---
author: Akbar Rahman
date: \today
title: MMME2051 // Transformers
tags: [ transformers, alternating_current, ac ]
uuid: 486f441f-14ec-41e5-94f9-06f25c534086
lecture_slides: [ ./lecture_slides/MMME2051EMD_Lecture8.pdf ]
exercise_sheets: [ ./exercise_sheets/Exercise Sheet 11 - Transformers.pdf ]
---

Transformers are used to convert between AC voltages.

Transmission is always done at very high voltage to reduce copper losses (heat loss, $E = i^2R$).

![](./images/how.png)

A current carrying coil induces a magnet inside the core.
Another coil is wrapped around the core.
This coil has a current induced in it by induced magnetic field.

![](./images/vimscrot-2023-03-23T11:15:40,310863581+00:00.png)

$$\frac{i_s}{i_p} = \frac{v_p}{v_s} = \frac{n_p}{n_s} = \text{turns ratio}$$

**Note that the current fraction is s over p, not p over s like the others.**
Transformers have very high efficiency so will not be considered for this module and
has been left out of the equation above.
Derivation in lecture slides (pp. 12-15).

Transformers are usually described as having a ratio $p:s$, where $p$ is the number of primary coils
and $s$ the number of secondary coils.

![Symbol of an "Isolaton Tranformer". The dot indicates polarity.](./images/vimscrot-2023-03-23T11:17:40,931099514+00:00.png)

## Referred Impedance

$$\frac{Z_P}{Z_S} = \left(\frac{n_p}{n_s}\right)^2$$

Derivation in in lecture slides (pp. 19-21).