V.K. Mehta & Rohit Mehta — Principles of Electrical Machines

ECE 2207 (Electrical Machine-I) Master Digitization Index & Topic Map

Source Document: Principles-of-Electrical-Machines-vk-Mehta.pdf (317 pages)
Digitized Scope: All Core ECE 2207 Syllabus Chapters (Chapters 7, 8, 9 — PDF pages 129 to 258, 130 pages total)
Status: 100% Digitized, Verified, Word-for-Word Obsidian Markdown with 117 Extracted High-Resolution Figures.

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1. Digitized Chapters & File Manifest

Chapter	Document Title	PDF Pages	File Size	Figures	Target Link
Ch 7	Transformer	129–186 (58 pp)	62.9 KB	56	VK_Mehta_Ch07_Transformer.md
Ch 8	Three Phase Induction Motors	187–232 (46 pp)	42.5 KB	36	VK_Mehta_Ch08_Three_Phase_Induction_Motors.md
Ch 9	Single-Phase Motors	233–258 (26 pp)	27.9 KB	25	VK_Mehta_Ch09_Single_Phase_Motors.md
Index	Master Index & Formula Map	—	—	—	VK_Mehta_ECE2207_Index.md

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2. ECE 2207 Course Syllabus to V.K. Mehta Chapter Mapping

ECE 2207: Electrical Machine-I
│
├── 1. Transformer (Syllabus Section 1)
│    ├── Ideal Transformer & Transformation Ratio ─────────► V.K. Mehta Sec 7.1 – 7.4 (pp. 129–133)
│    ├── No-Load & Load Phasor/Vector Diagrams ────────────► V.K. Mehta Sec 7.6 – 7.8 (pp. 134–139)
│    ├── Actual Transformer Equivalent Circuit ────────────► V.K. Mehta Sec 7.9 – 7.14 (pp. 139–148)
│    ├── Voltage Regulation & Voltage Drop ────────────────► V.K. Mehta Sec 7.15 – 7.16 (pp. 149–151)
│    ├── Transformer Testing (OC, SC, Sumpner) ────────────► V.K. Mehta Sec 7.17 – 7.23 (pp. 151–157)
│    ├── Losses, Efficiency & Maximum Efficiency ──────────► V.K. Mehta Sec 7.24 – 7.29 (pp. 157–161)
│    ├── Autotransformer (Theory, Copper Saving) ──────────► V.K. Mehta Sec 7.33 – 7.38 (pp. 163–170)
│    ├── Parallel Operation (Equal & Unequal Ratios) ──────► V.K. Mehta Sec 7.39 – 7.41 (pp. 170–176)
│    └── Three-Phase Connections, V-V, Scott (T-T) ────────► V.K. Mehta Sec 7.42 – 7.49 (pp. 176–186)
│
├── 2. Three-Phase Induction Motor (Syllabus Section 2)
│    ├── Rotating Magnetic Field (RMF: Graphical & Math) ──► V.K. Mehta Sec 8.3 – 8.4 (pp. 189–195)
│    ├── Construction (Squirrel-Cage & Wound Rotor) ───────► V.K. Mehta Sec 8.2 (pp. 188–189)
│    ├── Operating Principle & Slip Physics ───────────────► V.K. Mehta Sec 8.5 – 8.7 (pp. 195–197)
│    ├── Rotor Circuit Under Running Conditions ───────────► V.K. Mehta Sec 8.8 – 8.9 (pp. 197–199)
│    ├── Torque Equations & Maximum Torque Condition ──────► V.K. Mehta Sec 8.10 – 8.17 (pp. 199–205)
│    ├── Torque-Slip / Torque-Speed Characteristics ───────► V.K. Mehta Sec 8.18 – 8.19 (pp. 205–207)
│    ├── Power Stages Flow Diagram (1 : s : 1-s) ──────────► V.K. Mehta Sec 8.24 – 8.27 (pp. 210–213)
│    ├── Equivalent Circuit & Mechanical Load Model ───────► V.K. Mehta Sec 8.29 – 8.33 (pp. 216–222)
│    ├── Starting Methods (DOL, Resistor, Y-Δ, Auto) ──────► V.K. Mehta Sec 8.34 – 8.37 (pp. 222–228)
│    └── Double Squirrel-Cage Motor ───────────────────────► V.K. Mehta Sec 8.40 – 8.41 (pp. 229–232)
│
└── 3. Single-Phase Induction Motor (Syllabus Section 3)
     ├── Theory of Operation & Why Not Self-Starting ──────► V.K. Mehta Sec 9.2 (pp. 233–234)
     ├── Double-Field Revolving Theory (Forward & Backward) ► V.K. Mehta Sec 9.3 (pp. 234–237)
     ├── Phase-Splitting & 2-Phase RMF Production ────────► V.K. Mehta Sec 9.4 – 9.5 (pp. 237–241)
     ├── Split-Phase (Resistance) Induction Motor ─────────► V.K. Mehta Sec 9.6 (pp. 241–242)
     ├── Capacitor-Start & Two-Value Capacitor Motors ─────► V.K. Mehta Sec 9.7 – 9.8 (pp. 242–244)
     ├── Shaded-Pole Motor (Flux Shifting Mechanism) ──────► V.K. Mehta Sec 9.9 (pp. 244–245)
     ├── Equivalent Circuit (s and 2-s Forward/Backward) ──► V.K. Mehta Sec 9.10 (pp. 246–248)
     └── Universal, Repulsion, Reluctance & Hysteresis ────► V.K. Mehta Sec 9.11 – 9.17 (pp. 248–258)

