OpenLLM-France/wikimedia huggingface dataset:
# Dishwashing/Cleaning liquids
## Water

Good clean water is an essential part of the cleaning process.

## Hand soap

It is essential to wash your hands between handling dirty and clean dishes. Having and using hand soap by the sink or by the dish pit (With separate handwashing sink) is critical for proper sanitation.

## Detergent

Detergents help you remove bits of food and grease that are stuck on items. Detergent is common in both residential sinks and commercial dishpits.

## Degreaser

Degreasers are chemicals specifically aimed at removing grease from objects. This type of liquid is seen more often in commercial dishpits then in residential settings.

## Bleach

Bleach is good at sanitizing surfaces of harmful microbes. It is harmful to ingest, so you should handle it with care around yourself, and should not allow it to come into direct contact with food.
It is important to never mix bleach with ammonia.
Bleach can easily stain your clothing.
# ERP Internals/Modules/Inventory/Functions

Inventory has the following functions:
* Maintain Item Information
* Find an Item
* Enter Receipts
* Enter Issues
* Enter Adjustments
* Transfer Items
* Print Count Worksheets
* Print Labels
* Change Item Numbers
* Maintain Module Information
# ERP Internals/Modules/Inventory/Functions/Find an Item

This function is used when the user doesn't know the item's number or description but does know some information about the item. They enter what they know and the ERP displays all the items that match the criteria. This function becomes more and more useful as the size of the enterprise increases • Depending on the AccountPro module you are importing data for, the import module can import selected fields for: • Customer Lists • Product Lists • Vendor Lists • Employee Lists • Equipment Lists • Sales Commission Salespersons or Employees • Accounts Receivable Transactions • Sales Commission Transactions
# ERP Internals/Modules/Investment Manager/Functions

Investment Manager has the following functions:
* Maintain Investment Information
* Enter Transactions
* Print Investment Summary
* Maintain Module Information
# ERP Internals/Modules/Inventory

Businesses maintain stocks of items for sale to customers or for inclusion ("raw materials") in the manufacturing of new items ("finished goods"). Inventory ties up a lot of money in most businesses. The Inventory module's job is to minimize the amount of money tied up in Inventory without running out and being unable to fill customer orders. Every ERP package has an Inventory module.
Inventory analysis analyzes inventory items by category, supplier, product ID, date, etc. and combinations thereof. The Analysis function selects, sorts, and summarizes these transactions and presents them in numeric and graphic forms. It supports both pre-defined and ad hoc queries.
* Functions
* Reports

## Tables

The first table is the Item table which contains one record for every inventory item. Each Inventory item includes costing, purchasing, and location information (items can be stocked at more than one warehouse and more than one location within a warehouse). The second table is the Transaction table which contains one record for every transaction (receipt, issue, count, adjustment). There is at least one transaction for every item and there can be many.
Inventory Analysis has a separate, read-only table that is optimized for quick access. Each record in the sales analysis table represents an item receipt. The table is updated once a day.

## Data Exchange

Inventory receives data from Purchasing and Accounts Payable and sends transaction to General Ledger.
# ERP Internals/Modules/Inventory/Functions/Maintain Module Information/Modify GL Distribution

The GL Distribution parameters contain every General Ledger account number that the Inventory module can post to. This function allows the Systems Administrator or the Module Administrator to allocate/book the financial part change to all accounting segment and use to overwrite to all segments.
# ERP Internals/Modules/Inventory/Functions/Maintain Module Information/Modify Price Descriptions

The Price Description parameters contain a description for each of the six price categories that the Inventory module supports. This function allows the Systems Administrator or the Module Administrator to change those descriptions.
# ERP Internals/Modules/Investment Manager/Functions/Maintain Module Information

Some parameters and data tables are used by every module. These are maintained by Systems Administration. But, every module has some parameters and/or data tables that it alone uses. Systems Administration can change this information but each module has a function "Maintain Module Information" that can change it as well. This allows segments of systems administration to be delegated to the senior person in charge of a particular module.
# ERP Internals/Modules/Inventory/Functions/Maintain Module Information

