---
title: "10 kVA 200/400 V test parameters"
subject: "Electrical Machine"
chapter: 2
key: "semester_4/electrical_machine:transformer-10kva-test-params"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/transformer-10kva-test-params
site: BCT Engineering
---

# 10 kVA 200/400 V test parameters

Electrical Machine · Chapter 2: Transformer

- Asked in: 2075 Baisakh, 8 marks
- Video: [Numerical 7: A 10 kVA, 200/400V, 50Hz transformer has the following test results](https://www.youtube.com/watch?v=nFmiCeoM8Mc) — Progress Edu
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/transformer-10kva-test-params
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-2

## Question

A 10 KVA, 200/400 V, 50 Hz single-phase transformer gave the following test results:
O.C. test: 200 V, 1.3 A, 120 W, on L.V. side.
S.C. test: 22 V, 30 A, 200 W, on H.V. side.
Calculate: Iμ, Iw, Ro, Xo, Ro2, Xo2 and Zo2.

## Short answer

From OC test on LV: Iμ=1.153 A, Iw=0.600 A, Ro=333.3 Ω, Xo=173.4 Ω. From SC test on HV: Ro2=0.222 Ω, Xo2=0.699 Ω, Zo2=0.733 Ω.

## Answer

**Given:** 10 kVA, 200/400 V, 50 Hz. OC test on the LV (200 V) side; SC test on the HV (400 V) side. Subscript 2 refers to the HV (secondary) side, since the series parameters are from the HV-side test; Ro, Xo are on the LV side where the OC test was done.

#### No-load parameters (LV side, from OC test)
```text
cos φ0 = W0/(V0 I0) = 120/(200 × 1.3) = 0.4615
Iw  = I0 cos φ0 = 1.3 × 0.4615 = 0.600 A
Iμ  = √(I0² − Iw²) = √(1.69 − 0.36) = 1.153 A
Ro  = V0/Iw = 200/0.600 = 333.3 Ω
Xo  = V0/Iμ = 200/1.153 = 173.4 Ω
```

#### Series parameters (HV side, from SC test)
```text
Zo2 = Vsc/Isc = 22/30 = 0.7333 Ω
Ro2 = Wsc/Isc² = 200/30² = 0.2222 Ω
Xo2 = √(Zo2² − Ro2²) = √(0.5378 − 0.0494) = 0.6989 Ω
```

| Quantity | Value |
|---|---|
| Iμ | 1.153 A |
| Iw | 0.600 A |
| Ro | 333.3 Ω (LV side) |
| Xo | 173.4 Ω (LV side) |
| Ro2 | 0.222 Ω (HV side) |
| Xo2 | 0.699 Ω (HV side) |
| Zo2 | 0.733 Ω (HV side) |

**Answer:** Iμ = 1.153 A, Iw = 0.6 A, Ro = 333.3 Ω, Xo = 173.4 Ω, Ro2 = 0.222 Ω, Xo2 = 0.699 Ω, Zo2 = 0.733 Ω. The rated HV current is 10 000/400 = 25 A, so the 30 A used in the test is above rated (accepted as given).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. From which test, and on which side, are Ro and Xo obtained here?
   A. SC test on HV side
   B. OC test on LV side (200 V)
   C. SC test on LV side
   D. OC test on HV side
   Answer: B. The OC test was done at 200 V on the LV side, so Ro and Xo are LV-side values. (Key point: OC test side parameters)

2. What is the core-loss component of current Iw?
   A. 1.153 A
   B. 1.3 A
   C. 0.4615 A
   D. 0.600 A
   Answer: D. cos φ0 = 120/(200 × 1.3) = 0.4615, and Iw = 1.3 × 0.4615 = 0.6 A. (Key point: Iw)

3. How is Ro calculated?
   A. Ro = V0/Iw
   B. Ro = V0/Iμ
   C. Ro = W0/I0
   D. Ro = V0/I0
   Answer: A. Ro carries the loss component Iw, so Ro = V0/Iw = 333.3 Ω. (Key point: Ro formula)

4. What is Zo2 and how is Ro2 found from the SC test?
   A. Zo2 = 0.733 Ω; Ro2 = Wsc/Isc² = 0.222 Ω
   B. Zo2 = 0.733 Ω; Ro2 = Wsc/Isc = 6.67 Ω
   C. Zo2 = 1.36 Ω; Ro2 = Wsc/Isc² = 0.222 Ω
   D. Zo2 = 0.733 Ω; Ro2 = Vsc/Wsc
   Answer: A. Zo2 = 22/30 = 0.733 Ω and Ro2 = 200/900 = 0.222 Ω. (Key point: SC parameters)

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