GATE Electrical Engineering - Complete Master Library

 

📘 Transformer Equivalent Circuit – Complete Explanation

Equivalent circuit represents real transformer behavior using resistances and reactances. This model is essential for regulation and efficiency calculations.

---

🔹 1. Practical Transformer Components

Primary Side:

• R₁ – Primary resistance
• X₁ – Primary leakage reactance

Secondary Side:

• R₂ – Secondary resistance
• X₂ – Secondary leakage reactance

Core:

• Rc – Core loss resistance
• Xm – Magnetizing reactance

---

🔹 2. Referring Secondary to Primary

Turns ratio:

a = N₁ / N₂

Referred values:

R₂' = a² R₂ X₂' = a² X₂

Total equivalent resistance:

R_eq = R₁ + R₂'

Total equivalent reactance:

X_eq = X₁ + X₂'

---

🔹 3. Approximate Equivalent Circuit

Since magnetizing current is small: Shunt branch moved to input. Used for most numerical problems.

---

🔹 4. Example 1

Given: R₁ = 0.5 Ω R₂ = 0.02 Ω Turns ratio a = 10 Find R_eq referred to primary. Solution:

R₂' = 10² × 0.02 R₂' = 2 Ω R_eq = 0.5 + 2 R_eq = 2.5 Ω

---

🔹 5. Example 2 – Impedance Calculation

If: X₁ = 0.6 Ω X₂ = 0.03 Ω a = 5 Find X_eq.

X₂' = 5² × 0.03 = 0.75 Ω X_eq = 0.6 + 0.75 = 1.35 Ω

---

🔹 6. Important Concepts

• Parameters can be referred to either side
• Multiply by a² when referring resistance/reactance
• Used in regulation and efficiency problems

---

🎯 GATE Important Points

• Always check which side parameters are referred to
• Use approximate circuit for quick calculation
• Understand meaning of Rc and Xm
• Equivalent impedance used in voltage drop calculation

Equivalent Circuit = Key to All Transformer Numericals