feat: finished inductor chapter

Areas/electricity/ac.md

@@ -25,7 +25,8 @@ This helps calculating the current an equivalent DC Signal would need to provide
 
 $$
 \begin{flalign}
-V_{RMS} = 0.7 * V_{PEAK} &&\\
-V_{PEAK} = 1.4 * V_{RMS}
+&V_{RMS} = \frac{1}{\sqrt{2}} * V_{PEAK} &\\\
+\\
+&V_{PEAK} = \sqrt{2} * V_{RMS} 
 \end{flalign}
 $$

Areas/electricity/formulas.md

@@ -1,18 +1,12 @@
 # Ohms Law
 Solve for voltage:
 
-$$
-\begin{flalign}
-V &= \frac{I}{R}&
-\end{flalign}
-$$
+$\displaystyle V = \frac{I}{R}$
+
 *Solve for resistance:*
 
-$$
-\begin{flalign}
-R &= \frac{V}{I} &
-\end{flalign}
-$$
+$R = \frac{V}{I}$
+
 _Solve for current_
 $$
 \begin{flalign}
@@ -22,21 +16,17 @@ $$
 
 # Resistors in Series
 
-$$
-\begin{flalign}
-R &= R1 + R2 + R3 ... &
-\end{flalign}
-$$
+$R = R1 + R2 + R3 ...$
 
 # Resistors in Parallel
 
 $$
 \begin{flalign}
-\frac{1}{R} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} ... &&\\
+&\frac{1}{R} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} ... &\\
 \\
-\textit{For two resistors in parallel:} &&\\
+&\textit{For two resistors in parallel:} &\\
 \\
-R = \frac{R1 * R2}{R1 + R2} &&\\
+&R = \frac{R1 * R2}{R1 + R2} &\\\
 \end{flalign}
 $$
 
@@ -60,22 +50,23 @@ $$
 ![](./assets/kirchhoffs-law-01.svg)
 
 For this circuit kirchhoffs law states that:
-$$
-\begin{flalign}
-i1 = i2 + i3 + i4 &&
-\end{flalign}
-$$
+
+$\displaystyle i1 = i2 + i3 + i4$
 
 ## Conservation of Energy (Second Law)
 All the potential differences around the loop must sum to zero.
-$$
-\begin{flalign}
-\sum{V} = 0 &&
-\end{flalign}
-$$
+
+$\displaystyle \sum{V} = 0$
 
 ## Capacitors in Series
 
+$\displaystyle \frac{1}{C_{t}} = \frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} ...$
+
+### Impedance in a Circuit
+
 $$
-\frac{1}{C_{t}} = \frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} ...
+\begin{flalign}
+&Z = \sqrt{R^2 + X^2} &\\\
+&X = X_{L} - X_{C} \\ 
+\end{flalign}
 $$

Areas/electricity/glossary.md

@@ -1,60 +1,21 @@
 # Glossary
 
-## Volts
-Voltage
-
-## Amperes
-Current
-
-## Ohms
-Resistance 
-
-## Hertz (f)
-Term      | Symbol | Weight
-----------|------- | -----
-Hertz     | Hz     | $10^0$
-Kilohertz | kHz    | $10^{3}$
-Megahertz | mHz    | $10^6$
-
-
-
-## Watt (Power)
-
-$Power = V * I = \frac{V^{2}}{R} = I^{2}R$ 
-
-Joules per Second
-
-Term | Symbol | Weight
------------|----|------
- Nanowatt  | nW | 10-9
- Microwatt | $\micro$W | $10^{-6}$
- Milliwatt | mW | $10^{-3}$
- Watt      | W  | $10^{0}$
- Kilowatt  | kW | $10^{3}$
- Megawatt  | MW | $10^{6}$
- Gigawatt  | GW | $10^{9}$
-
-**Examples:**
-
-Device | Power
--------|----------
-Arduino| 167mW
-Laptop | 1.5W
-House  | 2.2kW
-
-
-## Ohms Law
-$$
-V = {I}*{R}
-$$
-
 ## Impedance (Z)
+In [electrical engineering](https://en.wikipedia.org/wiki/Electrical_engineering "Electrical engineering"), **impedance** is the opposition to [alternating current](https://en.wikipedia.org/wiki/Alternating_current "Alternating current") presented by the combined effect of [resistance](https://en.wikipedia.org/wiki/Electrical_resistance "Electrical resistance") and [reactance](https://en.wikipedia.org/wiki/Electrical_reactance "Electrical reactance") in a [circuit](https://en.wikipedia.org/wiki/Electrical_circuit "Electrical circuit").
+
+[[formulas#Impedance in a Circuit]]
 
 ## Voltage (V)
+**Voltage**, **electric potential difference**, **electric pressure** or **electric tension** is the difference in [electric potential](https://en.wikipedia.org/wiki/Electric_potential "Electric potential") between two points.
 
