Elektronix

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  • O Ohm's Law

    The famous one. Used almost everywhere. Star of every book.

  • K Kirchhoff’s Laws

    You know the name. Now, you will know the numbers!

  • T Thévenin’s Theorem

    You can run, but you cannot hide from this!

  • N Norton’s Theorem

    Nope. Not a virus scanner.

  • S Superposition Theorem

    Move like no one sees you!

  • R Reciprocity Theorem

    Inside out!

  • C Compensation Theorem

    You gotta pay up, son!

  • M Millman’s Theorem

    Willy, meet Milli!

  • J Joule’s Law

    Loads of heat here!

  • MPT Maximum Power Transfer Theorem

    Max Pain!

  • SD Star-Delta Transformation

    Twinkle Twinkle!

  • DS Delta-Star Transformation

    Delta to Echo! Come in Echo!

  • R Resistor

    Magically opposes electric flow though it. Very famous too.

  • C Capacitor

    Magically stores electric charge.

  • I Inductor

    Magically opposes sudden change in current.

  • D Diode

    One directional flow of current.

  • T Transistors

    One directional flow of current.

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Ohm's Law

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:

I = V/R,

where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.

The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. He presented a slightly more complex equation than the one above (see History section below) to explain his experimental results. The above equation is the modern form of Ohm's law.
In physics, the term Ohm's law is also used to refer to various generalizations of the law originally formulated by Ohm. The simplest example of this is:

J = σE,

where J is the current density at a given location in a resistive material, E is the electric field at that location, and σ (Sigma) is a material-dependent parameter called the conductivity. This reformulation of Ohm's law is due to Gustav Kirchhoff.

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Kirchhoff’s Laws

Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws.

Both of Kirchhoff's laws can be understood as corollaries of the Maxwell equations in the low-frequency limit. They are accurate for DC circuits, and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits.

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Thévenin's Theorem

As originally stated in terms of DC resistive circuits only, the Thévenin's theorem holds that:

1)Any linear electrical network with voltage and current sources and only resistances can be replaced at terminals A-B by an equivalent voltage source Vth in series connection with an equivalent resistance Rth.
2)This equivalent voltage Vth is the voltage obtained at terminals A-B of the network with terminals A-B open circuited.
3)This equivalent resistance Rth is the resistance obtained at terminals A-B of the network with all its independent current sources open circuited and all its independent voltage sources short circuited.

In circuit theory terms, the theorem allows any one-port network to be reduced to a single voltage source and a single impedance.

The theorem also applies to frequency domain AC circuits consisting of reactive and resistive impedances.

The theorem was independently derived in 1853 by the German scientist Hermann von Helmholtz and in 1883 by Léon Charles Thévenin (1857–1926), an electrical engineer with France's national Postes et Télégraphes telecommunications organization.

Thévenin's theorem and its dual, Norton's theorem, are widely used for circuit analysis simplification and to study circuit's initial-condition and steady-state response. Thévenin's theorem can be used to convert any circuit's sources and impedances to a Thévenin equivalent; use of the theorem may in some cases be more convenient than use of Kirchhoff's circuit laws.

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Norton's Theorem

Known in Europe as the Mayer–Norton theorem, Norton's theorem holds, to illustrate in DC circuit theory terms, that:

1) Any linear electrical network with voltage and current sources and only resistances can be replaced at terminals A-B by an equivalent current source INO in parallel connection with an equivalent resistance RNO.
2) This equivalent current INO is the current obtained at terminals A-B of the network with terminals A-B short circuited.
3) This equivalent resistance RNO is the resistance obtained at terminals A-B of the network with all its voltage sources short circuited and all its current sources open circuited.

For AC systems the theorem can be applied to reactive impedances as well as resistances.

The Norton equivalent circuit is used to represent any network of linear sources and impedances at a given frequency.

Norton's theorem and its dual, Thévenin's theorem, are widely used for circuit analysis simplification and to study circuit's initial-condition and steady-state response. Norton's theorem was independently derived in 1926 by Siemens & Halske researcher Hans Ferdinand Mayer (1895–1980) and Bell Labs engineer Edward Lawry Norton (1898–1983).

