feat: finished capacitor chapter

Areas/electricity/assets/rlc-capacitor.svg

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Areas/electricity/formulas.md

@@ -74,3 +74,8 @@ $$
 \end{flalign}
 $$
 
+## Capacitors in Series
+
+$$
+\frac{1}{C_{t}} = \frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} ...
+$$

Areas/electricity/glossary.md

@@ -9,6 +9,15 @@ Current
 ## Ohms
 Resistance 
 
+## Hertz (f)
+Term      | Symbol | Weight
+----------|------- | -----
+Hertz     | Hz     | $10^0$
+Kilohertz | kHz    | $10^{3}$
+Megahertz | mHz    | $10^6$
+
+
+
 ## Watt (Power)
 
 $Power = V * I = \frac{V^{2}}{R} = I^{2}R$ 
@@ -36,13 +45,18 @@ House  | 2.2kW
 
 ## Ohms Law
 $$
-V = \frac{I}{R}
+V = {I}*{R}
 $$
 
-## Impedance
+## Impedance (Z)
-= Resistance for Nerds
 
-## Current
+## Voltage (V)
+
+## Resistance (R)
+
+## Capacitance (C)
+
+## Current (I)
 How many electrons flow through a circuit in  a second
 
 ## Polarity
@@ -52,14 +66,20 @@ Polarised means that a component is not symmetric
 ## Voltage Divider
 
 ## Farad
+1 Farad = the ability to store 1 couloumb
+
 Term | Symbol | Weight
 -----------|----|------
  Picofarad  | pW | $10^{-12}$
  Nanofarad  | nF | $10^{-9}$
  Microfarad | $\micro$F | $10^{-6}$
  Milifarad  | mF | $10^{-3}$
+ Farad      | F  | $10^0$
  Kilofarad  | kF | $10^{3}$
 
+## Couloumb
+1 coulomb is the electric charge transported within one second through the cross-section of a conductor in which an electric current of the strength of 1 ampere flows.
+
 ## LED
 
 Anode - The shorter Leg

Areas/electricity/parts/capacitors.md

@@ -19,9 +19,39 @@ $$
 
 ### Important Metrics
 
-**Size:**
+**Size**
 Larger Capacity $\approx$ Larger Size
 
+**Charge**
+How much charge a capacitor is currently storing depends on the potential difference between its plates
+
+$$
+\begin{flalign}
+&Q = C*V &&\\\
+\\
+&Q = Charge \\
+&C = \textit{Capacitance (Constant Value)}\\
+&V = Voltage\\
+\end{flalign}
+$$
+**Voltage**
+The current that is flowing through a capacitor is the derivative of voltage
+
+**Charging Current**
+
+The charging current through a capacitor is proportional to the rate of change in voltage through it.
+
+The formular for calculating the current flowing through a capacitor is following
+
+*Note: only for linearly rising/falling voltages (not AC)*
+
+$$
+i = C\frac{dv}{dt}
+$$
+
+**Capacitance**
+The amount of charge a capacitor can store
+
 **Maximum Voltage**
 Each capacitor has a maximum voltage that can be dropped across it.
 
@@ -63,3 +93,5 @@ The capacity is not always exact, the tolerance describes how much it could vary
 - Low ESR
 - High Precision
 - High Cost
+
+

Areas/electricity/parts/capacitors/coupling.md

@@ -0,0 +1,2 @@
+# Coupling / Decoupling Capacitor
+

Areas/electricity/parts/capacitors/impedance-reactance.md

@@ -0,0 +1,91 @@
+# Impedance/Reactance of capacitors
+
+## Capacitive Reactance
+Is a measure of a capacitors opposition to alternating current.
+
+$Xc$  in $\ohm$
+
+$X_{c} = \frac{1}{2 \pi fC}$
+$Xc = \textit{Capacity in } \ohm$
+f = Frequency in Hertz
+C = Capacitance in Farads
+
+![](../../assets/graphXC.gif)
+
+Higher Frequence $\Rightarrow$ Lower Current Flow
+Higher Capacitance $\Rightarrow$ Lower Current Flow
+
+When the Frequency is 0, the capacitor acts as an open circuit
+When the Frequency is really high, the capacitor is equal to a simple wire
+
+**Example:**
+
+Calculate the capacitive reactance of a 220nF capacitor at a frequency of 1kHz and 20kHz
+
+$$
+\begin{flalign}
+&X_{c} = \frac{1}{2 \pi * 1000 * 220 * 10^{-9} } \\
+&X_{x} \approx \textbf{723.43} \ohm\\
+\\
+&X_{c} = \frac{1}{2 \pi * 20000 * 220 * 10^{-9} } \\
+&X_{x} \approx \textbf{36.17} \ohm\\
+\end{flalign}
+$$
+
+Here we can see when the frequency increases the reactive capacitance decreases
+
+**Example 2:**
+
+```circuitjs
+$ 1 0.000005 10.20027730826997 50 5 43 5e-11
+v 208 256 208 144 0 1 80 5 0 0 0.5
+r 208 144 336 144 0 100
+c 336 144 336 256 0 0.000029999999999999997 -2.4446139526159825 0.001
+w 336 256 208 256 0
+```
+
+How would we calculate the $I_{rms}$ of this circuit, we'll basically using Ohms Formular
+
+$$
+I_{rms} = \frac{V_{rms}}{R1+X_{c}}
+$$
+The Problem is, we can't just simply add up R1 and Xc, because Xc is shifted by 90°. We need to add them up as Vectors:
+
+$$
+Re = \sqrt{R1^2+Xx^2}
+$$
+
+Lets fill in the numbers from the circuit above and test it out:
+
+$$
+\begin{flalign}
+&X_{c} = \frac{1}{2 \pi * 80 * 30 * 10^{-6}} &&\\\
+&X_{c} \approx 66.3 \ohm \\
+&V_{rms} = 3.5v \\
+\\
+&I_{rms} = \frac{3.5}{\sqrt{100^2+66.3^2}} \\
+&I_{rms} = \frac{3.5}{119.98} \\
+&I_{rms} = 0.029171033 A \\
+&I_{rms} \approx 29.17mA
+
+\end{flalign}
+$$
+
+
+## Reality
+In reality capacitors are not perfect, they are more like:
+![](../../assets/rlc-capacitor.svg)
+
+So the have a $ESR$ and $X_{C}$ and $X_{L} / ESL$
+
+$$
+C_{IMP} = ESR + X_{C} + X_{L}
+$$
+
+Due to this the frequency to impedance curve of real capacitors look something like this.
+
+![](../../assets/EMC-9_graf_01.gif)
+
+When we add multiple capacitors we can get a curve looking like this
+
+![](../../assets/rlc-capacitor-multiple.png)

Areas/electricity/parts/inductors.md

@@ -0,0 +1,11 @@
+# Inductors
+The Inductive reactince is 
+
+**Inductance:**
+
+$$
+\begin{flalign}
+&X_{L} = 2\pi fL&&\\\
+&L = Inductance 
+\end{flalign}
+$$