---
title: "20 kVA 250/2500 V test parameters"
subject: "Electrical Machine"
chapter: 2
key: "semester_4/electrical_machine:transformer-20kva-250-2500-primary"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/transformer-20kva-250-2500-primary
site: BCT Engineering
---

# 20 kVA 250/2500 V test parameters

Electrical Machine · Chapter 2: Transformer

- Asked in: 2072 Asoj
- Video: [EE213 - 09b - Determining equivalent circuit parameters for a transformer - numerical example](https://www.youtube.com/watch?v=b_6NbUb7U1o) — MAFarooqi
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/transformer-20kva-250-2500-primary
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-2

## Question

A 20 kVA, 250V/2500V, 50 Hz single phase transformer gave the following test results:
No-load test (on L.V. side): 250 V, 1.4 A, 105 watts
Short circuit test (on H.V. side): 120 V, 8 A, 320 watts
Calculate the equivalent circuit parameters referred to primary side and draw the equivalent circuit.

## Short answer

Referred to primary: Ro=595.2 Ω, Xo=187.2 Ω, R01=0.05 Ω, X01=0.141 Ω (Z01=0.15 Ω).

## Answer

**Given:** 20 kVA, 250/2500 V, 50 Hz. No-load test (LV, 250 V side): 250 V, 1.4 A, 105 W. SC test (HV side): 120 V, 8 A, 320 W. Primary = the 250 V side; K = 2500/250 = 10.

#### Shunt branch (the no-load test is already on the primary)
```text
cos φ0 = 105/(250 × 1.4) = 0.300
Iw = 1.4 × 0.300 = 0.420 A
Iμ = √(1.4² − 0.42²) = 1.336 A
Ro = 250/0.420 = 595.2 Ω
Xo = 250/1.336 = 187.2 Ω
```

#### Series branch
On the HV side: Z02 = 120/8 = 15 Ω; R02 = 320/8² = 5 Ω; X02 = √(15² − 5²) = 14.14 Ω.

Refer to the primary (÷ K² = 100):
```text
Z01 = 0.150 Ω ;  R01 = 0.050 Ω ;  X01 = 0.1414 Ω
```

#### Equivalent circuit referred to primary
```text
        R01=0.05Ω   X01=0.1414Ω
 o──┬────┬───/\/\/───────(((────────o
    │    │                          
 595.2Ω 187.2Ω                  load
    │    │                       V2'
 o──┴────┴───────────────────────────o
```
**Answer: Ro = 595.2 Ω, Xo = 187.2 Ω, R01 = 0.05 Ω, X01 = 0.141 Ω (Z01 = 0.15 Ω).**

## Check yourself

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

1. Which side is the primary here, and what does that mean for the shunt branch?
   A. The 2500 V side; transfer by dividing by 100
   B. The 250 V side; the OC test is already on it, no transfer
   C. The 2500 V side; no transfer
   D. The 250 V side; multiply by 100
   Answer: B. OC test on 250 V (primary) gives Ro and Xo directly. (Key point: Primary side)

2. What is the no-load power factor?
   A. 0.300
   B. 0.42
   C. 0.75
   D. 0.105
   Answer: A. cos φ0 = 105/(250 × 1.4) = 0.3. (Key point: Power factor)

3. SC test on the HV side gives R02 = 5 Ω. What is R01?
   A. 0.5 Ω
   B. 500 Ω
   C. 0.05 Ω
   D. 5 Ω
   Answer: C. Divide by K² = 100. (Key point: Series referral)

## Close variants set in other exams

- [220/2200 V transformer test parameters](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Atransformer-220-2200-test-primary) — Electrical Machine, chapter 2, asked 2×

## Related in Electrical Machine

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## Related in other subjects

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