Your Question:

A 36 kVA, 2200/220 V step-down transformer has high voltage and low voltage side winding resistances of 10 2 and 0.3 2 respectively. The leakage reactance referred to the high voltage side is 25 2. The magnetizing impedance is 8 k2, and the resistance corresponding to the core loss is 12 k2, both are referred to the high voltage side.

Step By Step Answers with Explanation

Step 1: Calculate the secondary current (I2) at half load.

The transformer's apparent power (S) is given as 36 kVA, and at half load, it's 18 kVA. We know that:

Step 2: Calculate the impedance drop (Voltage Drop) on the secondary side.

Voltage Drop = I2(Z2), where Z2 is the impedance referred to the secondary side.

Voltage Regulation (%) = (Voltage Drop / V2) * 100

Voltage Regulation (%) = (24.55 V / 220 V) * 100

At 25% load, the apparent power (S) is 25% of the rated power, so S = 9 kVA.

I1 = S / V1, where V1 is the primary voltage (2200 V).

Pin = (2200 V) * (4.09 A)

Pin ≈ 9,018 W

Core Loss (Pcore) = V1^2 / Rm, where Rm is the magnetizing impedance referred to the primary side (8 kΩ).

Pcore = (2200^2) / (8,000 Ω)

Step 4: Calculate the efficiency.

Efficiency (%) = (Pout / (Pout + Pcore + Pcu)) * 100