Number of tappings to each equalizer ring is equal to number of

(a) poles.
(b) pole pairs.
(c) parallel paths.
(d) commutator segments.

Answer: (a) poles.

Explanation:

1. CONCEPT: Equalizer Rings in DC Machines

Equalizer rings are low-resistance copper conductors used in lap-wound DC armatures to connect points of equal potential.

Main Purpose:

• To prevent circulating currents

• To balance current in parallel paths

• To reduce sparking

• To protect brushes and commutator

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2. Number of Tappings on Each Equalizer Ring

Important Result:

👉 Number of tappings on each equalizer ring = Number of poles (P)

Reason:

• In lap winding:

  $$\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">A</span></span>}<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">=</span></span>\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">P</span></span>}$$

• Each parallel path corresponds to one pole

• Equalizer rings connect these paths

• Hence, one tapping per pole is required

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3. Brushes in DC Machines

Function:

• Collect current from commutator

• Supply current to armature

Material:

• Carbon / Graphite

Number of Brushes:

Winding Type	Parallel Paths (A)	Brushes
Lap Winding	A = P	P
Wave Winding	A = 2	2

👉 Number of brushes = Number of parallel paths

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4. Interpoles (Commutating Poles)

Location:

• Between main poles on yoke

Connection:

• Connected in series with armature

Function:

• Neutralize armature reaction

• Improve commutation

• Maintain Magnetic Neutral Axis (MNA)

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5. Equalizer Rings in Lap Winding

Why Required in Lap Winding?

In lap winding:

$$\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">A</span></span>}<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">=</span></span>\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">P</span></span>}$$

So:

• Many parallel paths

• Higher chances of imbalance

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Ideal Condition:

• All poles have same flux

• All paths carry equal current

Practical Condition:

Due to:

• Unequal air gap

• Different pole materials

• Manufacturing defects

→ Flux becomes unequal

→ EMF becomes unequal

→ Current imbalance occurs

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Effects of Imbalance:

• Some paths carry more current

• Some brushes overloaded

• Incomplete current reversal

• Heavy sparking

• Commutator damage

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Role of Equalizer Rings

They:

• Connect equal potential points

• Provide low-resistance path

• Carry circulating currents internally

• Prevent current through brushes

Result:
✔ Balanced current
✔ Sparkless commutation
✔ Longer machine life

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6. Why Equalizer Rings Are Used Only in Lap Winding

Feature	Lap Winding	Wave Winding
Parallel paths	Many (P, 2P, 3P)	Only 2
Current imbalance	High	Low
Need of equalizer	Yes	No

👉 Wave winding has only 2 paths → less imbalance → no equalizer rings

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7. Dummy Coils in Wave Winding

Used Only in Wave Winding

Wave winding is an incomplete winding.

Some slots remain empty.

These slots are filled with dummy coils.

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Dummy Coil Properties:

• Physically present

• Electrically disconnected

• Not connected to commutator

Purpose:

✔ Mechanical balance only
✔ No electrical role

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8. Lap vs Wave Winding Comparison

Feature	Lap Winding	Wave Winding
Other name	Parallel winding	Series winding
Parallel paths	A = mP	A = 2m
Voltage	Low	High
Current	High	Low
Efficiency	Lower	Higher
Equalizer rings	Required	Not required
Dummy coils	Not used	Used
Applications	Heavy current	High voltage

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9. Multiplicity of Windings

Lap Winding:

Type	Parallel Paths (A)
Simplex	A = P
Duplex	A = 2P
Triplex	A = 3P

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Wave Winding:

$$\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">A</span></span>}<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">=</span></span>\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">2</span></span>}\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">m</span></span>}$$

Type	A
Simplex	2
Duplex	4
Triplex	6

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10. Pitch Relations

Lap Winding

• Commutator pitch:

  $${\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">Y</span></span>}}_{\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">c</span></span>}}<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">=</span></span><span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">\pm </span></span>\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">1</span></span>}$$

• Resultant pitch:

  $${\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">Y</span></span>}}_{\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">R</span></span>}}<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">=</span></span>{\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">Y</span></span>}}_{\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">B</span></span>}}<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">-</span></span>{\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">Y</span></span>}}_{\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">F</span></span>}}$$

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Wave Winding

• Resultant pitch:

  $${\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">Y</span></span>}}_{\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">R</span></span>}}<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">=</span></span>{\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">Y</span></span>}}_{\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">B</span></span>}}<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">+</span></span>{\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">Y</span></span>}}_{\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">F</span></span>}}$$

• Commutator pitch:

  $${\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">Y</span></span>}}_{\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">c</span></span>}}<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">=</span></span>{\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">Y</span></span>}}_{\mathrm{<span\; style="font-size:\; medium;"><span\; style="font-family:\; Source\; Serif\; Pro;">A</span></span>}}$$

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11. Important Exam Facts ⭐

One-Line Answers:

✔ Equalizer rings are used in lap winding only.
✔ Number of tappings per ring = Number of poles.
✔ Dummy coils are used in wave winding.
✔ Number of brushes = Number of parallel paths.
✔ Lap winding → High current, low voltage.
✔ Wave winding → High voltage, low current.

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12. Summary for Revision (Very Important)

Equalizer Rings

• Used in lap winding

• Balance currents

• Reduce sparking

• Number of tappings = P

Dummy Coils

• Used in wave winding

• Provide mechanical balance

• No electrical function

Brushes

• Made of carbon

• Number = A

Interpoles

• Improve commutation

• Connected in series

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13. Final Exam-Oriented Conclusion ⭐

Equalizer rings are low-resistance conductors used in lap-wound DC machines to balance unequal currents in parallel paths. Each ring has as many tappings as poles. They prevent brush overloading and sparking. Wave windings do not require equalizer rings but use dummy coils for mechanical balance.