Some Important Formulas of Electrical Engineering

Electric Power Formulas:

P = V I         (1a)

P = R I²         (1b)

P = V²/ R         (1c)

where

P = power (watts, W)

V = voltage+ (volts, V)

I = current (amperes, A)

R = resistance (ohms, Ω)

Electric Current Formulas:

I = V / R         (2a)

I = P / V         (2b)

I = (P / R)^1/2   (2c)

Electric Resistance Formulas:

R = V / I         (3a)

R = V²/ P        (3b)

R = P / I²         (3c)

Electrical Potential Formulas - Ohms Law:

Ohms law can be expressed as:

V = R I         (4a)

V = P / I         (4b)

V = (P R)^1/2         (4c)

Example - Ohm's law:

A 12 volt battery supplies power to a resistance of 18 ohms.

I = (12 V) / (18 Ω)

    = 0.67 (A)

Electrical Motor Formulas:

Electrical Motor Efficiency

μ = 746 P_hp / P_{input_w}         (5a)

where

μ = efficiency

P_hp = output horsepower (hp)

P_{input_w} = input electrical power (watts)

or alternatively

μ = 746 P_hp / (1.732 V I PF)         (5b)

Electrical Motor - Power

P_3-phase = (V I PF 1.732) / 1,000         (6)

where

P_3-phase = electrical power 3-phase motor (kW)

PF = power factor electrical motor

Electrical Motor - Amps

I_3-phase = (746 P_hp) / (1.732 V μ PF)         (7)

where

I_3-phase = electrical current 3-phase motor (amps)

PF = power factor electrical motor

Opp amp

Introduction   :
The op amp is one of the basic building blocks of linear design. In its classic form it consists of two input terminals, one of which inverts the phase of the signal, the other preserves the phase, and an output terminal. The standard symbol for the op amp is given in Figure. This ignores the power supply terminals, which are obviously required for operation.  
Figure :  Standard op amp symbol
The name “op amp” is the standard abbreviation for operational amplifier. This name comes from the early days of amplifier design, when the op amp was used in analog computers. (Yes, the first computers were analog in nature, rather than digital). When the basic amplifier was used with a few external components, various mathematical “operations” could be performed. One of the primary uses of analog computers was during WWII, when they were used for plotting ordinance trajectories.

Insulator

Insulator:

An electrical insulator is a material whose internal electric charges do not flow freely, and therefore make it nearly impossible to conduct an electric current under the influence of an electric field. This contrasts with other materials, semiconductors and conductors, which conduct electric current more easily. The property that distinguishes an insulator is its resistivity; insulators have higher resistivity than semiconductors or conductors.

A perfect insulator does not exist, because even insulators contain small numbers of mobile charges (charge carriers) which can carry current. In addition, all insulators become electrically conductive when a sufficiently large voltage is applied that the electric field tears electrons away from the atoms. This is known as the breakdown voltage of an insulator. Some materials such as glass, paper and Teflon, which have high resistivity, are very good electrical insulators. A much larger class of materials, even though they may have lower bulk resistivity, are still good enough to prevent significant current from flowing at normally used voltages, and thus are employed as insulation for electrical wiring and cables. Examples include rubber-like polymers and most plastics.

Insulators are used in electrical equipment to support and separate electrical conductors without allowing current through themselves. An insulating material used in bulk to wrap electrical cables or other equipment is called insulation. The term insulator is also used more specifically to refer to insulating supports used to attach electric power distribution or transmission lines to utility poles and transmission towers. They support the weight of the suspended wires without allowing the current to flow through the tower to ground.