Some parameters and data tables are used by every module. These are maintained by Systems Administration. But, every module has some parameters and/or data tables that it alone uses. Systems Administration can change this information but each module has a function "Maintain Module Information" that can change it as well. This allows segments of systems administration to be delegated to the senior person in charge of a particular module.
* Modify GL Distribution
* Modify Price Descriptions
# ERP Internals/Modules/Inventory/Reports

Inventory generates the following reports:
* Item List
* Item Transactions
* Reorder List
* Physical Count Worksheet
* Trial Balance
* Labels
# ERP Internals/Modules/Investment Manager

Every enterprise has a reserve of funds. As the enterprise grows larger, the total reserve becomes larger and larger. Eventually, it is large enough that it is prudent for the enterprise to invest part of it to gain a higher rate of return than would be possible in a checking account. These investments include GICs, mutual funds, stocks, bonds, and other investment options. Investment Manager keeps track of these investments. Only large ERP packages have an Investment Manager module.
* Functions
* Reports

## Tables

The first table is the Investment table which contains one record for every investment and the second table is the Investment Transaction table which contains one record for every investment transaction. There is at least one transaction record for every investment and there can be many.

## Data Exchange

Investment Manager sends transactions to General Ledger.
# False Friends of the Slavist/Map holka

Semasiological map for *holka
R. иголка • Blr. іголка • Ukr. голка • Pol. • Cz. holka • Slk. • Sln. •
| *holka | Meanings: ‘needle’ ‘girl’   no such word (For areas without shading there is no information yet.) |
| *holka | Meanings | Meanings |
| *holka | needle | girl |
| R. иголка | + | |
| Blr. іголка | + | |
| Ukr. голка | + | |
| Pol. | | |
| Cz. holka | | + |
| Slk. | | |
| Sln. | | |
| < Index of semasiological maps | < False Friends of the Slavist Homepage |
# False Friends of the Slavist/Map kor

Semasiological map for [kor]
R. xop(1), хоры(3) • Blr. хор(1), хоры(3) • Ukr. хор(1), хори(3) • Pol. chór • Ka. chur • LSo. chor • USo. chór • Cz. chór • Slk. chór • Sln. kor • Cr. kor • Bo. kor • Sb. кор • Bg. xop •
| [kor] | Meanings: ‘choir’ ‘corps’ ‘choir (architecture)’   no such word (For areas without shading there is no information yet.) |
| [kor] | Meanings | Meanings | Meanings |
| [kor] | choir | corps | choir (architecture) |
| R. xop(1), хоры(3) | + | | + |
| Blr. хор(1), хоры(3) | + | | + |
| Ukr. хор(1), хори(3) | + | | + |
| Pol. chór | + | | + |
| Ka. chur | + | | + |
| LSo. chor | + | | |
| USo. chór | + | | |
| Cz. chór | | | + |
| Slk. chór | | | + |
| Sln. kor | | | + |
| Cr. kor | + | + | |
| Bo. kor | | + | |
| Sb. кор | | + | |
| Bg. xop | + | | |
| < Index of semasiological maps | < False Friends of the Slavist Homepage |
# False Friends of the Slavist/Map grěšiti

Semasiological map for *grěšiti
R. грешить • Blr. грашыць • Ukr. грішити • Pol. grzeszyć • Ka. grzeszëc • Cz. hřešit • Slk. hrešiť • Sln. grešiti • Cr. griješiti • Bo. griješiti • Sb. grešiti • Bg. греша •
| *grěšiti | Meanings: ‘to sin’ ‘to err’   no such word (For areas without shading there is no information yet.) |
| *grěšiti | Meanings |
| *grěšiti | to sin | to err |
| R. грешить | + | |
| Blr. грашыць | + | |
| Ukr. грішити | + | |
| Pol. grzeszyć | + | |
| Ka. grzeszëc | + | |
| Cz. hřešit | + | |
| Slk. hrešiť | + | |
| Sln. grešiti | + | |
| Cr. griješiti | + | + |
| Bo. griješiti | + | + |
| Sb. grešiti | + | + |
| Bg. греша | + | + |
| < Index of semasiological maps | < False Friends of the Slavist Homepage |
# False Friends of the Slavist/Map kolo