 ## Resistance (R)
+The **electrical resistance** of an object is a measure of its opposition to the flow of [electric current](https://en.wikipedia.org/wiki/Electric_current "Electric current").
 
 ## Capacitance (C)
+**Capacitance** is the ability of a component or circuit to collect and store energy in the form of an electrical charge.
+
+## Inductance (L)
+**Inductance** is the tendency of an [electrical conductor](https://en.wikipedia.org/wiki/Electrical_conductor "Electrical conductor") to oppose a change in the [electric current](https://en.wikipedia.org/wiki/Electric_current "Electric current") flowing through it.
 
 ## Current (I)
 How many electrons flow through a circuit in  a second
@@ -63,23 +24,6 @@ How many electrons flow through a circuit in  a second
 Means if a component is symmetric or not
 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
@@ -94,3 +38,6 @@ The negative end of a diode
 
 ## Conventional Current Flow
 When electricity was discovered people thought the electrons flow from the positive terminal to the negative, in actuality they flow in the opposite direction, but it is still possible to calculate the flow with the old way.
+
+## Reactive Components
+A component is a **reactive component** when it resists to changes in current or voltage.

Areas/electricity/parts/capacitors/rc-time-constant.md

@@ -0,0 +1,53 @@
+# RC Time Constant
+
+How much time does it take for a capacitor to charge up to a certain charge.
+
+$\tau = RC$
+
+**Example:**
+
+We have a capacitor with a capacitance of 200$\micro F$ and a circuit resistance of 100$\ohm$
+
+Then:
+
+$$
+\begin{flalign}
+\tau = RC \\
+\tau = 200 * 10^-6 * 100 \\
+\tau = 0.02s 
+\end{flalign}
+$$
+
+A capacitor is usually charged at around 5RC, so:
+$5RC = 5*0.02=0.1s$
+
+
+
+**Example 2:**
+
+$$
+\begin{flalign}
+&R = 47k\ohm &&\\\
+&C = 1000\micro F\\
+\\
+&\tau = 47.000 * 0.001 = 47s \\
+\end{flalign}
+$$
+In words this means after 47 seconds the capacitor will be at 63% of the input voltage, and after 235 Seconds, or around 4 minutes, it will be at 99% of the input voltage.
+
+## Usages
+
+**Low Pass Filter**
+
+We can use capacitors to filter out any signal above a certain frequency in a signal. This is called a low pass filter. This is usefull to filter out noise in a signal for example.
+
+![](../../assets/low-pass-filter.png)
+
+![](../../assets/low-pass-cutoff.png)
+
+We can see here that the high frequencies are reduced, while the low frequencies keep their strength. Above a certain frequency the signal is reduced by 70%, that point is called the cutoff frequency. We can calculate that point like this:
+$$
+\begin{flalign}
+f_{3db} = \frac{1}{2 \pi RC} &&\\
+\end{flalign}
+$$

Areas/electricity/parts/inductors.md

@@ -1,11 +1,98 @@
 # Inductors
-The Inductive reactince is 
+
+Inductors are similar to capacitors, but there are a few key differences:
+
+1. **They store energy in their magnetic field**
+2. **They resist to changes in current**
+3. 
+
+![[../assets/inductor_schematic.png]]
 
