---
title: "Equivalent circuit of 5 kVA 200/400 V transformer"
subject: "Electrical Machines I"
chapter: 2
key: "semester_4/electrical_machines_i:oc-sc-5kva-200-400-primary"
source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/oc-sc-5kva-200-400-primary
site: BCT Engineering
---

# Equivalent circuit of 5 kVA 200/400 V transformer

Electrical Machines I · Chapter 2: Transformer

- Asked in: 2076 Baisakh, 8 marks
- Video: [Open Circuit Test and Short Circuit Test on Transformer : Problem 1 - Single Phase Transformer](https://www.youtube.com/watch?v=LUGkAA-wipE) — Ekeeda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines_i/oc-sc-5kva-200-400-primary
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-2

## Question

The O.C. and S.C. test data are given below for a single phase, 5 kVA, 200V/400V, and 50 Hz transformer.
O.C. test from LV side: 200 V, 1.25 A, 150 W
S.C. test from HV side: 20 V, 12.5 A, 175 W
Calculate the equivalent circuit parameters referred to primary side and draw the equivalent circuit.

## Short answer

From OC test at 200 V, 1.25 A, 150 W, shunt referred to primary: R0 = 266.67 Ω, X0 = 200 Ω. From SC test at 20 V, 12.5 A, 175 W referred to primary: R01 = 0.28 Ω, X01 = 0.286 Ω, Z01 = 0.4 Ω.

## Answer

**Method.** The no-load (OC) test gives the shunt branch: $\cos\phi_0 = \frac{P_0}{V_0 I_0}$, $I_w = I_0\cos\phi_0$, $I_\mu = I_0\sin\phi_0$, $R_0 = \frac{V_0}{I_w}$, $X_0 = \frac{V_0}{I_\mu}$. The SC test gives the series branch: $Z = \frac{V_{sc}}{I_{sc}}$, $R = \frac{P_{sc}}{I_{sc}^2}$, $X = \sqrt{Z^2 - R^2}$. Values found on one side are moved to the other side by multiplying by the square of the voltage ratio.

Primary = LV side (200 V). Rated HV current $= 5000/400 = 12.5$ A, so the SC test is at full load. Factor HV to LV: $\left(\frac{200}{400}\right)^2 = 0.25$.

#### OC test (LV): 200 V, 1.25 A, 150 W
$$
\begin{aligned}
\cos\phi_0 &= \frac{150}{200 \times 1.25} = 0.6, \quad \sin\phi_0 = 0.8 \\
I_w &= 1.25 \times 0.6 = 0.75\ \text{A}, \quad I_\mu = 1.25 \times 0.8 = 1.0\ \text{A} \\
R_0 &= \frac{200}{0.75} = 266.67\ \Omega, \quad X_0 = \frac{200}{1.0} = 200\ \Omega
\end{aligned}
$$
These are already on the primary (LV) side.

#### SC test (HV): 20 V, 12.5 A, 175 W
$$
\begin{aligned}
Z_{02} &= \frac{20}{12.5} = 1.6\ \Omega, \quad R_{02} = \frac{175}{12.5^2} = 1.12\ \Omega \\
X_{02} &= \sqrt{1.6^2 - 1.12^2} = 1.143\ \Omega
\end{aligned}
$$
Referred to primary (multiply by 0.25):
$$
\begin{aligned}
R_{01} &= 1.12 \times 0.25 = 0.28\ \Omega \\
X_{01} &= 1.143 \times 0.25 = 0.286\ \Omega \\
Z_{01} &= 1.6 \times 0.25 = 0.4\ \Omega
\end{aligned}
$$

#### Equivalent circuit referred to primary
```text
 I1 ->        I0                 I2'
 o-----+--------+---[ R01 ]---[ jX01 ]---o
 +     |        |                        +
     [ R0 ]  [ jX0 ]                   load
 V1    |        |                       V2'
 -     |        |                        -
 o-----+--------+------------------------o
 All values referred to primary (LV):
 R0 = 266.67 ohm, X0 = 200 ohm
 R01 = 0.28 ohm, X01 = 0.286 ohm
```

**Answer (primary side):** $R_0 = 266.67\ \Omega$, $X_0 = 200\ \Omega$, $R_{01} = 0.28\ \Omega$, $X_{01} = 0.286\ \Omega$.

(Note: the no-load power factor of 0.6 is unusually high for a real transformer, but the given data are used as stated.)

## Check yourself

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

1. Which side is the primary and what is the SC referring factor?
   A. Primary is LV; multiply by 0.5
   B. Primary is the LV side (200 V); HV values multiplied by (200/400)^2 = 0.25
   C. Primary is HV; multiply by 0.25
   D. Primary is HV; multiply by 4
   Answer: B. Primary is 200 V, so HV values are referred by the square of the ratio, 0.25. (Key point: Primary side identification)

2. Which values result from the OC test (200 V, 1.25 A, 150 W)?
   A. R0 = 160 ohm, X0 = 120 ohm
   B. R0 = 1066 ohm, X0 = 250 ohm
   C. R0 = 200 ohm, X0 = 266.67 ohm
   D. R0 = 266.67 ohm, X0 = 200 ohm
   Answer: D. cos phi0 = 0.6, Iw = 0.75 A, Imu = 1.0 A giving R0 = 200/0.75 and X0 = 200/1.0. (Key point: OC test result)

3. How can you tell the SC test is at full load?
   A. Voltage equals rated voltage
   B. Power equals rated kVA
   C. Current equals LV rated current
   D. Rated HV current 5000/400 = 12.5 A equals the test current
   Answer: D. Test current of 12.5 A matches the HV rated current. (Key point: Why SC test is full load)

4. What are R01 and X01?
   A. 4.48 ohm and 4.57 ohm
   B. 0.56 ohm and 0.57 ohm
   C. 1.12 ohm and 1.143 ohm
   D. 0.28 ohm and 0.286 ohm
   Answer: D. R02 = 175/156.25 = 1.12 ohm and X02 = 1.143 ohm; multiplied by 0.25 give 0.28 and 0.286 ohm. (Key point: Series values on primary)

## Close variants set in other exams

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