Semasiological map for *kolo
R. Ø • Blr. кола • Ukr. коло • Pol. koło • Ka. kòło • LSo. koło • USo. koło • Cz. kolo • Slk. koleso(1), kolo(2,5) • Sln. kolo • Cr. kolo • Bo. • Sb. коло • Bg. около(round, around), колело(1,7) •
| *kolo | Meanings: ‘wheel’ ‘circle’ ‘ring’ ‘disc’ ‘round dance’ ‘near’ ‘bycicle’   no such word (For areas without shading there is no information yet.) |
| *kolo | Meanings | Meanings | Meanings | Meanings | Meanings | Meanings | Meanings |
| *kolo | wheel | circle | ring | disc | round dance | near | bycicle |
| R. Ø | | | | | | | |
| Blr. кола | + | + | | + | | | |
| Ukr. коло | | + | | | | | |
| Pol. koło | + | + | + | + | | + | |
| Ka. kòło | + | | | | | | + |
| LSo. koło | | + | | | + | | |
| USo. koło | | + | + | | | | |
| Cz. kolo | + | + | | + | + | | + |
| Slk. koleso(1), kolo(2,5) | + | + | | | + | | |
| Sln. kolo | + | | | | + | | + |
| Cr. kolo | + | | | | + | | |
| Bo. | + | | | | + | | |
| Sb. коло | + | + | | | + | | |
| Bg. около(round, around), колело(1,7) | + | | | | | | + |
| < Index of semasiological maps | < False Friends of the Slavist Homepage |
# False Friends of the Slavist/Map jaid

Semasiological map for *židъ
R. жид • Blr. жыд • Ukr. жид • Pol. Żyd/żyd • Ka. Żid/żid • LSo. Žyd • USo. Žid • Cz. Žid/žid • Slk. Žid/žid • Sln. Žid • Cr. Židov •
| *židъ | Meanings: ‘Jew (ethnically)’ ‘Jew (religiously)’ ‘Jew (pejoratively)’   no such word (For areas without shading there is no information yet.) |
| *židъ | Meanings | Meanings | Meanings |
| *židъ | Jew (ethnically) | Jew (religiously) | Jew (pejoratively) |
| R. жид | | | + |
| Blr. жыд | + | | + |
| Ukr. жид | + | | + |
| Pol. Żyd/żyd | + | + | + |
| Ka. Żid/żid | + | + | + |
| LSo. Žyd | + | + | |
| USo. Žid | + | + | |
| Cz. Žid/žid | + | + | |
| Slk. Žid/žid | + | + | |
| Sln. Žid | + | + | + |
| Cr. Židov | + | + | + |
| < Index of semasiological maps | < False Friends of the Slavist Homepage |
# False Friends of the Slavist/Map kovieg

Semasiological map for *kovъčegъ
R. ковчег • Blr. каўчэг • Ukr. ковчег • Pol. Ø • Ka. Ø • Cz. Ø • Slk. Ø • Sln. kovček • Cr. kovčeg • Bo. kovčeg • Sb. ковчег • Mk. • Bg. ковчег •
| *kovъčegъ | Meanings: ‘coffin’ ‘suitcase’ ‘trunk, box, chest’ ‘(Noah’s) Arch’   no such word (For areas without shading there is no information yet.) |
| *kovъčegъ | Meanings | Meanings | Meanings | Meanings |
| *kovъčegъ | coffin | suitcase | trunk, box, chest | (Noah’s) Arch |
| R. ковчег | | | | + |
| Blr. каўчэг | | | | + |
| Ukr. ковчег | | | | + |
| Pol. Ø | | | | |
| Ka. Ø | | | | |
| Cz. Ø | | | | |
| Slk. Ø | | | | |
| Sln. kovček | | + | | |
| Cr. kovčeg | | + | + | |
| Bo. kovčeg | + | + | + | |
| Sb. ковчег | + | | + | |
| Mk. | + | | | |
| Bg. ковчег | + | | | + |
| < Index of semasiological maps | < False Friends of the Slavist Homepage |
# False Friends of the Slavist/Map harbuz