Types of insulators:

1. Pin Insulator

2. Suspension Insulator

3. Strain Insulator

4. Shackle Insulator

Pin Insulator:

Pin Insulator is earliest developed overhead insulator, but still popularly used in power network up to 33KV system. Pin type insulator can be one part, two parts or three parts type, depending upon application voltage. In 11KV system we generally use one part type insulator where whole pin insulator is one piece of properly shaped porcelain or glass. As the leakage path of insulator is through its surface, it is desirable to increase the vertical length of the insulator surface area for lengthening leakage path. In order to obtain lengthy leakage path, one, tow or more rain sheds or petticoats are provided on the insulator body. In addition to that rain shed or petticoats on an insulator serve another purpose. These rain sheds or petticoats are so designed, that during raining the outer surface of the rain shed becomes wet but the inner surface remains dry and non-conductive. So there will be discontinuations of conducting path through the wet pin insulator surface.

In higher voltage like 33KV and 66KV manufacturing of one part porcelain pin insulator becomes difficult. Because in higher voltage, the thickness of the insulator become more and a quite thick single piece porcelain insulator can not manufactured practically. In this case we use multiple part pin insulator, where a number of properly designed porcelain shells are fixed together by Portland cement to form one complete insulator unit. For 33KV tow parts and for 66KV three parts pin insulator are generally used.

Suspension Insulator:

In higher voltage, beyond 33KV, it becomes uneconomical to use pin insulator because size, weight of the insulator become more. Handling and replacing bigger size single unit insulator are quite difficult task. For overcoming these difficulties, suspension insulator was developed.

In suspension insulator numbers of insulators are connected in series to form a string and the line conductor is carried by the bottom most insulator. Each insulator of a suspension string is called disc insulator because of their disc like shape.  

Strain Insulator:

When suspension string is used to sustain extraordinary tensile load of conductor it is referred as string insulator. When there is a dead end or there is a sharp corner in transmission line, the line has to sustain a great tensile load of conductor or strain. A strain insulator must have considerable mechanical strength as well as the necessary electrical insulating properties.  

Shackle Insulator:

The shackle insulator or spool insulator is usually used in low voltage distribution network. It can be used both in horizontal and vertical position. The use of such insulator has decreased recently after increasing the using of underground cable for distribution purpose. The tapered hole of the spool insulator distributes the load more evenly and minimizes the possibility of breakage when heavily loaded. The conductor in the groove of shackle insulator is fixed with the help of soft binding wire.

arduino uno datasheet with atmega328p

resistance

The electrical resistance of an electrical conductor is a measure of the difficulty to pass an electric current through that conductor. The inverse quantity is electrical conductance, the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with the notion of mechanical friction. The SI unit of electrical resistance is the ohm (Ω), while electrical conductance is measured in siemens (S).

An object of uniform cross section has a resistance proportional to its resistivity and length and inversely proportional to its cross-sectional area. All materials show some resistance, except for superconductors, which have a resistance of zero.

The resistance (R) of an object is defined as the ratio of voltage across it (V) to current through it (I), while the conductance (G) is the inverse:

For a wide variety of materials and conditions, V and I are directly proportional to each other, and therefore R and G are constant(although they can depend on other factors like temperature or strain). This proportionality is called Ohm's law, and materials that satisfy it are called "Ohmic" materials.

In other cases, such as a diode or battery, V and I are not directly proportional. The ratio V/I is sometimes still useful, and is referred to as a "chordal resistance" or "static resistance", since it corresponds to the inverse slope of a chord between the origin and an I–V curve. In other situations, the derivative  may be most useful; this is called the "differential resistance".

MTK3339 Ultimate GPS Breakout - 66 ch. W/10 Hz module -V.3

-165 dBm sensitivity, 10 Hz updates, 66 channels

5V friendly design and only 20mA current draw
Breadboard friendly + two mounting holes
RTC battery-compatible
Built-in datalogging
PPS output on fix
We have received reports that it works up to ~32Km altitude (the GPS theoretically does not have a limit until 40Km)
Internal patch antenna + u.FL connector for external active antenna
Fix status LED

The breakout is built around the MTK3339 chipset, a no-nonsense, high-quality GPS module that can track up to 22 satellites on 66 channels, has an excellent high-sensitivity receiver (-165 dB tracking!), and a built in antenna. It can do up to 10 location updates a second for high speed, high sensitivity logging or tracking. Power usage is incredibly low, only 20 mA during navigation.

