---
title: "10 kVA 200/400 V LV-side parameters"
subject: "Electrical Machine"
chapter: 2
key: "semester_4/electrical_machine:transformer-10kva-oc-sc-lv-circuit"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/transformer-10kva-oc-sc-lv-circuit
site: BCT Engineering
---

# 10 kVA 200/400 V LV-side parameters

Electrical Machine · Chapter 2: Transformer

- Asked in: 2068 Bhadra, 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-oc-sc-lv-circuit
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-2

## Question

A 10 kVA, 200/400 V, 50 Hz, 1-phase, transformer gave the following test results:
OC test (HV open): 200 V, 1.3 A, 120 W
SC test (LV short): 22 V, 30 A, 200 W
Determine shunt and series branch parameters referred to Low Voltage side and hence draw equivalent circuit diagram also.

## Short answer

Referred to LV side: shunt Ro=333.3 Ω, Xo=173.4 Ω; series R01=0.0556 Ω, X01=0.1747 Ω (Z01=0.1833 Ω).

## Answer

**Given:** 10 kVA, 200/400 V. OC test on LV side: 200 V, 1.3 A, 120 W. SC test on the HV side (HV supplied, LV shorted): 22 V, 30 A, 200 W. Turns ratio K = 400/200 = 2.

#### Shunt branch (LV side, directly from OC test)
```text
cos φ0 = 120/(200 × 1.3) = 0.4615
Iw = 1.3 × 0.4615 = 0.600 A ;  Iμ = √(1.3² − 0.6²) = 1.153 A
Ro = 200/0.600 = 333.3 Ω ;  Xo = 200/1.153 = 173.4 Ω
```

#### Series branch
SC on the HV side gives the parameters referred to the HV side:
```text
Z02 = 22/30 = 0.7333 Ω ;  R02 = 200/30² = 0.2222 Ω
X02 = √(0.7333² − 0.2222²) = 0.6989 Ω
```
Refer to the LV side by dividing by K² = 4:
```text
R01 = 0.2222/4 = 0.0556 Ω
X01 = 0.6989/4 = 0.1747 Ω
Z01 = 0.7333/4 = 0.1833 Ω
```

#### Equivalent circuit referred to the LV side
```text
  I1     R01=0.0556Ω  X01=0.1747Ω       I2'
 o──┬─────┬──────/\/\/───────(((─────────o
    │     │                              
   Ro    Xo                         load
 333.3Ω 173.4Ω                       V2' = V2/2
    │     │                              
 o──┴─────┴──────────────────────────────o
```

| Parameter | Value (LV side) |
|---|---|
| Ro | 333.3 Ω |
| Xo | 173.4 Ω |
| R01 | 0.0556 Ω |
| X01 | 0.1747 Ω |
| Z01 | 0.1833 Ω |

**Answer:** shunt branch Ro = 333.3 Ω, Xo = 173.4 Ω; series branch R01 = 0.0556 Ω, X01 = 0.1747 Ω, all referred to the LV (200 V) side.

## Check yourself

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

1. For the 200/400 V transformer, what is K and the factor used to refer HV-side series values to the LV side?
   A. K = 2; divide by K² = 4
   B. K = 2; multiply by 4
   C. K = 0.5; divide by 4
   D. K = 2; divide by 2
   Answer: A. Impedance from HV to LV is divided by K² = 4. (Key point: Turns ratio)

2. What is R01 (LV side)?
   A. 0.222 Ω
   B. 0.0556 Ω
   C. 0.889 Ω
   D. 0.1747 Ω
   Answer: B. R02 = 0.2222 Ω, divided by 4 gives 0.0556 Ω. (Key point: R01)

3. Why do Ro and Xo need no conversion here?
   A. They are always on the HV side
   B. They are not affected by turns ratio
   C. They are neglected
   D. The OC test was already done on the LV side
   Answer: D. The OC test at 200 V on the LV side gives LV-side values directly. (Key point: Shunt branch referral)

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