Semasiological map for harbuz
R. арбуз • Blr. гарбуз • Ukr. гарбуз • Pol. arbuz • Ka. arbùz • Slk. arbus • Sln. • Cr. Ø • Bo. Ø • Sb. Ø • Mk. Ø • Bg. карпуз •
| harbuz | Meanings: ‘pumpkin’ ‘watermelon’   no such word (For areas without shading there is no information yet.) |
| harbuz | Meanings |
| harbuz | pumpkin | watermelon |
| R. арбуз | | + |
| Blr. гарбуз | + | |
| Ukr. гарбуз | + | |
| Pol. arbuz | | + |
| Ka. arbùz | | + |
| Slk. arbus | | + |
| Sln. | | |
| Cr. Ø | | |
| Bo. Ø | | |
| Sb. Ø | | |
| Mk. Ø | | |
| Bg. карпуз | | + |
| < Index of semasiological maps | < False Friends of the Slavist Homepage |
# False Friends of the Slavist/Map igrati

Semasiological map for *jьgrati
R. играть • Blr. іграць • Ukr. грати • Pol. grać • Ka. grac • LSo. graś • USo. hrać • Cz. hrát • Slk. hrať • Sln. igrati • Cr. igrati • Bo. igrati • Sb. играти • Mk. игра • Bg. играя •
| *jьgrati | Meanings: ‘to play (a game)’ ‘to play (theatre)’ ‘to play (music)’ ‘to dance’ ‘to foam (wine, beer)’   no such word (For areas without shading there is no information yet.) |
| *jьgrati | Meanings | Meanings | Meanings | Meanings | Meanings |
| *jьgrati | to play (a game) | to play (theatre) | to play (music) | to dance | to foam (wine, beer) |
| R. играть | + | + | + | | + |
| Blr. іграць | | + | + | + | |
| Ukr. грати | + | + | + | | + |
| Pol. grać | + | + | + | | |
| Ka. grac | + | + | + | | |
| LSo. graś | + | + | + | | |
| USo. hrać | + | + | + | | |
| Cz. hrát | + | + | + | | |
| Slk. hrať | + | + | + | | |
| Sln. igrati | + | + | + | | |
| Cr. igrati | + | + | | | |
| Bo. igrati | + | + | | + | |
| Sb. играти | + | + | | + | |
| Mk. игра | + | + | | + | |
| Bg. играя | + | + | | + | |
| < Index of semasiological maps | < False Friends of the Slavist Homepage |
# False Friends of the Slavist/Map izъkusьstvo

Semasiological map for *izъkusьstvo
R. искусство • Blr. Ø • Ukr. Ø • Pol. Ø • Ka. Ø • Slk. Ø • Sln. izkustvo • Cr. iskustvo • Bo. iskustvo • Sb. искуство • Mk. искуство • Bg. изкуство •
| *izъkusьstvo | Meanings: ‘art’ ‘skill’ ‘experience’   no such word (For areas without shading there is no information yet.) |
| *izъkusьstvo | Meanings |
| *izъkusьstvo | art | skill | experience |
| R. искусство | + | + | |
| Blr. Ø | | | |
| Ukr. Ø | | | |
| Pol. Ø | | | |
| Ka. Ø | | | |
| Slk. Ø | | | |
| Sln. izkustvo | | | + |
| Cr. iskustvo | | | + |
| Bo. iskustvo | | | + |
| Sb. искуство | | | + |
| Mk. искуство | | | + |
| Bg. изкуство | + | + | |
| < Index of semasiological maps | < False Friends of the Slavist Homepage |
# False Friends of the Slavist/Map kalъ