Best of all, we added all the extra goodies you could ever want: a ultra-low dropout 3.3V regulator so you can power it with 3.3-5VDC in, 5V level safe inputs, ENABLE pin so you can turn off the module using any microcontroller pin or switch, a footprint for optional CR1220 coin cell to keep the RTC running and allow warm starts and a tiny bright red LED. The LED blinks at about 1Hz while it's searching for satellites and blinks once every 15 seconds when a fix is found to conserve power. If you want to have an LED on all the time, we also provide the FIX signal out on a pin so you can put an external LED on.

Two features that really stand out about version 3 MTK3339-based module is the external antenna functionality and the the built in data-logging capability. The module has a standard ceramic patch antenna that gives it -165 dB sensitivity, but when you want to have a bigger antenna, you can snap on any 3V active GPS antenna via the uFL connector. The module will automatically detect the active antenna and switch over! Most GPS antennas use SMA connectors so you may want to pick up one of our uFL to SMA adapters.

The other cool feature of the MTK3339-based module (which we have tested with great success) is the built in datalogging ability. Since there is a microcontroller inside the module, with some empty FLASH memory, the newest firmware now allows sending commands to do internal logging to that FLASH. The only thing is that you do need to have a microcontroller send the "Start Logging" command. However, after that message is sent, the microcontroller can go to sleep and does not need to wake up to talk to the GPS anymore to reduce power consumption. The time, date, longitude, latitude, and height is logged every 15 seconds and only when there is a fix. The internal FLASH can store about 16 hours of data, it will automatically append data so you don't have to worry about accidentally losing data if power is lost. It is not possible to change what is logged and how often, as its hardcoded into the module but we found that this arrangement covers many of the most common GPS datalogging requirements.

Silicon is a chemical element with symbol Si and atomic number 14. It is a tetravalent metalloid, more reactive than germanium, the metalloid directly below it in the table. Controversy about silicon's character dates to its discovery; it was first prepared and characterized in pure form in 1823. In 1808, it was given the name silicium (from Latin: silex, hard stone or flint), with an -iumword-ending to suggest a metal, a name which the element retains in several non-English languages. However, its final English name, first suggested in 1817, reflects the more physically similar elements carbon and boron.

Silicon is the eighth most common element in the universe by mass, but very rarely occurs as the pure free element in nature. It is most widely distributed in dusts, sands, planetoids, and planets as various forms of silicon dioxide (silica) or silicates. Over 90% of the Earth's crust is composed of silicate minerals, making silicon the second most abundant element in the Earth's crust (about 28% by mass) after oxygen.^[9]

Most silicon is used commercially without being separated, and indeed often with little processing of compounds from nature. These include direct industrial building-use of clays, silica sand and stone. Silicate goes into Portland cement for mortar andstucco, and when combined with silica sand and gravel, to make concrete. Silicates are also in whiteware ceramics such asporcelain, and in traditional quartz-based soda-lime glass and many other specialty glasses. More modern silicon compounds such as silicon carbide form abrasives and high-strength ceramics. Silicon is the basis of the widely used synthetic polymers called silicones.

Elemental silicon also has a large impact on the modern world economy. Although most free silicon is used in the steel refining,aluminium-casting, and fine chemical industries (often to make fumed silica), the relatively small portion of very highly purified silicon that is used in semiconductor electronics (< 10%) is perhaps even more critical. Because of wide use of silicon inintegrated circuits, the basis of most computers, a great deal of modern technology depends on it.

Silicon is an essential element in biology, although only tiny traces of it appear to be required by animals.^[10] However, varioussea sponges as well as microorganisms like diatoms and radiolaria secrete skeletal structures made of silica. Silica is often deposited in plant tissues, such as in the bark and wood of Chrysobalanaceae and the silica cells and silicified trichomes ofCannabis sativa, horsetails and many grasses