 **Inductance:**
+$$
+\begin{flalign}
+&L = \frac{N^2 * A * \micro}{l} &\\\
+\\
+&L = Inductance \\
+&N = \text{Coil Turns} \\
+&A = \text{Area of the coild} \\
+&\micro = \text{Permeability} \\
+&\textit{How easily a magnetic field can be crated} \\
+&l = \text{Length of coil} \\
+
+\end{flalign}
+$$
+### Inductors in Parallel
+$\displaystyle \frac{1}{L_{t}} =\frac{1}{L_{1}}+\frac{1}{L_{2}}+...+\frac{1}{L_{n}}$
+
+### Inductive Reactance
+Is the strength of opposition to alternating current in an inductor, measured in $\ohm$
 
 $$
 \begin{flalign}
 &X_{L} = 2\pi fL&&\\\
+&f = Frequency \\
 &L = Inductance 
 \end{flalign}
 $$
+
+**Example:**
+
+```circuitjs
+$ 1 0.000005 30.13683688681966 45 5 43 5e-11
+v 144 256 144 128 0 1 10000 5 0 0 0.5
+l 240 128 240 256 0 0.03 -0.004925046545906014 0
+w 144 128 240 128 0
+w 240 256 144 256 0
+o 1 64 0 4099 5 0.025 0 2 1 3
+```
+Calculate the Inductive Reactance in this circuit:
+
+$$
+\begin{flalign}
+&X_{L} = 2\pi fL &\\\
+&f = 10kHz = 10.000Hz\\
+&L = 30mH = 0.03H\\
+&X_{L} = 2\pi * 10.000 * 0.03 \\
+&X_{L} \approx 1885\ohm
+\end{flalign}
+$$
+
+
+**Example 2:**
+
+```circuitjs
+$ 1 0.000005 30.13683688681966 45 5 43 5e-11
+v 96 256 96 128 0 1 200 5 0 0 0.5
+l 240 128 240 256 0 0.4 0.00896251184146064 0
+w 240 256 96 256 0
+r 96 128 240 128 0 200
+o 1 64 0 4099 5 0.025 0 2 1 3
+```
+
+Calculate the [[glossary#Impedance Z|Impedance]] in this Circuit:
+
+$$
+\begin{flalign}
+Z = \sqrt{R^2 + X^2} \\
+X = X_{L} - {X_{C}} \\
+\\
+X_{L} = 2\pi fL \\
+X_{L} = 2\pi * 200Hz * 400mH \\
+X_{L} = 2\pi*200*0.4H\\
+X_{L} \approx 502.65\ohm\\
+\\
+Z = \sqrt{200^2+502.65^2}\\
+Z \approx 540.97 \ohm \\
+\\
+I_{RMS} = \frac{I_{max}}{\sqrt{2}} \\
+I_{RMS} = \frac{V_{rms}}{Z} \\
+V_{RMS} = \frac{5}{\sqrt{2}} \\
+V_{RMS} \approx 3.53V \\
+I_{RMS} = \frac{3.53}{540.97} \\
+I_{RMS} \approx 6.5mA\\
+I_{max} = 0.0065 * \sqrt{2} \\
+I_{max} \approx 9.12mA \\
+
+\end{flalign}
+$$

Areas/electricity/parts/inductors/back-emf.md

@@ -0,0 +1,18 @@
+# Back EMF
+
+**back electromotive force**
+
+The Back EMF is the voltage across an inductor, it is proportional to the change of current flowin through an inductor.
+
+It is caused by a changing magnetic field around the inductor, which itself is caused by a change in the current flowing through it.
+
+
+### Example:
+
+![](../../assets/back_emf_curve.png)
+
+After switch on (A $\rightarrow$ B) we see that the voltage spikes immediately, this causes the magnetic field to change rapidly, which creates a oppositional polarity, which causes a huge resistance to current flow, so the current flowing at the start is almot zero. As soon as the voltage begins to drop, the back emf becomes weaker and current is allowed to flow.
+
+After switch on (B $\rightarrow$ C) the magnetic field around the inductor collapses, which causes a back emf in to the inductor. And because the change in the strength of the magnetic field is opposite to switch on, the induced voltage across the inductor is opposite to the one on switch on. This Back EMF can cause very large spikes in voltage, because the voltage induced across the inductor is dependent on the rate of change the strength of the magentic field.
+
+For some circuits this large spikes in voltage can cause problems, as the voltage may be high enough to jump switches (arcing) or damage semiconductors.