To find the equivalent,

1) Find the Norton current INo. Calculate the output current, IAB, with a short circuit as the load (meaning 0 resistance between A and B). This is INo.
2) Find the Norton resistance RNo. When there are no dependent sources (all current and voltage sources are independent), there are two methods of determining the Norton impedance RNo.
3) Calculate the output voltage, VAB, when in open circuit condition (i.e., no load resistor – meaning infinite load resistance). RNo equals this VAB divided by INo.

or

Replace independent voltage sources with short circuits and independent current sources with open circuits. The total resistance across the output port is the Norton impedance RNo.
4) This is equivalent to calculating the Thevenin resistance.

However, when there are dependent sources, the more general method must be used. This method is not shown below in the diagrams.

Connect a constant current source at the output terminals of the circuit with a value of 1 Ampere and calculate the voltage at its terminals. This voltage divided by the 1 A current is the Norton impedance RNo. This method must be used if the circuit contains dependent sources, but it can be used in all cases even when there are no dependent sources.

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Superposition Theorem

The superposition theorem for electrical circuits states that for a linear system the response (voltage or current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, where all the other independent sources are replaced by their internal impedances.

To ascertain the contribution of each individual source, all of the other sources first must be "turned off" (set to zero) by:

1) Replacing all other independent voltage sources with a short circuit (thereby eliminating difference of potential i.e. V=0; internal impedance of ideal voltage source is zero (short circuit)).
2) Replacing all other independent current sources with an open circuit (thereby eliminating current i.e. I=0; internal impedance of ideal current source is infinite (open circuit)).

This procedure is followed for each source in turn, then the resultant responses are added to determine the true operation of the circuit. The resultant circuit operation is the superposition of the various voltage and current sources.

The superposition theorem is very important in circuit analysis. It is used in converting any circuit into its Norton equivalent or Thevenin equivalent.

The theorem is applicable to linear networks (time varying or time invariant) consisting of independent sources, linear dependent sources, linear passive elements (resistors, inductors, capacitors) and linear transformers.

Another point that should be considered is that superposition only works for voltage and current but not power. In other words the sum of the powers of each source with the other sources turned off is not the real consumed power. To calculate power we should first use superposition to find both current and voltage of each linear element and then calculate the sum of the multiplied voltages and currents.

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Reciprocity Theorem

Reciprocity in linear systems is the principle that a response Rab, measured at a location (and direction if applicable) a, when the system has an excitation signal applied at a location (and direction if applicable) b, is exactly equal to Rba which is the response at location b, when that same excitation is applied at a. This applies for all frequencies of the excitation signal. If Hab is the transfer function between a and b then Hab = Hba, if the system is linear.

In the special case of a modal analysis this is known as Maxwell's reciprocity theorem.

The reciprocity principle is also used in the analysis of structures. When combined with superposition, symmetry and anti-symmetry, it can be used to resolve complex load conditions.

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Compensation Theorem

This theorem is based on one basic concept. According to Ohm’s law , when current flows through any resistor, there would be a voltage drop across the resistor . This dropped voltage opposes the source voltage. Hence voltage drop across a resistance in any network can be assumed as a voltage source acting opposite to the source voltage. The compensation theorem depends upon this concept.

According to this theorem, any resistance in a network may be replaced by a voltage source that has zero internal resistance and a voltage equal to the voltage drop across the replace resistance due to the current which was flowing through it. This imaginary voltage source is directed opposite to the voltage source of that replaced resistance. Think about a resistive branch of any complex network that's resistance value is R. Let's assume current I is flowing through that resistor R and voltage drops due to this current across the resistor is V = I.R. According to compensation theorem, this resistor can be replaced by a voltage source that's generated voltage will be V ( = IR) and will be directed against the direction of network voltage or direction of current I.

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Millman's Theorem

In electrical engineering, Millman's theorem (or the parallel generator theorem) is a method to simplify the solution of a circuit. Specifically, Millman's theorem is used to compute the voltage at the ends of a circuit made up of only branches in parallel.

It is named after Jacob Millman, who proved the theorem.

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Joule's Law

Joule heating, also known as ohmic heating and resistive heating, is the process by which the passage of an electric current through a conductor releases heat. The amount of heat released is proportional to the square of the current such that

Q is proportional to I^2 x R x t

This relationship is known as Joule's first law or Joule–Lenz law. Joule heating is independent of the direction of current, unlike heating due to the Peltier effect.

