š Transformer – Ideal Theory & EMF Equation
Transformer works on the principle of mutual induction. It transfers power from one circuit to another without electrical connection.
š¹ 1. Basic Principle
Based on Faraday’s Law:e = -N dĪ¦/dt
Changing flux produces induced EMF.š¹ 2. EMF Equation
For sinusoidal flux:E = 4.44 f N Ī¦_max
Where: f = frequency N = number of turns Ī¦_max = maximum flux Very important formula for GATE.š¹ 3. Turns Ratio
a = N₁ / N₂
Voltage ratio:V₁ / V₂ = N₁ / N₂
Current ratio:I₁ / I₂ = N₂ / N₁
Power approximately constant:V₁ I₁ = V₂ I₂
š¹ 4. Ideal Transformer Assumptions
- No copper loss
- No core loss
- No leakage flux
- Infinite permeability
š¹ 5. Example 1 – EMF Calculation
Given: f = 50 Hz N = 500 turns Ī¦_max = 0.01 Wb Find induced EMF. Solution:E = 4.44 × 50 × 500 × 0.01 E = 1110 Volts
š¹ 6. Example 2 – Turns Ratio
Primary voltage = 2200 V Secondary voltage = 220 V Find turns ratio. Solution:a = 2200 / 220 = 10
Step-down transformer (10:1)šÆ GATE Important Points
- EMF equation frequently asked
- Voltage proportional to turns
- Current inversely proportional to turns
- Frequency affects induced voltage
Transformer = Magnetic Energy Transfer Device
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