Areas/electricity/parts/rlc-series-response.md

@@ -0,0 +1,51 @@
+#  Series RLC Resonance
+When we have an Inductive and a Capacitive part in an ac circuit there is a certain frequency when the Impedance of those two parts are equal.
+
+It can be calculated as follows
+
+$\displaystyle f_{r} = \frac{1}{2\pi \sqrt{LC}}$
+
+This formula is derived from 
+
+$$
+\begin{flalign}
+\frac{1}{2\pi f C} = 2\pi f L \\
+f^2 = \frac{1}{4\pi^4LC} \\
+f = \frac{1}{4\pi^2LC} \\
+\end{flalign}
+$$
+
+At this resonance frequency the impedance from capacitor and inductor cancel each other out, which means that $Z=R$ 
+
+When we graph out the impedance vs frequency in a circuit, it could look something like this:
+
+![](../assets/rlc-resonance.png)
+
+This could cause problems because the voltage is really high at that point, which maybe bad for some other parts.
+
+**Example:**
+
+```circuitjs
+$ 1 0.000005 30.13683688681966 45 5 43 5e-11
+v 256 256 256 128 0 1 10000 5 0 0 0.5
+l 432 128 432 256 0 1 0 0
+c 256 256 432 256 0 0.000014999999999999999 0 0.001
+r 256 128 432 128 0 10
+o 1 64 0 4099 5 0.025 0 2 1 3
+```
+
+Lets calculate $f_{r}$ for this circuit.
+
+$$
+\begin{flalign}
+f_{r} = \frac{1}{2\pi\sqrt{LC}} \\
+L = 1H \\
+C = 15\micro F = 0.000015F \\
+f_{r} = \frac{1}{2\pi \sqrt{1*0.000015}} \\
+\\
+f_{r} \approx 41.093Hz
+\end{flalign}
+$$
+As you can see in the following graph that result is correct:
+
+<iframe src="https://www.desmos.com/calculator/esdrlexq4y?embed" width="500" height="500" style="border: 1px solid #ccc" frameborder=0></iframe>

Areas/electricity/parts/transformers.md

@@ -0,0 +1,13 @@
+# Transformers
+
+![](../assets/new-transformer.jpg)
+
+The amount of primary and secondary windings dictate how much the voltage changes between the two. 
+
+There are two main types of transformers:
+
+![](../assets/transformer-types.jpg)
+
+When there are more turns on the primary winding, that means that the voltage on the secondary winding is lower, but the current is higher, and vice versa. Also this relationshop is linear, so half the amount of turns in the second winding, mean half the amount of voltage and double the amount of current. In formula this means:
+
+$\displaystyle \frac{V_{out}}{V_{in}} = \frac{N_{s}}{N_{p}} = \frac{I_{in}}{I_{out}}$

Areas/electricity/units.md

@@ -0,0 +1,75 @@
+## Farad
+Measures capacitance, the ability of a body to store an electrical charge.
+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.
+
+## Henry
+Measures electrical Inductance
+
+$\displaystyle V(t)=L{\frac {dI}{dt}}$
+
+## Volts
+Measures electric potential
+
+## Amperes
+Measures electric current
+
+## Ohms
+Measures resistance
+
+Term | Symbol | Weight
+-----------|----|------
+ Nanoohm  | n$\ohm$ | 10-9
+ Microohm | $\micro \ohm$ | $10^{-6}$
+ Milliohm | m$\ohm$ | $10^{-3}$
+ Ohm      | $\ohm$  | $10^{0}$
+ Kiloohm  | k$\ohm$ | $10^{3}$
+ Megaohm  | M$\ohm$ | $10^{6}$
+ Gigaohm  | G$\ohm$ | $10^{9}$
+
+## Hertz
+
+Measures frequency
+
+Term      | Symbol | Weight
+----------|------- | -----
+Hertz     | Hz     | $10^0$
+Kilohertz | kHz    | $10^{3}$
+Megahertz | mHz    | $10^6$
+
+
+## Watt
+Measures Power
+
+$Power = V * I = \frac{V^{2}}{R} = I^{2}R$ 
+
+Joules per Second
+
+Term | Symbol | Weight
+-----------|----|------
+ Nanowatt  | nW | $10^{-9}$
+ Microwatt | $\micro$W | $10^{-6}$
+ Milliwatt | mW | $10^{-3}$
+ Watt      | W  | $10^{0}$
+ Kilowatt  | kW | $10^{3}$
+ Megawatt  | MW | $10^{6}$
+ Gigawatt  | GW | $10^{9}$
+
+**Examples:**
+
+Device | Power
+-------|----------
+Arduino| 167mW
+Laptop | 1.5W
+House  | 2.2kW