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.

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)

  • PulsatingfieldresolvesintotwocounterrotatingfieldsPulsating field resolves into two counter-rotating fields

Formulas (Indian textbook notation)

  • StartingtorquezerowithoutauxiliarywindingcapacitorStarting torque zero without auxiliary \frac{winding}{capacitor}

Formulas (Indian textbook notation)

  • Equivalentcircuit:mainandauxiliarybranchesEquivalent circuit: main and auxiliary branches

Notation and sign conventions

Relation 1 —
PulsatingfieldresolvesintotwocounterrotatingfieldsPulsating field resolves into two counter-rotating fields

Formulas (Indian textbook notation)

  • PulsatingfieldresolvesintotwocounterrotatingfieldsPulsating field resolves into two counter-rotating fields
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 —
StartingtorquezerowithoutauxiliarywindingcapacitorStarting torque zero without auxiliary \frac{winding}{capacitor}

Formulas (Indian textbook notation)

  • StartingtorquezerowithoutauxiliarywindingcapacitorStarting torque zero without auxiliary \frac{winding}{capacitor}
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 —
Equivalentcircuit:mainandauxiliarybranchesEquivalent circuit: main and auxiliary branches

Formulas (Indian textbook notation)

  • Equivalentcircuit:mainandauxiliarybranchesEquivalent circuit: main and auxiliary branches
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:
PulsatingfieldresolvesintotwocounterrotatingfieldsPulsating field resolves into two counter-rotating fields
.
5. Use equation 2:
StartingtorquezerowithoutauxiliarywindingcapacitorStarting torque zero without auxiliary \frac{winding}{capacitor}
.
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

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
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.

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 MachinesNagrath & Kothari

    Read: Syllabus unit

    Transformers, DC machines, and induction motors