Question

A 200 KVA, 1000/400 V transformer has primary resistance and secondary resistance of 0.4 Ω and 0.3 Ω. Calculate the copper loss of the transformer.
1. 91 kW
2. 51 kW
3. 123 kW
4. 61 kW

Answer 1

Correct Answer - Option 1 : 91 kW

Concept:

There are two major losses in the transformer ie core loss and cu loss.

• Core loss occurs in the magnetic core of the transformer and it is constant.
• Copper loss occurs in the winding of the transformer and it is variable.

 

Total Cu loss = \(\rm I_1^2 R_1 + I_2^2 R_2\)

\(= \rm I_1^2 R_1 + I_1^2 R_2'\)

\(= I_1^2 (R_1 + R_2') = I_1^2R_{01}\)

Where R₂' = Resistance transferred from secondary to primary after transferring resistance Cu losses should be the same.

\(\rm I_1^2 R_x + I_1^2 R_2'\)

⇒ \(R_2' = \left( \frac{I_2}{I_1} \right) ^2 \cdot R_2 = \left( \frac{N_1}{N_2} \right)^2 R_2\)

⇒ R₂' = \(\frac{1}{K^2} R_2\)

Calculation:

Given, R₁ = 0.4 Ω,

 \(\rm R_2' = \left( \frac{1000}{400} \right)^2 × 0.3\)

\(= \frac{100}{16} × 0.3\)

= 1.875

∴ R₁ + R₂' = 0.4 + 1.875 = 2.275

\(I_1 = \frac{200 × 10^3}{1000} = 200 A\)

∴ Copper loss = \(I_1^2 (R_1 + R_2')\)

= (200)}2} × 2.275

= 91000 w

i.e., 91 kW

∴ option (1) is correct.