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3. Comprehensive Master Formula Cheatsheet

3.1 Transformers (Chapter 7)

1. EMF Equation: $$E_1=4.44f{N}_1{\Phi }_m,E_2=4.44f{N}_2{\Phi }_m$$ $$K=\frac{E_2}{E_1}=\frac{N_2}{N_1}=\frac{V_2}{V_1}=\frac{I_1}{I_2}$$

2. No-Load Phasor Parameters: $$I_w=I_0\cos {\varphi }_0,I_m=I_0\sin {\varphi }_0,I_0=\sqrt{I_w^2+I_m^2}$$ $$R_0=\frac{V_1}{I_w}=\frac{V_1^2}{W_0},X_0=\frac{V_1}{I_m},W_0=V_1{I}_0\cos {\varphi }_0=P_i$$

3. Impedance Shifting Rules:

   • From Primary to Secondary: multiply by $K^2$ ($R_1^{\prime }=K^2{R}_1$, $X_1^{\prime }=K^2{X}_1$).
   • From Secondary to Primary: divide by $K^2$ ($R_2^{\prime }=R_2/K^2$, $X_2^{\prime }=X_2/K^2$).
   • $R_{01}=R_1+\frac{R_2}{K^2},X_{01}=X_1+\frac{X_2}{K^2},Z_{01}=\sqrt{R_{01}^2+X_{01}^2}$
   • $R_{02}=R_2+K^2{R}_1,X_{02}=X_2+K^2{X}_1,Z_{02}=K^2{Z}_{01}$

4. Voltage Regulation & Drop: $$\Delta V_2=I_2{R}_{02}\cos {\varphi }_2\pm I_2{X}_{02}\sin {\varphi }_2(+\text{ lagging},-\text{ leading})$$ $$\%VR=\frac{E_2-V_2}{V_2}\times 100\approx \frac{I_2{R}_{02}\cos {\varphi }_2\pm I_2{X}_{02}\sin {\varphi }_2}{V_2}\times 100$$

   • Zero Regulation Condition: $\tan {\varphi }_2=\frac{R_{02}}{X_{02}}$ (leading p.f.)
   • Maximum Regulation Condition: $\tan {\varphi }_2=\frac{X_{02}}{R_{02}}$ (lagging p.f., $\cos {\varphi }_2=\frac{R_{02}}{Z_{02}}$)

5. Efficiency & Maximum Efficiency: $${\eta }_x=\frac{x\cdot \text{kVA}\cdot 10^3\cos \varphi }{x\cdot \text{kVA}\cdot 10^3\cos \varphi +P_i+x^2{P}_{c(FL)}}\times 100$$

   • Condition for ${\eta }_{max}$: $P_i=x^2{P}_{c(FL)}⟹\mathbf{x}=\sqrt{\frac{{\mathbf{P}}_{\mathbf{i}}}{{\mathbf{P}}_{\mathbf{c}(\mathbf{FL})}}}$
   • $\text{kVA for }{\eta }_{max}=\text{Full Load kVA}\times \sqrt{\frac{P_i}{P_{c(FL)}}}$

6. Autotransformer: $$W_a=(1-K)W_o,\text{Saving of Copper}=K\times W_o$$ $$\text{Inductive Power}=(1-K)\times \text{Input},\text{Conducted Power}=K\times \text{Input}$$ $${\text{kVA}}_{\text{auto}}=\frac{{\text{kVA}}_{\text{2-wdg}}}{1-K}$$

