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Details: Published: Friday, 11 August 2023 13:21; Hits: 525

Passive Elements = Resistors, Capacitors, Inductors

Almost all the matter around us has the 3 passive elements built as intrinsic part of that matter. These 3 elements are Resistors, Capacitors, Inductors. They arise due to physical properties of resistance, capacitance and Inductance that gives rise to these 3 passive elements respectively.

Resistance:

Ohm's Law ad resistivity:

Conductivity of a material is defined by ohm's law as: J = σ*E where J=current density=I/A (I=current, A=Area), σ = conductivity of material and E=Electric field thru that material.

Resistivity (ρ) = 1/σ = inverse of conductivity.

For a material with uniform cross section A and length L, E=V/L (In a medium with no source/sink point, electric field is constant. It it weren't, charges would start accumulating at the point where electric fields are different)

=> I/A = σ*V/L

=> Resistance R = V/I = ρ*L/A => This is the classic Ohm's law that is stated in books, but it applies only to special case of homogeneous material with uniform cross section.

Units of ρ are Ω-m. The value of ρ comes by experimentally measuring it for different materials. Metals are good conductors and have lower ρ.

Cu=1.7*10^-8 ohm-m (Cu less resistive than Al and used in most conductors now, including wires on chip)

Al=2.6*10^-8 ohm-m

Resistivity is also written in units of ohm-mm^2/m, so Cu resistivity is 17 mΩ-mm^2/m => For a wire with area=1mm^2, Resistance is 17mΩ/m. Or for 1km of 1mm thick wire, Resistance is 17Ω. Gauge (AWG) is used in transmission wires to specify the thickness and current carrying capacity of wire (see in Power Transmission section).

Mobility of electron:

Other term used in connection with resistivity is mobility. Looking at atomic level, we see that any conductor has free flowing electrons which are moving randomly in all directions. When we apply a n Electric field, these electrons experience F = q*E and start accelerating as per Newton's law. They hit the atom lattice, and scatter off and lose some of their energy. Then it again starts accelerating in same direction, and this process continues. The final result is that the electron moves with a finite average velocity, called the drift velocity. This causes an electric current in the direction of the Electric Field. This motion is lot smaller than normally occurring random motion.

F= m*a=e*E (where m is mass of electron, e is it's charge)

Avg drift velocity (V_d) = a/τ = e*E/(m*τ) where τ=mean free time (i.e avg time between collisions).

So, V_d = -μ*E, where μ=e*/(m*τ) and is known as mobility of electron. SI unit of mobility is m^2/(V.sec) but is almost always expressed in cm^2/(V.sec)

I = -n*(A*L)*e/t = -n*(A*L)*e/(L/V_d) = -n*(A*L)*e*V_d (n=electron density per unit volume, Length L of distance covered in time t)

J=I/A = -n*e*V_d = -(-n*e*μ*E) = n*e*μ*E

From Ohm's law J = σ*E => σ = n*e*μ

So, conductivity of any material is related to the mobility of electron in that conductor as well as the concentration of free electrons. That is why different metals with same number of free electrons may have different resistivity as electron mobility might be different between them, depending on the lattice scattering. Thus electron mobility depends on following:

Lattice structure: Depending on the lattice structure, scattering (or collision) may occur sooner, which will cause lower electron mobility.
Velocity saturation for electrons may occur. Electrons don't keep going faster and faster with increasing Electric field. At some point, sufficiently high drift velocity is reached, and velocity maxes out. This is called Velocity Saturation (v_sat). v_sat is on the order of 1×10⁷ cm/s for both electrons and holes in Si. It is on the order of 6×10⁶ cm/s for Ge. So, basically μ starts decreasing as velocity sat approaches, and finally goes to very low values.
Temperature affects electron mobility => With increasing temperature, phonon concentration increases and causes increased scattering, thus lowering the carrier mobility. In semi Conductors (Si, Ge), μ ∝ 1/T^2. The power to T isn't exactly but varies based on material and whether it's electrons or holes. So, conductivity is supposed to decrease with increasing Temperature (as mobility decreases), but at the same time, carrier concentration may increase due to higher Temperature (true for semiconductors)

Typical electron mobility at room temperature (300 K) in metals like gold, Cu, Silver is 30–50 cm²/ (V⋅s). Carrier mobility in semiconductors is doping dependent. In Silicon (Si) the electron mobility is of the order of 1,000, while in germanium it's around 4,000.

