From fd3141bd706ef77aa72006cca6ca35d0cca88121 Mon Sep 17 00:00:00 2001 From: Max Richter Date: Sun, 20 Mar 2022 18:30:04 +0100 Subject: [PATCH] feat: finished inductor chapter --- Areas/electricity/ac.md | 5 +- Areas/electricity/assets/back_emf_curve.png | Bin 0 -> 98231 bytes .../electricity/assets/inductor_schematic.png | Bin 0 -> 57081 bytes Areas/electricity/assets/low-pass-cutoff.png | Bin 0 -> 197338 bytes Areas/electricity/assets/low-pass-filter.png | Bin 0 -> 21197 bytes Areas/electricity/assets/new-transformer.jpg | Bin 0 -> 20044 bytes Areas/electricity/assets/rlc-resonance.png | Bin 0 -> 7070 bytes .../electricity/assets/transformer-types.jpg | Bin 0 -> 23700 bytes Areas/electricity/formulas.md | 49 ++++------ Areas/electricity/glossary.md | 79 +++------------- .../parts/capacitors/rc-time-constant.md | 53 +++++++++++ Areas/electricity/parts/inductors.md | 89 +++++++++++++++++- Areas/electricity/parts/inductors/back-emf.md | 18 ++++ .../electricity/parts/rlc-series-response.md | 51 ++++++++++ Areas/electricity/parts/transformers.md | 13 +++ Areas/electricity/units.md | 75 +++++++++++++++ 16 files changed, 334 insertions(+), 98 deletions(-) create mode 100644 Areas/electricity/assets/back_emf_curve.png create mode 100644 Areas/electricity/assets/inductor_schematic.png create mode 100644 Areas/electricity/assets/low-pass-cutoff.png create mode 100644 Areas/electricity/assets/low-pass-filter.png create mode 100644 Areas/electricity/assets/new-transformer.jpg create mode 100644 Areas/electricity/assets/rlc-resonance.png create mode 100644 Areas/electricity/assets/transformer-types.jpg create mode 100644 Areas/electricity/parts/capacitors/rc-time-constant.md create mode 100644 Areas/electricity/parts/inductors/back-emf.md create mode 100644 Areas/electricity/parts/rlc-series-response.md create mode 100644 Areas/electricity/parts/transformers.md create mode 100644 Areas/electricity/units.md diff --git a/Areas/electricity/ac.md b/Areas/electricity/ac.md index e1b9d85..1e36641 100644 --- a/Areas/electricity/ac.md +++ b/Areas/electricity/ac.md @@ -25,7 +25,8 @@ This helps calculating the current an equivalent DC Signal would need to provide $$ \begin{flalign} -V_{RMS} = 0.7 * V_{PEAK} &&\\ -V_{PEAK} = 1.4 * V_{RMS} +&V_{RMS} = \frac{1}{\sqrt{2}} * V_{PEAK} &\\\ +\\ +&V_{PEAK} = \sqrt{2} * V_{RMS} \end{flalign} $$ diff --git a/Areas/electricity/assets/back_emf_curve.png b/Areas/electricity/assets/back_emf_curve.png new file mode 100644 index 0000000000000000000000000000000000000000..8e4819b78f724380abda7d3a10d05330c57a29b9 GIT binary patch literal 98231 zcmbSRWm6nXvt3|uhsE7l+}+*X-3jjQZo%E%-GjTkLm;?A&;S8Kc=Oz!aBDtHO^?(} zRd>(n(;cItB#n%Kj{pDwkY!~g)Bpeo7XScK8V>TGXi4gh$t005UJ003VW0D$A1*R3k>Zvw_lURnb1`ClvQ zt4#eTfpwQvl!QHn0-=!b_^rAz{@VC{K^+@(wp(+#BghLI4gteU zlLCM^rBy3wN$<;`;%#_*|LJFE*Z17e_w44~VL#JCXh9#Bf;*Zg3ZRr36`c>8;`L~# z@e2&n(DYg`NrEL+_(c<&chlf}wcdAD;5Y0QovkW?E(u~4N4xcailr@ye!+@mD~~3R 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z%(<0$M7r&qUY>edDSS=ox08%5Q#+1o6BB!u&Pb}dPpA(pWhBs0;#CTq#7>F&Wb@uI z1CW6iMWOb*%hwG?PU3J>HCF!(TANUfH(KGFLk0FweEwYTXEu*D@0e0oiOfQ~WL0D3 z7e5JZ`?;5EmfhX1A#%JmdqGuyb3eK82BIwOZq28DPShA<>F7tCW5dm!c$+*f6G-5vF(D*wgym3yogZ@~d|j_P zEF5tOO?fjlB4xj!