add power factor

uni/mmme/2046_dynamics_and_control/control.md

@@ -4,12 +4,19 @@ date: \today
 title: MMME2046 // Control
 tags: [ mmme2046, uon, uni, control ]
 uuid: 73e04dd2-ee4c-4952-a9b7-7df3930d2d2d
-lecture_slides: ./lecture_slides/Control 2 2022.pdf
+lecture_slides: [ ./lecture_slides/Control 1 2023.pdf, ./lecture_slides/Control 2 2022.pdf, ./lecture_slides/Control Lecture 3 2022.pptx ]
+exercise_sheets: [ ./exercise_sheets/control.pdf, ./exercise_sheets/control_sols_odd.pdf ]
 ---
 
-# Lecture Slides Corrections
+# Errata
 
-## p26
+## Exercise Sheets
+
+### ES1, Q5 (p3)
+
+Output column on row 3c should be $h_2$ not $h_3$.
+
+## Lecture Slides 2 p26
 
 First line should be
 

uni/mmme/2051_electromechanical_devices/ac_intro.md

@@ -75,9 +75,11 @@ Ohm's law generalised to incorporate complex resistance, reactance, $X$:
 
 \begin{align*}
 v &= iX \\
-V\angle\Phi_v &= i\angle\Phi_iX \\
-&= i\angle\Phi_ij\omega L \\
-\frac{V}{j\omega L}\angle\Phi_v &= I\angle\Phi_i
+V\angle\Phi_v &= I\angle\Phi_iX \\
+&= I\angle\Phi_ij\omega L \\
+\frac{V}{j\omega L}\angle\Phi_v &= I\angle\Phi_i\\
+\frac{{V}\omega L}\angle\left(\Phi_v - \frac{\pi}{2}\right) &= I\angle\Phi_i
+\end{align*}
 
 # Power
 

uni/mmme/2051_electromechanical_devices/ac_power.md

@@ -8,6 +8,8 @@ lecture_slides: [ ./lecture_slides/MMME2051EMD_Lecture3B.pdf ]
 exercise_sheets: [ ./exercise_sheets/Exercise Sheet 4 - Power factor and three phase.pdf ]
 ---
 
+This section builds on [introduction to AC](/permalink?uuid=0c90c691-cbf8-43e9-bfa5-7b277c853151).
+
 # Definitions
 
 - Phase voltage - voltage across any phase
@@ -49,3 +51,7 @@ $$I_\text{line} = I_\text{phase}$$
 $$|V_\text{line}| = |V_\text{phase}|$$
 
 $$I_\text{line} = \sqrt 3 I_\text{phase}$$
+
+# Power Factor (PF)
+
+$$\text{PF} = \cos{\gamma} = \cos{\left(\Phi_v-\Phi_i\right)}$$