Leading And Lagging Current
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Leading And Lagging Current
Leading and lagging current are phenomena that occur as a result of alternating current. In a circuit with alternating current, the value of voltage and current vary sinusoidally. In this type of circuit, the terms ''lead, lag,'' and ''in phase'' are used to describe current with reference to voltage. Current is in phase with voltage when there is no phase shift between the sinusoids describing their time varying behavior. This generally occurs when the load drawing the current is resistive. In electric power flow, it is important to know how much current is leading or lagging because it creates the reactive power in the system, as opposed to the AC power#Active, reactive, and apparent power, active (real) power. It can also play an important role in the operation of three phase electric power systems. Angle notation Angle notation can easily describe leading and lagging current:  A \angle \theta. In this equation, the value of theta is the important factor for leading and ...
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Voltage With Leading And Lagging Current
Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), work needed per unit of Electric charge, charge to move a positive Test particle#Electrostatics, test charge from the first point to the second point. In the SI unit, International System of Units (SI), the SI derived unit, derived unit for voltage is the ''volt'' (''V''). The voltage between points can be caused by the build-up of electric charge (e.g., a capacitor), and from an electromotive force (e.g., electromagnetic induction in a Electric generator, generator). On a macroscopic scale, a potential difference can be caused by electrochemical processes (e.g., cells and batteries), the pressure-induced piezoelectric effect, and the thermoelectric effect. Since it is the difference in electric potential, it is a physical Scalar (physics ...
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Cartesian Coordinate
In geometry, a Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called ''coordinates'', which are the signed distances to the point from two fixed perpendicular oriented lines, called '' coordinate lines'', ''coordinate axes'' or just ''axes'' (plural of ''axis'') of the system. The point where the axes meet is called the '' origin'' and has as coordinates. The axes directions represent an orthogonal basis. The combination of origin and basis forms a coordinate frame called the Cartesian frame. Similarly, the position of any point in three-dimensional space can be specified by three ''Cartesian coordinates'', which are the signed distances from the point to three mutually perpendicular planes. More generally, Cartesian coordinates specify the point in an -dimensional Euclidean space for any dimension . These coordinates are the signed distances from the point to mutually perpendicular fixed h ...
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Electric Power
Electric power is the rate of transfer of electrical energy within a electric circuit, circuit. Its SI unit is the watt, the general unit of power (physics), power, defined as one joule per second. Standard prefixes apply to watts as with other SI units: thousands, millions and billions of watts are called kilowatts, megawatts and gigawatts respectively. In common parlance, electric power is the production and delivery of electrical energy, an essential public utility in much of the world. Electric power is usually produced by electric generators, but can also be supplied by sources such as Electric battery, electric batteries. It is usually supplied to businesses and homes (as domestic mains electricity) by the electric power industry through an electrical grid. Electric power can be delivered over long distances by electric power transmission, transmission lines and used for applications such as Electric motor, motion, Electric light, light or Electric heat, heat with high ...
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Electrical Parameters
Electricity is the set of physical phenomena associated with the presence and motion of matter possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwell's equations. Common phenomena are related to electricity, including lightning, static electricity, electric heating, electric discharges and many others. The presence of either a positive or negative electric charge produces an electric field. The motion of electric charges is an electric current and produces a magnetic field. In most applications, Coulomb's law determines the force acting on an electric charge. Electric potential is the work done to move an electric charge from one point to another within an electric field, typically measured in volts. Electricity plays a central role in many modern technologies, serving in electric power where electric current is used to energise equipment, and in electronics dealing with electrical ...
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Les Besser
Les Besser (born 1936) is an American electronics engineer, an expert in microwave technology. He is the founder (1973) of Compact Software, the first commercially successful microwave computer-aided design (CAD) company, which commercialize his program COMPACT (Computerized Optimization of Microwave Passive and Active CircuiTs).Les Besser bio
at Microwaves 101 Hall of Fame
Les Besser bio
at Besser Associates
Les Besser was born and raised in Hungary ( and

Volt-ampere Reactive
The volt-ampere ( SI symbol: VA, sometimes V⋅A or V A) is the unit of measurement for apparent power in an electrical circuit. It is the product of the root mean square voltage (in volts) and the root mean square current (in amperes). Volt-amperes are usually used for analyzing alternating current (AC) circuits. In direct current (DC) circuits, this product is equal to the real power, measured in watts. The volt-ampere is dimensionally equivalent to the watt: in SI units, 1 V⋅A = 1 W. VA rating is most used for generators and transformers, and other power handling equipment, where loads may be reactive (inductive or capacitive). Formulation For a simple electrical circuit running on direct current, the electrical current and voltage are constant. In that case, the real power (''P'', measured in watts) is the product of the current (''I'', measured in amperes) and the voltage from one side of the circuit to the other (''V'', measured in volts): :P = I ...
