Qwestrum Engineering360 · Electrical & Electronics · Electrical Machines – II
Single Phase Induction Motor
A single-phase induction motor produces no starting torque on its own because its pulsating field splits into two equal counter-rotating fields; an auxiliary winding or capacitor creates the phase split needed to start it.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.
Key formulas & points
Skim these first — then read the full notes below.
- Capacitor start/run improves starting torque and pf
- Shaded pole motor: low starting torque, small fans
- Double revolving field theory explains zero starting torque
Topic details
Introduction
Double revolving field theory explains the zero starting torque: a single stator winding produces a pulsating MMF equivalent to two fields of half amplitude rotating in opposite directions. At standstill their torques cancel, so the rotor will not self-start but will continue if given a push.
Scope in B.Tech and GATE syllabus
Starting methods create a rotating field by adding a second, displaced winding. Split-phase uses a high-resistance auxiliary winding; capacitor-start adds a series capacitor for a near-90° phase split and much higher starting torque.
Key relations & formulas
Formulas (Indian textbook notation)
Formulas (Indian textbook notation)
Formulas (Indian textbook notation)
Notation and sign conventions
Relation 1 —
Formulas (Indian textbook notation)
Write this relation with symbols exactly as in Electrical Machines — Nagrath & Kothari before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
Formulas (Indian textbook notation)
Write this relation with symbols exactly as in Electrical Machines — Nagrath & Kothari before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
Formulas (Indian textbook notation)
Write this relation with symbols exactly as in Electrical Machines — Nagrath & Kothari before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Fundamentals and definitions
In the equivalent circuit, the rotor impedance splits into a forward branch (slip s) and a backward branch (slip 2−s). The forward field produces most of the useful torque; the backward field produces a small braking torque and extra loss.
Governing relations in practice
Capacitor-run motors keep the capacitor in circuit for better running power factor and smoother torque; capacitor-start-capacitor-run uses two capacitors for both high starting torque and good running performance.
Design and analysis considerations
Shaded-pole motors use a shorted copper ring on part of each pole to create a weak rotating field — cheap, low torque, used in small fans.
Assumptions and validity limits
State assumptions explicitly before using any relation for single phase induction motor — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Electrical Machines II viva and GATE descriptive questions, listing valid assumptions often earns separate marks.
Step-by-step problem approach
1. Read the question and list given data with SI units (common in Electrical Machines II papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to single phase induction motor.
4. Use equation 1:
5. Use equation 2:
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to single phase induction motor.
4. Use equation 1:
.
5. Use equation 2:
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.
Applications & exam relevance
Single Phase Induction Motor appears in industrial motors and generators. In Indian electrical curricula this topic is tested because it connects theory to induction and synchronous machines.
GATE and semester exams often combine single phase induction motor with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use single phase induction motor?" — answer with a lab, mini-project, or plant visit example if possible.
Common mistakes in exams
• Claiming a single-phase motor has zero running torque (it is only starting torque that is zero)
• Using slip s for the backward field branch instead of (2−s)
• Ignoring the backward-field losses when computing efficiency
• Confusing capacitor-start (start only) with capacitor-run configurations
• Using slip s for the backward field branch instead of (2−s)
• Ignoring the backward-field losses when computing efficiency
• Confusing capacitor-start (start only) with capacitor-run configurations
Quick revision checklist
Before attempting single phase induction motor problems, confirm you can:
1. Capacitor start/run improves starting torque and pf
2. Shaded pole motor: low starting torque, small fans
3. Double revolving field theory explains zero starting torque
2. Shaded pole motor: low starting torque, small fans
3. Double revolving field theory explains zero starting torque
Revise the solved examples in Electrical Machines — Nagrath & Kothari and one previous-year GATE or university paper for this unit.
Worked examples
Try the problem first — open the solution when you are ready to check.
Backward-field slip
Problem
A single-phase induction motor runs at a slip of 0.05 with respect to its forward field. Find the slip of the rotor with respect to the backward rotating field.
Solution
Forward slip s = 0.05.
Backward field rotates opposite to the rotor, so backward slip = 2 − s.
s_b = 2 − 0.05 = 1.95.
This high slip is why the backward branch impedance is low and its torque acts as a small brake.
Backward field rotates opposite to the rotor, so backward slip = 2 − s.
s_b = 2 − 0.05 = 1.95.
This high slip is why the backward branch impedance is low and its torque acts as a small brake.
Conceptual check — Single Phase Induction Motor
Problem
In a Electrical Machines II semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of single phase induction motor." What should a complete answer include?
Exams & GATE
Nagrath & Kothari — why single-phase motor needs starting aid.
📖 Standard books (India)
Electrical Machines — Nagrath & Kothari
Read: Syllabus unit
Transformers, DC machines, and induction motors
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