7. Parallel Operation (Equal Ratio): $$I_A=I\frac{Z_B}{Z_A+Z_B},I_B=I\frac{Z_A}{Z_A+Z_B}$$ $$S_A=S\frac{Z_B}{Z_A+Z_B},S_B=S\frac{Z_A}{Z_A+Z_B}$$

8. Three-Phase Open-Delta (V-V): $$S_{V-V}=\sqrt{3}{V}_L{I}_L=\frac{1}{\sqrt{3}}{S}_{\Delta -\Delta }=0.577S_{\Delta -\Delta }=86.6\%\times (2\times \text{Rating})$$ $$\text{p.f. of Transformer 1}=\cos (30^{\circ }-\varphi ),\text{p.f. of Transformer 2}=\cos (30^{\circ }+\varphi )$$

9. Scott Connection (T-T):

   • Teaser primary turns: $N_T=0.866N_1=\frac{\sqrt{3}}{2}{N}_1$
   • Converts 3-phase to balanced 2-phase at identical secondary voltage $V_2=V_L(N_2/N_1)$ in $90^{\circ }$ quadrature.

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3.2 Three-Phase Induction Motors (Chapter 8)

1. Synchronous Speed & Slip: $$N_s=\frac{120f}{P},s=\frac{N_s-N}{N_s},N=N_s(1-s)$$ $$f^{\prime }=sf,E_2^{\prime }=s{E}_2,X_2^{\prime }=s{X}_2,Z_2^{\prime }=\sqrt{R_2^2+(s{X}_2{)}^2}$$

2. Rotor Current & Power Factor: $$I_2^{\prime }=\frac{s{E}_2}{\sqrt{R_2^2+(s{X}_2{)}^2}},\cos {\theta }_2^{\prime }=\frac{R_2}{\sqrt{R_2^2+(s{X}_2{)}^2}}$$

3. Torque Equations:

   • Starting Torque ($s=1$): $$T_s=\frac{k{E}_2^2{R}_2}{R_2^2+X_2^2}$$ Maximum Starting Torque occurs when: ${\mathbf{R}}_2={\mathbf{X}}_2$
   • Running Torque at slip $s$: $$T=\frac{k\cdot s\cdot E_2^2\cdot R_2}{R_2^2+(s{X}_2{)}^2}$$
   • Maximum Running Torque ($T_{max}$): $$s_m=\frac{R_2}{X_2},{\mathbf{T}}_{\mathbf{max}}=\frac{\mathbf{k}{\mathbf{E}}_2^2}{2{\mathbf{X}}_2}(\text{independent of }{R}_2!)$$
   • Full-load to Maximum Torque ratio: $$\frac{T_{FL}}{T_{max}}=\frac{2s_m{s}_f}{s_m^2+s_f^2}$$
   • Starting to Maximum Torque ratio: $$\frac{T_s}{T_{max}}=\frac{2s_m}{1+s_m^2}$$

4. Power Flow Ratio (The Golden Rule): $${\mathbf{P}}_2:{\mathbf{P}}_{\mathbf{cu}}:{\mathbf{P}}_{\mathbf{m}}=1:\mathbf{s}:(1-\mathbf{s})$$

   • Rotor Input: $P_2=T_g\times {\omega }_s=\frac{2\pi N_s}{60}{T}_g$
   • Rotor Copper Loss: $P_{cu}=3(I_2^{\prime }{)}^2{R}_2=s{P}_2$
   • Gross Mechanical Power: $P_m=(1-s)P_2=T_g\times \omega =\frac{2\pi N}{60}{T}_g$
   • Shaft Output: $P_{out}=P_m-P_{\text{friction\&windage}}$

5. Mechanical Load Representation: $$R_L^{\prime }=R_2^{\prime }\left(\frac{1-s}{s}\right)=\frac{R_2^{\prime }}{s}-R_2^{\prime }$$

