The EMF equation of transformer is a fundamental topic in electrical engineering and is frequently asked in SSC JE, RRB JE, State AE, and GATE exams. This article explains the EMF equation in a clear, step-by-step, and exam-oriented manner with derivation, numerical examples, and FAQs.
What is EMF in a Transformer?
In a transformer, Electromotive Force (EMF) is the voltage induced in the primary and secondary windings due to mutual electromagnetic induction when an alternating magnetic flux links both windings.
The induced EMF exists only when the transformer is supplied with AC voltage.
Principle of Transformer
A transformer works on the principle of:
Mutual Induction – When an alternating current flows in the primary winding, it produces an alternating magnetic flux that links the secondary winding and induces EMF in it.
The phenomenon follows Faraday’s Laws of Electromagnetic Induction.
Assumptions for EMF Equation of Transformer
- Flux varies sinusoidally with time
- Winding resistance is negligible
- Leakage flux is neglected
- Core losses are ignored
Derivation of EMF Equation of Transformer
Step 1: Expression for Magnetic Flux
Let the maximum flux in the core be:
Φm = Maximum flux (Weber)
For sinusoidal flux:
Φ = Φm sin ωt
Step 2: Rate of Change of Flux
Induced EMF is given by Faraday’s law:
e = N × dΦ/dt
Differentiating:
dΦ/dt = ω Φm cos ωt
Step 3: Maximum Value of Induced EMF
Maximum value occurs when cos ωt = 1:
emax = N × ω × Φm
Where ω = 2πf
emax = 2πf N Φm
Step 4: RMS Value of Induced EMF
RMS value of sinusoidal EMF:
E = emax / √2
Substituting:
E = (2πf N Φm) / √2
After simplification:
E = 4.44 f N Φm
Standard EMF Equation of Transformer
EMF per Winding
E = 4.44 f N Φm
EMF Equation for Primary and Secondary
Primary Winding EMF
E1 = 4.44 f N1 Φm
Secondary Winding EMF
E2 = 4.44 f N2 Φm
EMF per Turn of Transformer
EMF per turn is:
Et = 4.44 f Φm
This relation is very important for transformer design and numericals.
Voltage Ratio of Transformer
From EMF equations:
E1 / E2 = N1 / N2
Hence, voltage ratio equals turns ratio.
Numerical Example (SSC JE / AE Level)
Question:
A single-phase transformer has 400 primary turns and 100 secondary turns. If the supply frequency is 50 Hz and maximum flux is 0.02 Wb, calculate the primary and secondary EMF.
Solution:
Given:
- N1 = 400
- N2 = 100
- f = 50 Hz
- Φm = 0.02 Wb
Primary EMF:
E1 = 4.44 × 50 × 400 × 0.02 = 1776 V
Secondary EMF:
E2 = 4.44 × 50 × 100 × 0.02 = 444 V
Important Exam-Oriented Points
- Transformer EMF exists only with AC supply.
- EMF is directly proportional to frequency.
- EMF is directly proportional to number of turns.
- DC supply produces zero induced EMF.
- EMF equation is independent of load.
Difference Between EMF Equation of DC Generator and Transformer
| DC Generator | Transformer |
|---|---|
| EMF due to rotation | EMF due to alternating flux |
| Mechanical input required | No mechanical motion |
| Depends on speed | Depends on frequency |
Frequently Asked Questions (FAQs)
Q1. What is the EMF equation of transformer?
The EMF equation of transformer is E = 4.44 f N Φm.
Q2. Why 4.44 constant is used in EMF equation?
The constant 4.44 comes from RMS value conversion and sinusoidal waveform of flux.
Q3. Can transformer work on DC supply?
No, because DC does not produce alternating flux and hence no induced EMF.
Q4. On which factors does transformer EMF depend?
Transformer EMF depends on frequency, number of turns, and maximum flux.
Q5. Is EMF same on load and no-load?
Yes, induced EMF remains nearly constant as it depends only on supply voltage and frequency.
Conclusion
The EMF equation of transformer is a core concept in electrical engineering. A clear understanding of its derivation, physical meaning, and numerical application is essential for scoring well in JE, AE, and GATE exams.
For more exam-focused electrical engineering content, keep following Electrical JE Education.