add notes on transformers

uni/mmme/2051_electromechanical_devices/transformers.md

@@ -0,0 +1,37 @@
+---
+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.**
+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).