Semasiological map for *kalъ
R. кал • Blr. кал • Ukr. кал • Pol. kał • Ka. kôł • Cz. kal • Slk. kal • Sln. ∅ • Cr. kal • Bo. kal • Sb. кал • Mk. кал • Bg. кал •
| *kalъ | Meanings: ‘feces’ ‘sludge’ ‘mud’   no such word (For areas without shading there is no information yet.) |
| *kalъ | Meanings | Meanings | Meanings |
| *kalъ | feces | sludge | mud |
| R. кал | + | | |
| Blr. кал | + | | |
| Ukr. кал | + | | |
| Pol. kał | + | | |
| Ka. kôł | | | + |
| Cz. kal | | + | |
| Slk. kal | | + | |
| Sln. ∅ | | | |
| Cr. kal | | | + |
| Bo. kal | | | + |
| Sb. кал | | | + |
| Mk. кал | | | + |
| Bg. кал | | | + |
| < Index of semasiological maps | < False Friends of the Slavist Homepage |
# Nuclear Reactions

Those of you who studied chemistry, are familiar with the notion of chemical reaction, which, in essence, is just regrouping of atoms that constitute molecules. As a result, reagent chemical compounds are transformed into product compounds.
In the world of nuclear particles, similar processes are possible. When nuclei are close to each other, nucleons from one nucleus can jump into another one. This happens because there are attractive and repulsive forces between the nucleons. The complicated interplay of these forces may cause their regrouping. As a result, the reagent particles are transformed into product particles. Such processes are called nuclear reactions.
For example, when two isotopes $_{2}^{3}$He collide, the six nucleons constituting them, can rearrange in such a way that the isotope $_{2}^{4}$He is formed and two protons are liberated. Similarly to chemical reactions, this process is denoted as
* ${\begin{matrix}_{2}^{3}{\rm {He}}+_{2}^{3}{\rm {He}}\longrightarrow_{2}^{4}{\rm {He}}+p+p+12.86\,{\rm {MeV}}\ \end{matrix}}$
* (15.3)
The same as in chemical reactions, nuclear reactions can also be either exothermic (i.e. releasing energy) or endothermic (i.e. requiring an energy input). The above reaction releases 12.86MeV of energy. This is because the total mass on the left hand side of Eq. (15.3) is in 12.86MeV greater than the total mass of the products on the right hand side (you can check this using Table 15.1).
Thus, when considering a particular nuclear reaction, we can always learn if it releases or absorbs energy. For this, we only need to compare total masses on the left and right hand sides of the equation. Now, you can understand why it is very convenient to express masses in the units of energy.
Composing equations like (15.3), we should always check the superscripts and subscripts of the nuclei in order to have the same number of nucleons and the same charge on both sides of the equation. In the above example, we have six nucleons and the charge +4 in both the initial and final states of the reaction. To make the checking of nucleon number and charge conservation easier, sometimes the proton and neutron are denoted with superscripts and subscripts as well, namely, $_{1}^{1}p$and $_{0}^{1}n$.
In this case, all we need is to check that sum of superscripts and sum of subscripts are the same on both sides of the equation.
# Elementary Particles

In our quest for the elementary building blocks of the universe, we delved inside the atomic nucleus and found that it is composed of protons and neutrons. Are the three particles, $e$, $p$ and $n$, the blocks we are looking for? The answer is no. Even before the structure of the atom was understood, Becquerel discovered the radioactivity (see Discovery of radioactivity) that afterwards puzzled physicists and forced them to look deeper - inside protons and neutrons.
# Nuclear force

