From 7bac5fc073ea11dc399650870a3fc90b71207046 Mon Sep 17 00:00:00 2001 From: Max Richter Date: Tue, 15 Mar 2022 19:59:12 +0100 Subject: [PATCH] feat: finished capacitor chapter --- Areas/electricity/{ac.md.md => ac.md} | 0 Areas/electricity/assets/EMC-9_graf_01.gif | Bin 0 -> 14244 bytes Areas/electricity/assets/graphXc.gif | Bin 0 -> 2024 bytes .../assets/rlc-capacitor-multiple.png | Bin 0 -> 85460 bytes Areas/electricity/assets/rlc-capacitor.svg | 1 + Areas/electricity/formulas.md | 5 + Areas/electricity/glossary.md | 28 +++++- .../parts/{capacitors.md.md => capacitors.md} | 36 ++++++- .../electricity/parts/capacitors/coupling.md | 2 + .../parts/capacitors/impedance-reactance.md | 91 ++++++++++++++++++ .../electricity/parts/capacitors/smoothing.md | 0 Areas/electricity/parts/inductors.md | 11 +++ Areas/electricity/parts/{led.md.md => led.md} | 0 .../parts/{resistors.md.md => resistors.md} | 0 14 files changed, 168 insertions(+), 6 deletions(-) rename Areas/electricity/{ac.md.md => ac.md} (100%) create mode 100644 Areas/electricity/assets/EMC-9_graf_01.gif create mode 100644 Areas/electricity/assets/graphXc.gif create mode 100644 Areas/electricity/assets/rlc-capacitor-multiple.png create mode 100644 Areas/electricity/assets/rlc-capacitor.svg rename Areas/electricity/parts/{capacitors.md.md => capacitors.md} (67%) create mode 100644 Areas/electricity/parts/capacitors/coupling.md create mode 100644 Areas/electricity/parts/capacitors/impedance-reactance.md create mode 100644 Areas/electricity/parts/capacitors/smoothing.md create mode 100644 Areas/electricity/parts/inductors.md rename Areas/electricity/parts/{led.md.md => led.md} (100%) rename Areas/electricity/parts/{resistors.md.md => resistors.md} (100%) diff --git a/Areas/electricity/ac.md.md b/Areas/electricity/ac.md similarity index 100% rename from Areas/electricity/ac.md.md rename to Areas/electricity/ac.md diff --git a/Areas/electricity/assets/EMC-9_graf_01.gif b/Areas/electricity/assets/EMC-9_graf_01.gif 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end of file diff --git a/Areas/electricity/formulas.md b/Areas/electricity/formulas.md index e3dfa6d..5bfc2d2 100644 --- a/Areas/electricity/formulas.md +++ b/Areas/electricity/formulas.md @@ -74,3 +74,8 @@ $$ \end{flalign} $$ +## Capacitors in Series + +$$ +\frac{1}{C_{t}} = \frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} ... +$$ \ No newline at end of file diff --git a/Areas/electricity/glossary.md b/Areas/electricity/glossary.md index 82fdc86..b11ac34 100644 --- a/Areas/electricity/glossary.md +++ b/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 -= Resistance for Nerds +## Impedance (Z) -## 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 diff --git a/Areas/electricity/parts/capacitors.md.md b/Areas/electricity/parts/capacitors.md similarity index 67% rename from Areas/electricity/parts/capacitors.md.md rename to Areas/electricity/parts/capacitors.md index e543369..18b5097 100644 --- a/Areas/electricity/parts/capacitors.md.md +++ b/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} +$$ + +**Capacitance** +The amount of charge a capacitor can store + **Maximum Voltage** Each capacitor has a maximum voltage that can be dropped across it. @@ -62,4 +92,6 @@ The capacity is not always exact, the tolerance describes how much it could vary - Can work in hot environments > $200\deg$ - Low ESR - High Precision -- High Cost \ No newline at end of file +- High Cost + + diff --git a/Areas/electricity/parts/capacitors/coupling.md b/Areas/electricity/parts/capacitors/coupling.md new file mode 100644 index 0000000..1606598 --- /dev/null +++ b/Areas/electricity/parts/capacitors/coupling.md @@ -0,0 +1,2 @@ +# Coupling / Decoupling Capacitor + diff --git a/Areas/electricity/parts/capacitors/impedance-reactance.md b/Areas/electricity/parts/capacitors/impedance-reactance.md new file mode 100644 index 0000000..f6aef84 --- /dev/null +++ b/Areas/electricity/parts/capacitors/impedance-reactance.md @@ -0,0 +1,91 @@ +# Impedance/Reactance of capacitors + +## Capacitive Reactance +Is a measure of a capacitors opposition to alternating current. + +$Xc$ in $\ohm$ + +$X_{c} = \frac{1}{2 \pi fC}$ +$Xc = \textit{Capacity in } \ohm$ +f = Frequency in Hertz +C = Capacitance in Farads + +![](../../assets/graphXC.gif) + +Higher Frequence $\Rightarrow$ Lower Current Flow +Higher Capacitance $\Rightarrow$ Lower Current Flow + +When the Frequency is 0, the capacitor acts as an open circuit +When the Frequency is really high, the capacitor is equal to a simple wire + +**Example:** + +Calculate the capacitive reactance of a 220nF capacitor at a frequency of 1kHz and 20kHz + +$$ +\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} +$$ + +Due to this the frequency to impedance curve of real capacitors look something like this. + +![](../../assets/EMC-9_graf_01.gif) + +When we add multiple capacitors we can get a curve looking like this + +![](../../assets/rlc-capacitor-multiple.png) \ No newline at end of file diff --git a/Areas/electricity/parts/capacitors/smoothing.md b/Areas/electricity/parts/capacitors/smoothing.md new file mode 100644 index 0000000..e69de29 diff --git a/Areas/electricity/parts/inductors.md b/Areas/electricity/parts/inductors.md new file mode 100644 index 0000000..657da9b --- /dev/null +++ b/Areas/electricity/parts/inductors.md @@ -0,0 +1,11 @@ +# Inductors +The Inductive reactince is + +**Inductance:** + +$$ +\begin{flalign} +&X_{L} = 2\pi fL&&\\\ +&L = Inductance +\end{flalign} +$$ \ No newline at end of file diff --git a/Areas/electricity/parts/led.md.md b/Areas/electricity/parts/led.md similarity index 100% rename from Areas/electricity/parts/led.md.md rename to Areas/electricity/parts/led.md diff --git a/Areas/electricity/parts/resistors.md.md b/Areas/electricity/parts/resistors.md similarity index 100% rename from Areas/electricity/parts/resistors.md.md rename to Areas/electricity/parts/resistors.md