Question

A 4kVA, 400V/200V single-phase transformer has resistance of 0.02 pu and reactance of 0.06 pu. The resistance and reactance referred to HV side are:

• A. 0.2 ohm and 0.6 ohm
• B. 0.8 ohm and 2.4 ohm
• C. 0.08 ohm and 0.24 ohm
• D. 1 ohm and 3 ohm

Hint:

To convert per-unit values to ohmic values, multiply by the square of the ratio of the rated voltage of the HV and LV sides.

Answer 1

The Correct Option is C

The transformer is given with per-unit values, and we need to convert these to ohmic values referred to the HV side. The formula for converting the per-unit values to ohms is: \[ R_{\text{ohms}} = R_{\text{pu}} \times \left( \frac{V_{\text{rated}}}{\text{base voltage}} \right)^2 \] For the given transformer:
- \( R_{\text{pu}} = 0.02 \) and \( X_{\text{pu}} = 0.06 \)
- Rated voltage \( V_{\text{rated}} = 400V \) (HV side)
Using the per-unit system for conversion:
- Resistance referred to HV side:
\[ R_{\text{ohms}} = 0.02 \times \left( \frac{400}{200} \right)^2 = 0.02 \times 4 = 0.08 \, \text{ohms} \] - Reactance referred to HV side:
\[ X_{\text{ohms}} = 0.06 \times \left( \frac{400}{200} \right)^2 = 0.06 \times 4 = 0.24 \, \text{ohms} \] Thus, the resistance and reactance referred to the HV side are 0.08 ohms and 0.24 ohms, which corresponds to option (3).