Since atomic nuclei are very stable, the protons and neutrons must be kept inside them by some force and this force must be rather strong. What is this force? All of modern particle physics was discovered in the effort to understand this force!
Trying to answer this question, at the beginning of the twentieth century, physicists found that all they knew before, was inadequate to explain how the nucleus held together in spite of the electrostatic repulsion of the protons pushing it apart. They knew only gravitational and electromagnetic forces. It was clear that the forces holding nucleons were not electromagnetic. Indeed, the protons, being positively charged, repel each other and all nuclei would decay in a split of a second if some other forces would not hold them together. On the other hand, it was also clear that they were not gravitational, which would be too weak for the task.
The simple conclusion was that nucleons are able to attract each other by yet unknown nuclear forces, which are stronger than the electromagnetic ones. Further studies proved that this hypothesis was correct.
Nuclear force has rather unusual properties. Firstly, it is charge independent. This means that in all pairs $nn$, $pp$, and $np$ nuclear forces are the same.
Secondly, at distances of about $10^{-15}$ meter, the nuclear force is attractive and very strong, roughly 100 times stronger than electromagnetic repulsion.
Thirdly, the nuclear force is of a very short range. If the nucleons move away from each other for more than few fermi (1 fermi = 1 fm [femtometer] = $10^{-15}$ meter) the nuclear attraction practically disappears. Therefore the nuclear force looks like a strong man with very short arms.
# Electronics/Electronics Formulas/Series Circuits

* Series RL
* Series RC
* Series LC
* Series RLC
# Electronics/Electronics Formulas/Series Circuits/Series RC
## Formula

The total impedance of the circuit
    $Z=Z_{R}+Z_{L}$
    $Z=R+j\omega L$
    $Z={\frac {1}{R}}(1+j\omega T)$
    $T={\frac {L}{R}}$
ist order Differential equation of the circuit
    $L{\frac {di}{dt}}+iR=0$
    ${\frac {di}{dt}}+i{\frac {R}{L}}=0$
    $\int {\frac {di}{i}}=-{\frac {R}{L}}\int dt$
    $Lni=-{\frac {t}{T}}+c$
The root of the equation is an Exponential Decaqy function characterised the Natural Response of the circuit
    $i=Ae^{-{\frac {t}{T}})$
    $Z=Z_{R}+Z_{L}$
    $Z=R\angle 0+\omega L\angle 90$
    $Z=|Z|\angle \theta$
    $Z={\sqrt {R^{2}+(\omega L)^{2}}}\angle \omega {\frac {L}{R}}$
Phase Change, Frequency change relate to the change in value of RC
    $Tan\theta =\omega {\frac {L}{R}}=2\pi f{\frac {L}{R}}=2\pi {\frac {1}{t}}{\frac {L}{R}}$

## Summary

Series RC is characterised by
1st ordered Differential equation of the circuit at equilibrium.
    ${\frac {di}{dt}}+{\frac {1}{T}}=0$
Natural Reponse of the circuit is the Exponential Decay
    $v=Ae^{-{\frac {t}{T}})$
    $T=RC$
# Electronics/Electronics Formulas/Series Circuits/Series RL
## Formula

The total Impedance of the circuit
    $Z=Z_{R}+Z_{L}$
    $Z=R+j\omega L$
    $Z={\frac {1}{R}}(1+j\omega T)$
    $T={\frac {L}{R}}$
The 1st order Differential equation of the circuit in equilibrium
    $L{\frac {di}{dt}}+iR=0$
    ${\frac {di}{dt}}+i{\frac {R}{L}}=0$
    $\int {\frac {di}{i}}=-{\frac {R}{L}}\int dt$
    $Lni=-{\frac {t}{T}}+c$
The root of the equation is a Exponential Decay function characterised the Natural Response of the circuit
    $i=Ae^{-{\frac {t}{T}})$
    $Z=Z_{R}+Z_{L}$
    $Z=R\angle 0+\omega L\angle 90$
    $Z=|Z|\angle \theta$
    $Z={\sqrt {R^{2}+(\omega L)^{2}}}\angle \omega {\frac {L}{R}}$
Phase Shift , Change in Frequency relate to change in RL value
    $Tan\theta =\omega {\frac {L}{R}}=2\pi f{\frac {L}{R}}=2\pi {\frac {1}{t}}{\frac {L}{R}}$

