---
title: "Constant flux from no load to full load"
subject: "Electrical Machines"
chapter: 2
key: "semester_4/electrical_machines:flux-constant-no-load-full-load"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/flux-constant-no-load-full-load
site: BCT Engineering
---

# Constant flux from no load to full load

Electrical Machines · Chapter 2: Transformer

- Asked in: 2070 Bhadra, 4 marks
- Video: [Iron losses | Constant flux |  Transformers | Lec - 21](https://www.youtube.com/watch?v=H_g6hy8P2uM) — Education 4u
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines/flux-constant-no-load-full-load
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-2

## Question

The flux in transformer remains practically constant from no load to full load. Justify the statement.

## Short answer

Primary voltage V1 ≈ E1 = 4.44 f N1 φm; since V1 and f are fixed, φm is practically constant. Also, load current's mmf is balanced by primary load component N1 I1' = N2 I2, leaving net core mmf unchanged. Thus flux remains nearly constant from no-load to full-load.

## Answer

The core flux of a transformer is fixed by the applied primary voltage, not by the load. Therefore it stays practically constant from no load to full load.

**Reason 1: voltage balance in the primary**

$$
V_1 = E_1 + I_1Z_1 \approx E_1 = 4.44fN_1\phi_m
$$

The primary impedance drop $I_1Z_1$ is only 1 to 3% of $V_1$ at full load. Since the supply voltage $V_1$ and frequency $f$ are constant, $\phi_m = \dfrac{V_1}{4.44fN_1}$ stays practically constant.

**Reason 2: mmf balance**

When a load current $I_2$ flows, its mmf $N_2I_2$ tends to reduce the flux. The primary current immediately increases by $I_1'$, so that

$$
N_1I_1' = N_2I_2
$$

The net mmf in the core is then again $N_1I_\mu$, the no-load value, so the flux does not change.

**Conclusion:** the only change in flux comes from the small primary impedance drop $I_1Z_1$, which is about 1 to 3% at full load. Because the flux is constant, the core (iron) loss is constant at all loads, and the core loss measured at no load can be taken as the core loss at full load.

## Check yourself

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

1. What fixes the core flux in a transformer?
   A. The load current
   B. The secondary turns
   C. The primary supply voltage and frequency
   D. The load power factor
   Answer: C. V1 ~ E1 = 4.44 f N1 phi_m gives phi_m = V1/(4.44 f N1). (Key point: What fixes flux)

2. Why is the flux only 'practically' constant?
   A. The secondary voltage changes a lot
   B. Iron loss is zero
   C. The supply frequency falls on load
   D. The primary impedance drop I1Z1 is 1 to 3% of V1, so E1 falls slightly
   Answer: D. E1 = V1 - I1Z1, and the small drop causes a slight change. (Key point: Primary drop)

3. The net mmf in the core on load is:
   A. N1 I_mu, the no-load value
   B. N1 I1 + N2 I2
   C. Zero
   D. N2 I2
   Answer: A. The load component I1' cancels N2I2. (Key point: mmf balance)

4. A consequence of constant flux is:
   A. Copper loss is the same at all loads
   B. Core loss is the same at all loads
   C. Core loss rises with load
   D. Efficiency is constant
   Answer: B. Core loss depends on flux, so the no-load core loss applies at full load. (Key point: Consequence)

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