---
title: "Equivalent circuits; transformer on dc supply"
subject: "Electrical Machine"
chapter: 2
key: "semester_4/electrical_machine:equivalent-circuits-dc-supply"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/equivalent-circuits-dc-supply
site: BCT Engineering
---

# Equivalent circuits; transformer on dc supply

Electrical Machine · Chapter 2: Transformer

- Asked in: 2075 Baisakh, 6+2 marks
- Video: [Equivalent Circuit of Transformer Referred to Primary and Secondary - Single Phase Transformer](https://www.youtube.com/watch?v=3Jc8MN8HiQI) — Ekeeda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/equivalent-circuits-dc-supply
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-2

## Question

Explain how we can make equivalent circuits referred to primary side and referred to secondary side. What happens when a power transformer is connected to a d.c. supply of the same voltage ratings?

## Short answer

Referred to primary: R₂′ = R₂/K², X₂′ = X₂/K²; R₀₁ = R₁ + R₂′, X₀₁ = X₁ + X₂′. Referred to secondary: R₁′ = K²R₁, etc. A transformer on DC has no induced back emf, current limited only by winding resistance, so I = V/R₁ causes severe overheating and burnout.

## Answer

#### Equivalent circuit referred to primary or secondary
A real transformer has winding resistances R1, R2, leakage reactances X1, X2, and a no-load branch (Ro, Xo). To solve it as a single-voltage circuit, all quantities are expressed on one side, with K = N2/N1.

**Rules for transferring impedance from one side to the other**
- Voltage, current and impedance transform as: V2′ = V2/K, I2′ = K I2, Z2′ = Z2/K² (secondary to primary).
- The reverse: Z1′ = K² Z1 (primary to secondary).
- The VA, power and losses stay the same, only the base voltage changes.

| Referred to primary | Referred to secondary |
|---|---|
| R2′ = R2/K², X2′ = X2/K² | R1′ = K² R1, X1′ = K² X1 |
| R01 = R1 + R2/K² | R02 = R2 + K² R1 |
| X01 = X1 + X2/K² | X02 = X2 + K² X1 |
| Z01 = √(R01² + X01²) | Z02 = √(R02² + X02²) |
| Ro, Xo from the OC test (on the primary side) | Ro′ = K² Ro, Xo′ = K² Xo |

The magnetising branch is usually moved to the input terminals (approximate circuit), since the no-load current is small.
```text
 I1     R01      X01         I2'
 o──┬───/\/\/──────(((────────────o
    │                           
   Ro∥Xo                    load, V2'
    │                           
 o──┴─────────────────────────────o
   (referred to primary; reverse for secondary)
```
Referring to the secondary uses R02, X02, and the shunt branch Ro′, Xo′ at the output side in the same way.

#### Transformer connected to a d.c. supply of the same voltage rating
- A transformer works only on a changing flux. A d.c. supply creates a constant flux, so no back emf (E1 = −N dΦ/dt = 0) is induced in the primary.
- The only opposition to the current is the very low winding resistance R1. The current is I = V/R1, which is many times (often 20 to 100 times) the rated current.
- The large current heats the winding (I²R) and the insulation, and the primary winding burns out unless a fuse or circuit breaker acts quickly.
- The core may also saturate. A transformer must never be connected to d.c.

## Check yourself

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

1. When a secondary impedance Z2 is referred to the primary side (K = N2/N1), what is Z2'?
   A. K² Z2
   B. Z2/K
   C. Z2 K
   D. Z2/K²
   Answer: D. Secondary impedance referred to primary is divided by K². (Key point: Referring impedance)

2. Which gives the equivalent resistance referred to the primary?
   A. R01 = R1 + R2/K²
   B. R01 = R1 + K² R2
   C. R01 = R1 + R2/K
   D. R01 = R1 + K R2
   Answer: A. R2 is divided by K² when moved to the primary side. (Key point: Total resistance referred to primary)

3. Why does a transformer draw a very large current when connected to a d.c. supply of rated voltage?
   A. The core permeability becomes zero
   B. Constant flux induces no back emf, so only the low R1 limits current
   C. DC has a higher rms voltage than AC
   D. The leakage reactance increases
   Answer: B. With d.c. there is no dΦ/dt, so E1 = 0 and I = V/R1 is many times rated current. (Key point: Transformer on DC)

4. What is the likely result of connecting a transformer to d.c.?
   A. The secondary delivers d.c. output
   B. The secondary voltage doubles
   C. Nothing, since it only works at no load
   D. The primary winding overheats and burns out
   Answer: D. The huge I²R heating burns the primary unless protection acts quickly. (Key point: Result of DC connection)

## Related in Electrical Machine

- [Transformer equivalent circuit referred to primary](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aequivalent-circuit-referred-primary) — Electrical Machines I, chapter 2
- [25 kVA transformer: load voltage and primary current](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Atf-25kva-11kv-load-voltage) — Electrical Machines, chapter 2
- [1000 VA 230/115 V transformer equivalent circuit](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Atf-1000va-230-115-equivalent-circuit) — Electrical Machines, chapter 2
- [OC and SC tests to build transformer equivalent circuit](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aoc-sc-test-10kva-6600-220) — Electrical Machines I, chapter 2
- [Equivalent impedance and copper loss of 50 kVA transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3A50kva-4400-220-equivalent-copper-loss) — Electrical Machines I, chapter 2
- [Equivalent circuit and half-load efficiency of 50 kVA transformer](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3A50kva-2500-250-test-secondary-half) — Electrical Machines I, chapter 2

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