## Summary

Series RL is characterised by
1st ordered Differential equation of the circuit at equilibrium.
    ${\frac {di}{dt}}+{\frac {1}{T}}=0$
Natural Reponse of the circuit is the Exponential Decay
    $i=Ae^{-{\frac {t}{T}})$
# Electronics/Electronics Formulas/Series Circuits/Series RLC
## Formula
### Circuit's Impedance

The total Impedance of the circuit
    $Z=Z_{R}+Z_{L}$
    $Z=R+j\omega L$
    $Z={\frac {1}{R}}(1+j\omega T)$
    $T={\frac {L}{R}}$

### Differential Equation

The Differential equation of the circuit at equilibrium
    $L{\frac {di}{dt}}+{\frac {1}{C}}\int idt+iR=0$
    ${\frac {d^{2}i}{dt^{2}}}+{\frac {R}{L}}{\frac {di}{dt}}+{\frac {1}{LC}}=0$
    $s^{2}+{\frac {R}{L}}s+{\frac {1}{LC}}=0$
    $s=(-\alpha \pm \lambda )t$
    $\lambda ={\sqrt {\alpha ^{2}-\beta ^{2}}}$
    $\alpha ={\frac {R}{2L}}$
    $\beta ={\frac {1}{LC}}$

#### The Natural Response of the circuit

* $\lambda =0$ . $\alpha ^{2}=\beta ^{2}$
       $i=e^{-\alpha t)$
* $\lambda =0$ . $\alpha ^{2}=\beta ^{2}$
       $i=e^{-\alpha t)[e^{\lambda t)+e^{-\lambda t)]$
* $\lambda =0$ . $\alpha ^{2}=\beta ^{2}$
       $i=e^{-\alpha t)[e^{j\lambda t)+e^{-j\lambda t)]$

#### The Resonance Response of the circuit

    $Z_{L}-Z_{C}=0$ . $Z_{L}=Z_{C}$ . $\omega L={\frac {1}{\omega C}}$ . $\omega ={\sqrt {\frac {1}{LC}}}$
    $V_{L}+V_{C}=0$ .
    $\omega =0$ . $\omega =0$
# Electronics/Expanded Edition Afterword
## Electrolysis

Description, Faraday's rule, battery in reverse, maybe fuel cells

## Ultra high frequency AC

Show how things change at ultra high frequency, wires becoming waveguides. This points the way to unification of electricity and radio.

## Maxwell

Math free description, ubiquity of EM

## Quantum stuff

Math free

## Computers

Path from small circuits to PCs

## Final word

Math free piece on how electronics fits into the wider scheme
# Electronics/Electronics Formulas/Series Circuits/Series LC
## Formula

The total Impedance of the circuit
    $Z=Z_{R}+Z_{L}$
    $Z=R+j\omega L$
    $Z={\frac {1}{R}}(1+j\omega T)$
    $T={\frac {L}{R}}$
The Differential equation of the circuit at equilibrium
    $L{\frac {di}{dt}}+{\frac {1}{C}}\int idt=0$
    ${\frac {d^{2}i}{dt^{2}}}+{\frac {1}{LC}}=0$
    $s^{2}+{\frac {1}{LC}}=0$
    $s=\pm j{\sqrt {\frac {1}{LC}}}t$
    $s=\pm j\omega t$
The Natural Response of the circuit
    $i=ASin\omega t$
The Resonance Response of the circuit
    $Z_{L}-Z_{C}=0$ . $Z_{L}=Z_{C}$ . $\omega L={\frac {1}{\omega C}}$ . $\omega ={\sqrt {\frac {1}{LC}}}$
    $V_{L}+V_{C}=0$ . $V_{C}=-V_{L}$

## Summary

Series LC can be characterised by
2nd order Differential Equation
    ${\frac {d^{2}i}{dt^{2}}}+{\frac {1}{T}}=0$
    $T=LC$
With Natural Response of a Wave function
    $i=ASin\omega t$
With Resonance Response of a Standing Wave function
    $i=ASin\omega t$