(Oir8^nSap`#aS{=8IH%L3P_yYr5BpV>29i>Iv4D0=!97GAL4&YFYAkroen$!kq|%B_Cad{#C08!LhhP%-twpr=othWV=Fs!g2PNj4Zn zi=<=IBa%`y6is0~lOKsT&z&BTt3WRtafw}>a$4E>&U*NcO4~5BUOOy_1R|ju?qFyW RJMNiVPF4=|1Z=vF>C+; literal 0 HcmV?d00001 diff --git a/Areas/electricity/formulas.md b/Areas/electricity/formulas.md index 5bfc2d2..7d3443e 100644 --- a/Areas/electricity/formulas.md +++ b/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} $$ \ No newline at end of file diff --git a/Areas/electricity/glossary.md b/Areas/electricity/glossary.md index b11ac34..8e4fc83 100644 --- a/Areas/electricity/glossary.md +++ b/Areas/electricity/glossary.md @@ -1,60 +1,21 @@ # Glossary -## Volts -Voltage - -## Amperes -Current - -## Ohms -Resistance - -## Hertz (f) -Term | Symbol | Weight -----------|------- | ----- -Hertz | Hz | $10^0$ -Kilohertz | kHz | $10^{3}$ -Megahertz | mHz | $10^6$ - - - -## Watt (Power) - -$Power = V * I = \frac{V^{2}}{R} = I^{2}R$ - -Joules per Second - -Term | Symbol | Weight ------------|----|------ - Nanowatt | nW | 10-9 - Microwatt | $\micro$W | $10^{-6}$ - Milliwatt | mW | $10^{-3}$ - Watt | W | $10^{0}$ - Kilowatt | kW | $10^{3}$ - Megawatt | MW | $10^{6}$ - Gigawatt | GW | $10^{9}$ - -**Examples:** - -Device | Power --------|---------- -Arduino| 167mW -Laptop | 1.5W -House | 2.2kW - - -## Ohms Law -$$ -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 @@ -93,4 +37,7 @@ The positive end of a diode 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. \ No newline at end of file +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. \ No newline at end of file diff --git a/Areas/electricity/parts/capacitors/rc-time-constant.md b/Areas/electricity/parts/capacitors/rc-time-constant.md new file mode 100644 index 0000000..b456c7f --- /dev/null +++ b/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} +$$ diff --git a/Areas/electricity/parts/inductors.md b/Areas/electricity/parts/inductors.md index 657da9b..77220ff 100644 --- a/Areas/electricity/parts/inductors.md +++ b/Areas/electricity/parts/inductors.md @@ -1,11 +1,98 @@ # Inductors -The Inductive reactince is + +Inductors are similar to capacitors, but there are a few key differences: + +1. **They store energy in their magnetic field** +2. **They resist to changes in current** +3. + +![[../assets/inductor_schematic.png]] **Inductance:** +$$ +\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} $$ \ No newline at end of file diff --git a/Areas/electricity/parts/inductors/back-emf.md b/Areas/electricity/parts/inductors/back-emf.md new file mode 100644 index 0000000..7cb6ecc --- /dev/null +++ b/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. \ No newline at end of file diff --git a/Areas/electricity/parts/rlc-series-response.md b/Areas/electricity/parts/rlc-series-response.md new file mode 100644 index 0000000..a2eebab --- /dev/null +++ b/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: + + \ No newline at end of file diff --git a/Areas/electricity/parts/transformers.md b/Areas/electricity/parts/transformers.md new file mode 100644 index 0000000..ca898f6 --- /dev/null +++ b/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: + +$\displaystyle \frac{V_{out}}{V_{in}} = \frac{N_{s}}{N_{p}} = \frac{I_{in}}{I_{out}}$ \ No newline at end of file diff --git a/Areas/electricity/units.md b/Areas/electricity/units.md new file mode 100644 index 0000000..71e2337 --- /dev/null +++ b/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