Problem Topic
L-03	B.L. Theraja (Vol-II)	Example 34.3, 34.4, 34.5	Synchronous speed, slip speed, percentage slip, rotor frequency
L-04	B.L. Theraja (Vol-II)	Example 34.6, 34.7, 34.8, 34.9, 34.11	Starting torque, max starting torque condition, full-load torque
L-05	Stephen J. Chapman / Sen	Worked-Out 40-hp Problem (Slide 15)	Complete equivalent circuit parameter calculation from No-load, Blocked rotor, and DC tests
L-06	B.L. Theraja (Vol-II)	Example 34.10	Power stages, air-gap power, rotor copper loss, mechanical power, starter ratios
L-07	B.L. Theraja (Vol-II)	Example 35.29, 35.30	Induction motor speed control via rotor resistance
L-07	B.L. Theraja (Vol-II)	Example 34.26	Induction generator operation
L-07	B.L. Theraja (Vol-II)	Example 35.3, 35.5, 35.6, 35.8, 35.9	Circle diagram construction, graphical performance evaluation
L-09	Rosenblatt / Theraja	Rosenblatt Ex 14.4; Theraja Ex 32.9	Transformer no-load parameters ($I_0,I_{\mu },I_w,\cos {\phi }_0$)
L-09	B.L. Theraja (Vol-II)	Example 32.12, 32.13, 32.14	Loaded transformer primary current, power factor under reactive loads
L-10	Rosenblatt / Theraja	Rosenblatt Ex 14.7–14.10; Theraja Ex 32.27, 32.35, 32.36, 32.40	Transformer equivalent circuits, OC/SC tests, voltage regulation, efficiency
L-11	Rosenblatt	Example 14.4, 14.5	Three-phase transformer connections and Open-$\Delta$ (V-V) capacity

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6. Master Alphabetical Cross-Reference Index (A–Z)

• Air-gap Power ($P_g$): L-06_ECE-2107.md (Slides 4–5)
• Auto-Transformer Starter: L-06_ECE-2107.md (Slides 15–17)
• Blocked-Rotor Test: L-05_ECE-2107.md (Slides 9–11, 15)
• Braking (Dynamic, DC Injection, Capacitor, Plugging): L-07_ECE-2107.md (Slides 6–9)
• Capacitor-Start / Capacitor-Run Motors: L-07_ECE-2107.md (Slides 19–21)
• Circle Diagram: L-07_ECE-2107.md (Slides 22–24)
• Clock Representation of Vector Groups: L-11_ECE-2107.md (Slides 26–29)
• Core Type vs Shell Type Transformer: L-09_ECE-2107.md (Slide 3)
• DC Injection Braking: L-07_ECE-2107.md (Slide 7)
• DC Test for Stator Resistance: L-05_ECE-2107.md (Slides 12–14, 15)
• Delta-Delta ($\Delta$-$\Delta$) Connection: L-11_ECE-2107.md (Slide 14)
• Delta-Wye ($\Delta$-Y) Connection: L-11_ECE-2107.md (Slide 13)
• Direct-On-Line (DOL) Starting: L-06_ECE-2107.md (Slide 12)
• Double Revolving Field Theory: L-07_ECE-2107.md (Slide 16)
• Dyn11 Vector Group: L-11_ECE-2107.md (Slide 29)
• Efficiency of Transformer: L-08_ECE-2107.md (Slide 8)
• EMF Equation of Transformer: L-08_ECE-2107.md (Slide 14)
• Equivalent Circuit (Induction Motor): L-03_ECE-2107.md (Slides 13–20)
• Equivalent Circuit (Transformer): L-10_ECE-2107.md (Slides 9–13)
• Faraday's Law of Induction: L-01_ECE-2207.md (Slide 9), L-08_ECE-2107.md
• Fleming's Left-Hand & Right-Hand Rules: L-01_ECE-2207.md (Slides 10–11)
• Floating Neutral / Third Harmonics in Y-Y: L-11_ECE-2107.md (Slides 8–9)
• Flux Revolving Theory: L-02_ECE-2207.md (Slide 8)
• Induction Generator (Grid & Self-Excited): L-07_ECE-2107.md (Slides 10–12)
• Leakage Reactance & Leakage Flux: L-10_ECE-2107.md (Slides 3–7)
• Maximum Starting Torque Condition ($R_2=X_2$): L-04_ECE-2107.md (Slide 6)
• Maximum Running Torque Condition ($s=R_2/X_2$): L-04_ECE-2107.md (Slides 12–14)
• No-Load Phasor Diagram (Transformer): L-09_ECE-2107.md (Slides 5–8)
• No-Load Test (Induction Motor): L-05_ECE-2107.md (Slides 4–8)
• Open-Circuit (OC) Test (Transformer): L-10_ECE-2107.md (Slide 17)
• Open-$\Delta$ (or V-V) Connection (57.7%): L-11_ECE-2107.md (Slides 16–19)
• Open-Wye Open-Delta Connection: L-11_ECE-2107.md (Slide 20)
• Phasor Diagram with Winding Leakage: L-10_ECE-2107.md (Slides 14–15)
• Plugging of Induction Motor: L-07_ECE-2107.md (Slide 9)
• Power Flow & Division ($P_g:P_{cu}:P_{dev}$): L-06_ECE-2107.md (Slides 4–5)
• Pull-Out / Breakdown Torque: L-04_ECE-2107.md (Slides 14–16)
• Rotor Rheostat Starter: L-06_ECE-2107.md (Slides 19–20)
• Rotating Magnetic Field (2-Phase & 3-Phase): L-02_ECE-2207.md (Slides 9–14)
• Scott-T Connection (3-$\varphi$ to 2-$\varphi$): L-11_ECE-2107.md (Slides 21–23)
• Short-Circuit (SC) Test (Transformer): L-10_ECE-2107.md (Slide 18)
• Single-Phase Induction Motor: L-07_ECE-2107.md (Slides 15–21)
• Slip & Slip Speed: L-03_ECE-2107.md (Slides 6–7)
• Speed Control Methods (Induction Motor): L-07_ECE-2107.md (Slides 3–5)
• Split-Phase Machine: L-07_ECE-2107.md (Slide 18)
• Star-Delta Starter: L-06_ECE-2107.md (Slide 18)
• Synchronous Speed ($N_s=120f/P$): L-03_ECE-2107.md (Slide 3)
• Synchronous Watt: L-06_ECE-2107.md (Slide 10)
• Three-Phase T-Connection: L-11_ECE-2107.md (Slide 24)
• Torque-Slip & Torque-Speed Curves: L-04_ECE-2107.md (Slides 15–17)
• Transient DC Input on Transformer: L-08_ECE-2107.md (Slides 9–12)
• Vector Groups (Clock Method): L-11_ECE-2107.md (Slides 25–29)
• Voltage Regulation of Transformer: L-10_ECE-2107.md (Slide 16)
• Wye-Delta (Y-$\Delta$) Connection: L-11_ECE-2107.md (Slides 11–12)
• Wye-Wye (Y-Y) Connection: L-11_ECE-2107.md (Slides 7–10)