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Maximum Power Transfer Theorem

In electrical engineering, the maximum power transfer theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must equal the resistance of the source as viewed from its output terminals. Moritz von Jacobi published the maximum power (transfer) theorem around 1840; it is also referred to as "Jacobi's law".

The theorem results in maximum power transfer, and not maximum efficiency. If the resistance of the load is made larger than the resistance of the source, then efficiency is higher, since a higher percentage of the source power is transferred to the load, but the magnitude of the load power is lower since the total circuit resistance goes up.

If the load resistance is smaller than the source resistance, then most of the power ends up being dissipated in the source, and although the total power dissipated is higher, due to a lower total resistance, it turns out that the amount dissipated in the load is reduced.

The theorem states how to choose (so as to maximize power transfer) the load resistance, once the source resistance is given. It is a common misconception to apply the theorem in the opposite scenario. It does not say how to choose the source resistance for a given load resistance. In fact, the source resistance that maximizes power transfer is always zero, regardless of the value of the load resistance.

The theorem can be extended to alternating current circuits that include reactance, and states that maximum power transfer occurs when the load impedance is equal to the complex conjugate of the source impedance.

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Star to Delta Transformation

The Y-Δ transform, also written wye-delta and also known by many other names, is a mathematical technique to simplify the analysis of an electrical network. The name derives from the shapes of the circuit diagrams, which look respectively like the letter Y and the Greek capital letter Δ. This circuit transformation theory was published by Arthur Edwin Kennelly in 1899. It is widely used in analysis of three-phase electric power circuits.

The Y-Δ transform can be considered a special case of the star-mesh transform for three resistors.

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Delta to Star Transformation

The replacement of delta or mesh by equivalent star connection is known as delta - star transformation. The two connections are equivalent or identical to each other if the impedance is measured between any pair of lines. That means, the value of impedance will be the same if it is measured between any pair of lines irrespective of whether the delta is connected between the lines or its equivalent star is connected between that lines.

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Resistor

A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. Resistors act to reduce current flow, and, at the same time, act to lower voltage levels within circuits. In electronic circuits resistors are used to limit current flow, to adjust signal levels, bias active elements, terminate transmission lines among other uses. High-power resistors that can dissipate many watts of electrical power as heat may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements (such as a volume control or a lamp dimmer), or as sensing devices for heat, light, humidity, force, or chemical activity.

Resistors are common elements of electrical networks and electronic circuits and are ubiquitous in electronic equipment. Practical resistors as discrete components can be composed of various compounds and forms. Resistors are also implemented within integrated circuits.

The electrical function of a resistor is specified by its resistance: common commercial resistors are manufactured over a range of more than nine orders of magnitude. The nominal value of the resistance will fall within a manufacturing tolerance.

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Resistor

A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. Resistors act to reduce current flow, and, at the same time, act to lower voltage levels within circuits. In electronic circuits resistors are used to limit current flow, to adjust signal levels, bias active elements, terminate transmission lines among other uses. High-power resistors that can dissipate many watts of electrical power as heat may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements (such as a volume control or a lamp dimmer), or as sensing devices for heat, light, humidity, force, or chemical activity.

Resistors are common elements of electrical networks and electronic circuits and are ubiquitous in electronic equipment. Practical resistors as discrete components can be composed of various compounds and forms. Resistors are also implemented within integrated circuits.

The electrical function of a resistor is specified by its resistance: common commercial resistors are manufactured over a range of more than nine orders of magnitude. The nominal value of the resistance will fall within a manufacturing tolerance.

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Capacitor

A capacitor (originally known as a condenser) is a passive two-terminal electrical component used to store energy electrostatically in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors (plates) separated by a dielectric (i.e. insulator). The conductors can be thin films, foils or sintered beads of metal or conductive electrolyte, etc. The nonconducting dielectric acts to increase the capacitor's charge capacity. A dielectric can be glass, ceramic, plastic film, air, vacuum, paper, mica, oxide layer etc. Capacitors are widely used as parts of electrical circuits in many common electrical devices. Unlike a resistor, an ideal capacitor does not dissipate energy. Instead, a capacitor stores energy in the form of an electrostatic field between its plates.

When there is a potential difference across the conductors (e.g., when a capacitor is attached across a battery), an electric field develops across the dielectric, causing positive charge +Q to collect on one plate and negative charge −Q to collect on the other plate. If a battery has been attached to a capacitor for a sufficient amount of time, no current can flow through the capacitor. However, if a time-varying voltage is applied across the leads of the capacitor, a displacement current can flow.