Determine ρ of Cu using mobility:

1 mole of Cu has weight = 64g => 1 atom of Cu has weight = 64g/(6.02*10^23 ) = 10^-22 g.

Density(Cu)=9g/cm^3 => # of atoms in 1cm^3 = 9g/(10^-22) = 10^23 atoms. Assume 1 free electron per Cu atoms

σ = n*e*μ = 10^23*1.6*10^-19*40 cm²/ (V⋅s) = 0.6*10^6 => ρ = 1/σ = 1.6 * 10^-6 ohm-cm = 1.6*10^-8 ohm-m, which matches closely to the ρ shown above (1.7*10^-8 ohm-m)

Capacitance:

Capacitance of a material is defined by gauss's law.

We saw insulators above which don't conduct electrons that well (i.e electrons drift very slowly in response to Electric field). Within insulators, we have a subset of materials which will get polarized when an Electric field is applied. This is called permittivity of the material. The electrons in such materials don't drift, but instead just shift slightly causing an internal Electric field. Such materials are called dielectric. A perfect dielectric is a material with zero electrical conductivity.

Dielectrics: https://en.wikipedia.org/wiki/Dielectric

Atomic level: Every material is made up of atoms. Atoms contain a =ve proton and -ve electrons around it. In presence of electric field, the charge is distorted slightly with electrons moving in the opposite direction to the direction of electric field. In insulator type materials (called as dielectric), these electrons don't flow from one end to other, but instead shift just slightly. This creates a dipole for each atom (think of it as separated +ve and -ve charges at 2 ends with some distance b/w them). When the electric field is removed, the atom returns to its original state. This shift of electrons from their average equilibrium positions, causes dielectric polarisation and creates an internal electric field that reduces the overall field within the dielectric itself (the applied electric field minus the dielectric polarisation induced Electric field). This tendency to polarize is referred to as the permittivity of the material, an is expressed as:

D (displacement field) = ε . E (electric field) where ε is the permittivity of material. Vacuum has a permittivity of ε₀ =

A material with high permittivity polarizes more in response to an applied electric field than a material with low permittivity, thereby storing more energy in the material.

Details: Published: Wednesday, 02 August 2023 15:24; Hits: 763

Car Buying: Electric Vehicle (EV) vs Internal Combustion Engine (ICE)

Which Car should you buy? One that runs on Battery (Called an Electric Vehicle or EV) or one that is traditional, still running on Internal Combustion Engine (ICE) which burns gasoline (petrol/diesel). Then there are hybrid cars. These are the cars that have an Electric battery as well as gasoline tank (a mix of EV and ICE as they have both). Hybrids are divided into Conventional Hybrids and Plug in Hybrid Electric Vehicles (PHEV). The conventional Hybrid car runs 100% on gasoline, but uses the battery pack to provide to provide extra boost where needed. Thus, the range of car in miles per gallon improves, as some of the energy is provided by Battery. The battery doesn't need to be charged separately, as Car's alternator keeps charging this battery. On the contrary, in PHEV, the car is mostly run by the battery, and gasoline is used only when battery is almost out of Juice. However the range of car on Battery is not too large. It ranges from 10 miles to 50 miles, before switching to gasoline. They are on purpose designed for smaller range on battery, so that battery pack won't be too large.

Cost of Car:

Let's look at the cost side. Pure EV sell for around $40K, while similar ICE can be had for $20K.

Cost of upkeep

Depreciation

Cost of gas vs electricy

Also, it's not cheaper to get electricity compared to gasoline. Gasoline costs $4/gallon, while electricity cost is $0.15/KwHr (Avg for residential pricing).

Link on msn comparing price of gas vs electricity => https://www.msn.com/en-us/autos/news/most-cars-still-cost-more-to-charge-than-to-fill-up-with-gas/ar-AA1eDQ0R

Details: Published: Sunday, 30 July 2023 14:56; Hits: 747

Home maintenance and Repairs

As a homeowner, you will soon find that there are a lot of things that will breaking every year. If you go out to hire someone for each and every repair, it will easily cost you 1000's of $, as any service is very expensive in USA. You will probably give the same hourly rate as what you make in hiring someone,and that is if you lucky. So, we'll save that money and try to learn to do it ourselves. You can think of the money saved as extra non taxable pay. The learning that you gain as DIY is un measurable.

