---
title: "Transformer principle and maximum efficiency"
subject: "Basic Electrical and Electronics Engineering"
chapter: 2
key: "semester_1/basic_electrical_and_electronics_engineering:transformer-principle-efficiency"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_and_electronics_engineering/transformer-principle-efficiency
site: BCT Engineering
---

# Transformer principle and maximum efficiency

Basic Electrical and Electronics Engineering · Chapter 2: Electrical Machines

- Asked in: 2081 Baishakh (new course), 2 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_and_electronics_engineering/transformer-principle-efficiency
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_and_electronics_engineering/chapter-2

## Question

Describe the operating principle of a single-phase transformer.

## Answer

A transformer is a static device that transfers electrical energy from one circuit to another at the same frequency by electromagnetic induction, usually changing the voltage level.

**Principle (mutual induction).** It has two windings, primary and secondary, wound on a laminated silicon-steel core. When an alternating voltage $V_1$ is applied to the primary, an alternating current flows and produces an alternating flux $\Phi$ in the core. This flux links the secondary winding and, by Faraday's law, induces an emf in it:

$$
e=-N\frac{d\Phi}{dt}
$$

The same flux links both windings, so the emf per turn is the same, giving

$$
\frac{E_2}{E_1}=\frac{N_2}{N_1}=K
$$

If $N_2>N_1$ it is a step-up transformer; if $N_2<N_1$ it is step-down. There is no electrical connection between windings, and ideally input power = output power ($V_1I_1=V_2I_2$).

## Check yourself

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

1. On what principle does a transformer work?
   A. Self-induction in a single coil
   B. Mutual induction between two windings sharing a changing flux
   C. Electrostatic induction
   D. The Hall effect
   Answer: B. Alternating flux produced by the primary links the secondary and induces an emf in it. (Key point: Mutual induction)

2. Which relation holds, and which type is a transformer with N2 < N1?
   A. E2/E1 = N1/N2; step-up
   B. E2/E1 = N2/N1; step-up
   C. E2/E1 = N2/N1; step-down
   D. E2/E1 = N1/N2; step-down
   Answer: C. Same flux links both windings, so emf is proportional to turns; N2 < N1 gives lower secondary voltage (step-down). (Key point: Turns ratio)

3. In an ideal transformer, what happens to frequency and power?
   A. Frequency doubles; power is halved
   B. Frequency changes by the turns ratio; power is constant
   C. Frequency is the same; V1 I1 = V2 I2
   D. Frequency is the same; I1 = I2
   Answer: C. It transfers energy at the same frequency, with input power equal to output power. (Key point: Frequency and power)

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