6. Starting Methods & Torques:

   • DOL Starter: $$\frac{T_{st}}{T_{FL}}={\left(\frac{I_{sc}}{I_{FL}}\right)}^2\times s_f$$
   • Stator Resistor Starter (ratio $x$): $$\frac{T_{st}}{T_{FL}}=x^2{\left(\frac{I_{sc}}{I_{FL}}\right)}^2\times s_f,I_{st}=x{I}_{sc}$$
   • Autotransformer Starter (tapping $x$): $$\frac{T_{st}}{T_{FL}}=x^2{\left(\frac{I_{sc}}{I_{FL}}\right)}^2\times s_f,I_{line}=x^2{I}_{sc}$$
   • Star-Delta Starter: $$I_{st(Y)}=\frac{1}{3}{I}_{sc(\Delta )},T_{st(Y)}=\frac{1}{3}{T}_{st(\Delta )}$$ $$\frac{T_{st}}{T_{FL}}=\frac{1}{3}{\left(\frac{I_{sc}}{I_{FL}}\right)}^2\times s_f$$

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3.3 Single-Phase Induction Motors (Chapter 9)

1. Double-Field Revolving Theory: $$\Phi (t)={\Phi }_m\cos \omega t=\frac{{\Phi }_m}{2}{e}^{j\omega t}+\frac{{\Phi }_m}{2}{e}^{-j\omega t}$$

   • Forward slip: $s_f=s$
   • Backward slip: $s_b=\frac{N_s-(-N)}{N_s}=\frac{N_s+N}{N_s}=2-\mathbf{s}$
   • Standstill ($s=1$): $s_f=1,s_b=1⟹T_f=T_b⟹T_{\text{start}}=0$.

2. Starting Torque from Phase-Splitting: $$T_s\propto I_m{I}_s\sin \alpha$$ (Maximum torque when $\alpha =90^{\circ }$).

3. Equivalent Circuit Impedances: $$Z_f=R_f+j{X}_f=\frac{j\frac{X_m}{2}\left(\frac{R_2^{\prime }}{2s}+j\frac{X_2^{\prime }}{2}\right)}{\frac{R_2^{\prime }}{2s}+j\left(\frac{X_m}{2}+\frac{X_2^{\prime }}{2}\right)}$$ $$Z_b=R_b+j{X}_b=\frac{j\frac{X_m}{2}\left(\frac{R_2^{\prime }}{2(2-s)}+j\frac{X_2^{\prime }}{2}\right)}{\frac{R_2^{\prime }}{2(2-s)}+j\left(\frac{X_m}{2}+\frac{X_2^{\prime }}{2}\right)}$$ $$Z_{\text{total}}=(R_1+j{X}_1)+Z_f+Z_b$$ $$T_{\text{net}}=\frac{I_1^2(R_f-R_b)}{{\omega }_s}\text{N-m}$$

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4. Past Exam Questions Cross-Reference (ECE 2207)

Year & Question	Topic Tested	V.K. Mehta Chapter & Section
2023 Q1(a)	EMF equation & transformation ratio derivation	Ch 7, Sec 7.3–7.4
2023 Q1(b)	Transformer equivalent circuit parameter determination from OC & SC tests	Ch 7, Sec 7.18–7.19
2023 Q2(a)	Voltage regulation derivation for lagging & leading power factors	Ch 7, Sec 7.15–7.16
2023 Q2(b)	Maximum efficiency condition & output kVA at ${\eta }_{max}$	Ch 7, Sec 7.27–7.28
2023 Q3(a)	Autotransformer copper saving proof ($W_a=(1-K)W_o$)	Ch 7, Sec 7.34–7.35
2023 Q3(b)	Open-Delta (V-V) connection & 57.7% capacity derivation	Ch 7, Sec 7.45–7.46
2022 Q5(a)	Rotating Magnetic Field proof ($1.5{\Phi }_m$ constant magnitude)	Ch 8, Sec 8.3–8.4
2022 Q5(b)	Torque-slip characteristic and breakdown torque derivation ($R_2=s{X}_2$)	Ch 8, Sec 8.16–8.18
2022 Q6(a)	Power stages ratio ($P_2:P_{cu}:P_m=1:s:1-s$) derivation	Ch 8, Sec 8.24–8.27
2022 Q6(b)	Starting torque comparison: DOL vs Star-Delta vs Autotransformer	Ch 8, Sec 8.36
2021 Q7(a)	Double-Field Revolving Theory and why single-phase motor is not self-starting	Ch 9, Sec 9.2–9.3
2021 Q7(b)	Shaded-pole motor working principle (flux shifting mechanism)	Ch 9, Sec 9.9
2021 Q8(a)	Equivalent circuit of single-phase induction motor based on DFRT	Ch 9, Sec 9.10
2021 Q8(b)	Universal Motor & Repulsion Motor operation	Ch 9, Sec 9.11–9.12

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Created for ECE 2207 — Academic Session 2026