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Volt-ampere
The volt-ampere ( SI symbol: VA, sometimes V⋅A or V A) is the unit of measurement for apparent power in an electrical circuit. It is the product of the root mean square voltage (in volts) and the root mean square current (in amperes). Volt-amperes are usually used for analyzing alternating current (AC) circuits. In direct current (DC) circuits, this product is equal to the real power, measured in watts. The volt-ampere is dimensionally equivalent to the watt: in SI units, 1 V⋅A = 1 W. VA rating is most used for generators and transformers, and other power handling equipment, where loads may be reactive (inductive or capacitive). Formulation For a simple electrical circuit running on direct current, the electrical current and voltage are constant. In that case, the real power (''P'', measured in watts) is the product of the current (''I'', measured in amperes) and the voltage from one side of the circuit to the other (''V'', measured in volts): ...
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Power Factor
In electrical engineering, the power factor of an AC power system is defined as the ratio of the ''real power'' absorbed by the electrical load, load to the ''apparent power'' flowing in the circuit. Real power is the average of the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the product of root mean square (RMS) current and voltage. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power may be greater than the real power, so more current flows in the circuit than would be required to transfer real power alone. A power factor magnitude of less than one indicates the voltage and current are not in phase, reducing the average Product (mathematics), product of the two. A negative power factor occurs when the device (normally the load) generates real power, which then flows back to ...
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Electrical Impedance
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of Electrical_resistance, resistance and Electrical_reactance, reactance in a electrical circuit, circuit. Quantitatively, the impedance of a two-terminal Electrical element, circuit element is the ratio of the phasor, complex representation of the Sine wave, sinusoidal voltage between its terminals, to the complex representation of the current flowing through it. In general, it depends upon the frequency of the sinusoidal voltage. Impedance extends the concept of Electrical resistance, resistance to alternating current (AC) circuits, and possesses both Euclidean vector, magnitude and Phase (waves), phase, unlike resistance, which has only magnitude. Impedance can be represented as a complex number, with the same units as resistance, for which the SI unit is the ohm (). Its symbol is usually , and it may be represented by writing its magnitude and phase in the Polar ...
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Arthur E
Arthur is a masculine given name of uncertain etymology. Its popularity derives from it being the name of the legendary hero King Arthur. A common spelling variant used in many Slavic, Romance, and Germanic languages is Artur. In Spanish and Italian it is Arturo. Etymology The earliest attestation of the name Arthur is in the early 9th century Welsh-Latin text '' Historia Brittonum'', where it refers to a circa 5th century Romano-British general who fought against the invading Saxons, and who later gave rise to the famous King Arthur of medieval legend and literature. A possible earlier mention of the same man is to be found in the epic Welsh poem '' Y Gododdin'' by Aneirin, which some scholars assign to the late 6th century, though this is still a matter of debate and the poem only survives in a late 13th century manuscript entitled the Book of Aneirin. A 9th-century Breton landowner named Arthur witnessed several charters collected in the '' Cartulary of Redon''. The Iris ...
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American Academy Of Arts And Sciences
The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other Founding Fathers of the United States. It is headquartered in Cambridge, Massachusetts. Membership in the academy is achieved through a nominating petition, review, and election process. The academy's quarterly journal, '' Dædalus'', is published by the MIT Press on behalf of the academy, and has been open-access since January 2021. The academy also conducts multidisciplinary public policy research. Laurie L. Patton has served as President of the Academy since January 2025. History The Academy was established by the Massachusetts legislature on May 4, 1780, charted in order "to cultivate every art and science which may tend to advance the interest, honor, dignity, and happiness of a free, independent, and virtuous people." The sixty-tw ...
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Phasor
In physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude and initial phase are time-invariant and whose angular frequency is fixed. It is related to a more general concept called analytic representation,Bracewell, Ron. ''The Fourier Transform and Its Applications''. McGraw-Hill, 1965. p269 which decomposes a sinusoid into the product of a complex constant and a factor depending on time and frequency. The complex constant, which depends on amplitude and phase, is known as a phasor, or complex amplitude, and (in older texts) sinor or even complexor. A common application is in the steady-state analysis of an electrical network powered by time varying current where all signals are assumed to be sinusoidal with a common frequency. Phasor representation allows the analyst to represent the amplitude and phase of the signal using a single complex number. The only difference in their analytic rep ...
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