--- title: "Long shunt compound generator speed, lap and wave" subject: "Electrical Machines" chapter: 3 key: "semester_4/electrical_machines:gen-long-shunt-10kw-lap-wave" source: https://www.bctengineer.com/q/semester_4/electrical_machines/gen-long-shunt-10kw-lap-wave site: BCT Engineering --- # Long shunt compound generator speed, lap and wave Electrical Machines · Chapter 3: DC Generator - Asked in: 2078 Poush, 8 marks - Video: [Problems on DC Generators, shunt and compound generators](https://www.youtube.com/watch?v=69kUeAA1dYk) — Electrical and Electronics engg classes made easy - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/electrical_machines/gen-long-shunt-10kw-lap-wave - Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-3 ## Question A 4 pole, 250 V dc long shunt compound generator supplies a load of 10 kW at rated voltage. The armature, series field and shunt field resistances are $0.1\ \Omega$, $0.15\ \Omega$ and $250\ \Omega$ respectively. The armature is lap wound with 50 slots, each slot containing 6 conductors. If the flux per pole is 50 mWb, calculate the speed of generator. What would be the speed of same generator if armature is wave wound? ## Short answer With 40 A load at 250 V, shunt field current 1 A, armature current 41 A, generated emf = 260.25 V. For lap winding (300 conductors, A=4): speed = 1041.0 rpm. For wave winding (A=2): speed = 520.5 rpm. ## Answer In a long shunt compound generator the shunt field is across the **armature plus series field combination** (i.e. across the load terminals), so the series field carries the armature current. ```text Ia Rse +--->---[~~~~]---+---------+----o + | | | (E,Ra) [Rsh] Load | | | +----------------+---------+----o - ``` #### Currents $$ I_L = \frac{10000}{250} = 40\ \text{A}, \qquad I_{sh} = \frac{250}{250} = 1\ \text{A} $$ $$ I_a = I_{se} = I_L + I_{sh} = 40 + 1 = 41\ \text{A} $$ #### Generated emf $$ E_g = V + I_a(R_a + R_{se}) = 250 + 41(0.1 + 0.15) = 260.25\ \text{V} $$ #### Speed with lap winding Slots $\times$ conductors per slot: $Z = 50\times 6 = 300$. For lap winding $A = P = 4$. $$ E_g = \frac{\Phi Z N P}{60A} \;\Rightarrow\; N = \frac{60AE_g}{\Phi Z P} = \frac{60\times 4\times 260.25}{0.05\times 300\times 4} = 1041.0\ \text{rpm} $$ #### Speed with wave winding For wave winding $A = 2$; $E_g$, $\Phi$, $Z$ and $P$ are unchanged. $$ N = \frac{60\times 2\times 260.25}{0.05\times 300\times 4} = 520.5\ \text{rpm} $$ The wave-wound machine needs only half the speed because it has half the parallel paths (twice the conductors in series per path). **Answer:** lap wound: $N = 1041.0\ \text{rpm}$; wave wound: $N = 520.5\ \text{rpm}$. (Brush drop is not given, so it is neglected.) ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In a long shunt compound generator, the armature current Ia equals: A. I_L only B. I_L - I_sh C. I_L + I_sh, and the series field carries the same current D. I_sh only Answer: C. The shunt is across armature plus series, so the series carries Ia = IL + Ish. (Key point: Long shunt currents) 2. Which expression gives the generated emf of a long shunt generator (brush drop neglected)? A. E = V + Ia Ra B. E = V - Ia(Ra + Rse) C. E = V + IL(Ra + Rse) D. E = V + Ia(Ra + Rse) Answer: D. Both armature and series field resistances carry Ia and drop voltage. (Key point: Generated emf) 3. With E = 260.25 V, Phi = 0.05 Wb, Z = 300, P = 4 and lap winding (A = 4), the speed is: A. 1041 rpm B. 520.5 rpm C. 2082 rpm D. 260 rpm Answer: A. N = 60x4x260.25/(0.05x300x4) = 1041 rpm. (Key point: Lap speed) 4. Why does the same generator need only about half the speed when wave wound? A. Flux per pole doubles B. A = 2 instead of 4, so conductors in series per path double C. Generated emf halves D. Armature resistance halves Answer: B. N is proportional to A, so changing A from 4 to 2 halves the speed to 520.5 rpm. (Key point: Wave winding speed) ## Close variants set in other exams - [Long shunt compound generator speed, 300 conductors](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Agen-long-shunt-10kw-300-conductors) — Electrical Machines, chapter 3, asked 2× ## Related in Electrical Machines - [4-pole shunt generator, wave wound, 3 kW](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Agen-wave-wound-3kw-120v) — Electrical Machines, chapter 3, asked 3× - [Short shunt to long shunt compound generator (10 kW, 220 V)](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashort-shunt-cumulative-10kw-220v-long) — Electrical Machines I, chapter 3 - [EMF of short shunt compound generator (6 kW, 250 V)](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashort-shunt-compound-6kw-250v) — Electrical Machines I, chapter 3 - [EMF and efficiency of short shunt compound generator (50 A, 200 V)](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashort-shunt-compound-50a-200v) — Electrical Machines I, chapter 3, asked 2× - [Wave-wound shunt generator, power absorbed by load](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Agen-shunt-378-conductors-load-power) — Electrical Machines, chapter 3 - [Compound generator EMF in long and short shunt](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Acompound-gen-120a-120v-long-short) — Electrical Machines I, chapter 3, asked 2× ## Related in other subjects - [Long shunt compound generator speed](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Along-shunt-compound-300-conductors-speed) — Electrical Machine, chapter 3 - [Armature dimensions of 50 kW shunt generator](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Adc-generator-50kw-armature) — Electric Machine Design, chapter 5 - [EMF of short shunt compound generator (0.5 Ω armature)](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashort-shunt-compound-50a-200v-0p5ohm) — Electrical Machines I, chapter 3, asked 2× - [4-pole shunt generator, 3 kW at 120 V](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Ashunt-generator-4pole-wave-3kw) — Electrical Machine, chapter 3, asked 2×