Garage:

The one thing that goes bad in your garage is your garage door. Installing a garage door by yourself is NOT a DIY. I would be surprised if your house didn't come with a garage door already installed. Most of the times, there will be issues with the automatic garage door opener (Chamberlain Brand for ex). At that point, you might have to replace it or fix it, which is certainly a DIY. Or fix the sensors on the side, or issue with the wireless button on the side of the garage outside your house. These are all DIY, and don't cost much.

Plumbing:

Plumbing is the one of the highest cost repair after the AC. Plumbing and AC are 2 things, that you can't do much about. With an AC, may be you can live for a couple of days/weeks, while you shop around, but plumbing issues need to be taken care of immediately.

Cracked Pipes: There are both copper and PVC (plastic) pipes carrying water in and around the house. The drainage pipes taking waste water out of your house are all PVC pipes. Most of the pipes going under the ground are also PVC pipes. It's easy to get cracks in these PVC pipes 9usually the ones in your yard). Number 1 reason is someone just hit the pipe while shovellingor digging. Calling a plumber isn't required, as this can be fixed for couple of dollars.

How to fix PVC pipes in your yard => https://www.youtube.com/watch?v=x7NWmdlvVIQ

Electric:

Installing lights/Fans:

Very easy to install a fan, if the box is already there in place. It will take good 2 hours to do it, but is well worth the effort. You can get a very good fan with lights for about $50-$100.They regularly go on clearance for 75% off at HomeDepot and Lowes, usually after summer. So, no reason to pay full price.

Details: Published: Sunday, 30 July 2023 02:04; Hits: 426

Questions and interrogative words:

Interrogative words are very essential in any language to form a question. Even if you don't know any other word, you can just use an interrogative word, and get the message across (i.e Where Bathroom?). In spanish, we add question mark ¿ ..... ? around a question. In English, the verb and pronoun placement is interchanged. i.e "You are tall" becomes Are you tall? when phrased as a question. In Spanish, there's lot of flexibility around the order.

There are multiple ways to form a question. Let's explore 3 of them

No change in order (keep SVO order): This is the most common way for questions in Spanish. It's different order than what we use in English for asking Questions. Here, there's no difference b/w question and answer, the order in both of them is the same. By keeping SVO order, the emphasis is on the 1st word in sentence, which is the subject. Does Juan read books => Here we translate "Juan reads books", and just raise our inclination at the end, to pose it as a question. So, translation is ¿Juan lee libros? => We are placing emphasis on Juan.
Change to English order (VSO order): By changing to VSO order, the emphasis is still on the 1st word in sentence, but here it is the subject. This is how we ask questions in English. Only subject and verb are interchanged. Object remain unchanged no matter where it appears in sentence (it may not necessarily be at the end, it may may be in beginning too). Does Juan read books? => Does read juan, the books? => So, translation is ¿lee Juan libros? => We are placing emphasis on Read (or lee).
- ex: Which book would you want? => Here "you want" is changed in order to "want you". So, ¿Qué libro quiere usted? (Here object "libro" is in front, remains unchanged)
- ex: What did the man order? => Here "man ordered" is changed to "ordered the man". ¿Qué ordenó el hombre? (Here there is no object)
Informal way: Add "right?" at end: Juan read books, right? OR Juan read books, didn't he? Here we translate the answer as in case 1, but add "no/right" at the end to make it a question.
- No?: ¿no? => Juan read books, didn't he? => translation is Juan lee libros ¿no?
- Right/true? => ¿verdad? (i.e Your name is Jose, right? => ¿tu es nombre Jose, verdad? ). es verdad => It is true (or right).

In Spanish, most of the times pronoun is not explicitly used. In such cases, both "You are good" and "Are you good?" translate to same thing, except for question mark. ex: You are good => Eres Bueno. But Are you good => ¿Eres Bueno? is also translated the same, as we omitted the word "tu" for you in both of them. With "tu", it would be ¿Tu Eres Bueno?

Link => https://www.thoughtco.com/asking-questions-spanish-3079427

Common Interrogative words: Shown below are common words used for questions. One thing to note that all such words shown below have accent on the vowel. Without the accent, the meaning changes.

