The EMF equation of a DC generator is one of the most important and frequently asked topics in SSC JE, RRB JE, State AE, and GATE Electrical Engineering exams. This article explains the EMF equation in a step-by-step, conceptual, and numerical-oriented manner to help students score confidently in competitive examinations.
What is EMF in a DC Generator?
In a DC generator, Electromotive Force (EMF) is the voltage induced in the armature conductors due to electromagnetic induction when they rotate under the magnetic field of poles.
According to Faraday’s Law of Electromagnetic Induction, whenever a conductor cuts magnetic flux, an EMF is induced in it.
Principle of DC Generator
A DC generator works on the principle that:
Whenever a conductor rotates in a magnetic field and cuts magnetic flux, an EMF is induced in the conductor.
The direction of induced EMF is given by Fleming’s Right-Hand Rule.
Derivation of EMF Equation of DC Generator
Step 1: Flux Cut by One Conductor in One Revolution
Let:
- Φ = Flux per pole (Weber)
- P = Number of poles
Total flux cut by one conductor in one complete revolution:
Total Flux = P × Φ Weber
Step 2: Time Taken for One Revolution
Let:
- N = Speed of armature in RPM
Time taken for one revolution:
Time = 60 / N seconds
Step 3: EMF Induced in One Conductor
Using EMF equation:
EMF = Flux cut / Time
So,
EMF per conductor = (P × Φ) / (60 / N)
EMF per conductor = (P × Φ × N) / 60 volts
Step 4: EMF Induced in Entire Armature
Let:
- Z = Total number of armature conductors
- A = Number of parallel paths
Conductors in series per parallel path:
Z / A
Hence, generated EMF:
E = (P × Φ × Z × N) / (60 × A)
Standard EMF Equation of DC Generator
The standard EMF equation is:
E = (P Φ Z N) / (60 A) volts
Meaning of Each Term in EMF Equation
| Symbol | Meaning | Unit |
|---|---|---|
| E | Generated EMF | Volts |
| P | Number of poles | — |
| Φ | Flux per pole | Weber |
| Z | Total armature conductors | — |
| N | Speed of armature | RPM |
| A | Parallel paths | — |
Value of Parallel Paths (A)
Lap Winding
For lap winding:
A = P
Wave Winding
For wave winding:
A = 2
EMF Equation for Different Windings
1. DC Generator with Lap Winding
Substitute A = P:
E = (Φ × Z × N) / 60
2. DC Generator with Wave Winding
Substitute A = 2:
E = (P × Φ × Z × N) / 120
Numerical Example (SSC JE / AE Level)
Question:
A 4-pole DC generator has 720 armature conductors, flux per pole of 0.03 Wb, and runs at 600 rpm. If the armature is wave-wound, calculate the generated EMF.
Solution:
- P = 4
- Φ = 0.03 Wb
- Z = 720
- N = 600 rpm
- A = 2 (wave winding)
E = (P × Φ × Z × N) / (60 × A)
E = (4 × 0.03 × 720 × 600) / (60 × 2)
E = 432 volts
Important Exam-Oriented Points
- Generated EMF is directly proportional to flux (Φ).
- Generated EMF is directly proportional to speed (N).
- At constant speed, EMF ∝ Φ.
- At constant flux, EMF ∝ N.
- Wave winding produces higher voltage than lap winding.
Difference Between EMF of Lap and Wave Winding
| Lap Winding | Wave Winding |
|---|---|
| More parallel paths | Only two parallel paths |
| Low voltage, high current | High voltage, low current |
| Used in high-current machines | Used in high-voltage machines |
Frequently Asked Questions (FAQs)
Q1. What is the EMF equation of a DC generator?
The EMF equation of a DC generator is: E = (P Φ Z N) / (60 A).
Q2. On which factors does generated EMF depend?
Generated EMF depends on flux per pole, speed of rotation, number of armature conductors, and winding type.
Q3. Why wave winding gives higher EMF?
Because wave winding has only two parallel paths, more conductors are connected in series, resulting in higher voltage.
Q4. Is EMF proportional to speed?
Yes, EMF is directly proportional to speed when flux is constant.
Q5. Is EMF equation same for DC motor?
Yes, the EMF equation is same, but in motors it represents back EMF instead of generated EMF.
Conclusion
The EMF equation of a DC generator is a fundamental and scoring topic in electrical engineering exams. Understanding its derivation, physical meaning, and numerical application helps students solve a wide range of questions in SSC JE, RRB JE, State AE, and GATE examinations with confidence.
For more PYQs, numericals, and concept-based explanations, keep following Electrical JE Education.