An ideal capacitor is characterized by a single constant value for its capacitance. Capacitance is expressed as the ratio of the electric charge Q on each conductor to the potential difference V between them. The SI unit of capacitance is the farad (F), which is equal to one coulomb per volt (1 C/V). Typical capacitance values range from about 1 pF (10^−12 F) to about 1 mF (10^−3 F).

The capacitance is greater when there is a narrower separation between conductors and when the conductors have a larger surface area. In practice, the dielectric between the plates passes a small amount of leakage current and also has an electric field strength limit, known as the breakdown voltage. The conductors and leads introduce an undesired inductance and resistance.

Capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass. In analog filter networks, they smooth the output of power supplies. In resonant circuits they tune radios to particular frequencies. In electric power transmission systems, they stabilize voltage and power flow.

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Inductor

An inductor, also called a coil or reactor, is a passive two-terminal electrical component which resists changes in electric current passing through it. It consists of a conductor such as a wire, usually wound into a coil. When a current flows through it, energy is stored temporarily in a magnetic field in the coil. When the current flowing through an inductor changes, the time-varying magnetic field induces a voltage in the conductor, according to Faraday’s law of electromagnetic induction, which opposes the change in current that created it.

As a result, inductors always oppose a change in current, in the same way that a flywheel oppose a change in rotational velocity. Care should be taken not to confuse this with the resistance provided by a resistor.

An inductor is characterized by its inductance, the ratio of the voltage to the rate of change of current, which has units of henries (H). Inductors have values that typically range from 1 µH (10−6H) to 1 H. Many inductors have a magnetic core made of iron or ferrite inside the coil, which serves to increase the magnetic field and thus the inductance. Along with capacitors and resistors, inductors are one of the three passive linear circuit elements that make up electric circuits. Inductors are widely used in alternating current (AC) electronic equipment, particularly in radio equipment. They are used to block AC while allowing DC to pass; inductors designed for this purpose are called chokes. They are also used in electronic filters to separate signals of different frequencies, and in combination with capacitors to make tuned circuits, used to tune radio and TV receivers.

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Diode

In electronics, a diode is a two-terminal electronic component with asymmetric conductance; it has low (ideally zero) resistance to current in one direction, and high (ideally infinite) resistance in the other. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material with a p–n junction connected to two electrical terminals. A vacuum tube diode has two electrodes, a plate (anode) and a heated cathode. Semiconductor diodes were the first semiconductor electronic devices. The discovery of crystals' rectifying abilities was made by German physicist Ferdinand Braun in 1874. The first semiconductor diodes, called cat's whisker diodes, developed around 1906, were made of mineral crystals such as galena. Today, most diodes are made of silicon, but other semiconductors such as selenium or germanium are sometimes used.

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Resistor

A transistor is a semiconductor device used to amplify and switch electronic signals and electrical power. It is composed of semiconductor material with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals changes the current through another pair of terminals. Because the controlled (output) power can be higher than the controlling (input) power, a transistor can amplify a signal. Today, some transistors are packaged individually, but many more are found embedded in integrated circuits.

The transistor is the fundamental building block of modern electronic devices, and is ubiquitous in modern electronic systems. Following its development in 1947 by American physicists John Bardeen, Walter Brattain, and William Shockley, the transistor revolutionized the field of electronics, and paved the way for smaller and cheaper radios, calculators, and computers, among other things. The transistor is on the list of IEEE milestones in electronics, and the inventors were jointly awarded the 1956 Nobel Prize in Physics for their achievement.

The electrical function of a resistor is specified by its resistance: common commercial resistors are manufactured over a range of more than nine orders of magnitude. The nominal value of the resistance will fall within a manufacturing tolerance.

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Troy McGrath


Troy McGrath is my pseudoname.

I like making HTML/CSS/Javascript based web apps because they are very simple. I am not a computer student, infact I am an "Electronics and Communication" student, and have recently started to make app because they are fun.

I always wanted to make video games because I like story telling and feel that video games are the greatest way to do so. When I am not coding, I am learning languages (German, Spanish, French and a little bit Italian) and making electronics based projects. Also, I think that web apps are a great initiative for my country, India.
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Elektronix


A simple app with basic info about some theorems and components.

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Elektronix


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