A verb usually follows the interrogative word, which makes it easy to understand. Noun/pronoun follows the verb. ex: What is the capital of Peru? => ¿Qué es la capital del Peru? => Here, es verb comes right after interrogative word.
When the verb needs a subject other than the interrogative, the subject follows the verb (VSO order). In short, verb always follows the interrogative word. ex: Why did he go to the city? => ¿Por qué fue él a la ciudad? Here él follows the verb. With multiple nouns, some nouns may come before verb, but the noun associated with the verb comes after the verb , i.e How many dollars does he have? => ¿Cuántos dólares tiene el?
ex: Where does your grandma go on Fridays? => ¿Dónde/ADónde va tu abuela los viernes? (It's translated as => where go, your grandma, on Fridays?)
ex: What do you do on Mondays? => Que haces (tú) los lunes? (What do you, on Mondays?)

english	spanish	ex
what	¿Qué? => pronounced "kay" NOTE: que (w/o accemt on e) is used as "to" in verb "have to".	What is that? => ¿Qué es eso?
which or which one	¿Cuál / Cuáles? => pronouned kual / kuales, (add es for plural) NOTE: In spanish, "which" is used in a lot of places where "what" should be used, there's no hard rule about it. Just remember this when interpreting.	Which is your car? – ¿Cuál es tu carro? What is your profession? => ¿Cuál es tu profesión? (NOTE: Cuál used even though it's what?) What is the price? => ¿Cuál es el precio?
when	¿Cuándo? => pronounced kuaando ("when=Cuándo" and "how many=Cuánto" are similar translations)	When is your birthday? – ¿Cuándo es tu cumpleaños? When is Independence day? – ¿Cuándo es el día de la independencia?
how many or how much	¿Cuánto / Cuántos? =>for masculine noun (singular/plural) ¿Cuánta / Cuántas? =>for feminine noun (singular/plural) These act like adjective, and need to match gender and number of the noun. Sounds like count.	How much coffee do you have? - ¿Cuánto café tienes? (café is singular maculine)
how	¿Cómo? => NOTE the accent on o. NOTE: ¿cómo? is also a common way to say “huh?” in Spanish	How are you? – ¿Cómo estás? =>This is the most common way to greet someone. See in "general greetings" below.
where	¿Dónde?	Where are you? – ¿Dónde estás? (temporary condition, so estar). I'm at home => estoy en casa Where is the store? – ¿Dónde esta la tienda? (where is something => this is temporary condition)
who whose = of who	Who => ¿Quién/ Quienes? => pronounced kee-en / kee-enes. (add es for plural). Remember as hindi "kaun" which means who (Quién sounds like kaun) Whose => ¿De quién/ De quienes? (of who)	Who is she? – ¿Quién es ella? Who are those people? – ¿Quiénes son esas personas? Whose TV is that? – ¿De quién es el televisor? Whose shoes are those? – ¿ De quiénes son esos zapatos?
why / because	¿Por qué? / Porque => pronouned por-kay "why" in spanish is 2 separate words (por+que), while "because" is just single word (porque). Basically, if you combine Por+que as 1 word (no accent on e), it becomes "because". Por translates to "because of", while qué translates to what => Porque (accent left out when combining) => because of what => why? Por also translates to "for" and many other words, but it also means "because of".	Why are you sad? – ¿Por qué estás triste? Because I’m sick – Porque estoy enfermo Why not? => ¿Por qué no?

NOTE: Several of these interrogatives can be preceded by prepositions: a quién (to whom), de quién (of whom), de dónde (from where), de qué (of what), etc.

Personal "a" in questions: "a" is also added in front of a question. This happens when a question will require an answer with a personal A in response. Then we need to add it in front of the interrogative word. personal "a" can be thought of as English "to" in a loose sense.

Examples:

¿A Dónde vamos? => Where are we going? "vamos" means "we go", so ¿Dónde vamos? means "where we go?". Response will be "we go to Mexico" or "vamos a mexico", which requires "a" in response (since verb "go" is being done to mexico)
¿A quién crees que engañas? – Who do you think you are fooling? A nadie. – Nobody. Here response is "someone" which is a person.
¿A cuántas clases faltaste? – How many classes did you miss? Falté a cinco clases. – I missed five classes. Here "verb" miss is being done on classes, which is inanimate, so not sure why "a" used in response.

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