1.
AC power
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Power in an electric circuit is the rate of flow of energy past a given point of the circuit. In alternating current circuits, energy storage such as inductors and capacitors may result in periodic reversals of the direction of energy flow. The portion of power that, averaged over a cycle of the AC waveform. The portion of power due to stored energy, which returns to the source in each cycle, is known as reactive power, in a simple alternating current circuit consisting of a source and a linear load, both the current and voltage are sinusoidal. If the load is resistive, the two quantities reverse their polarity at the same time. At every instant the product of voltage and current is positive or zero, in this case, only active power is transferred. If the load is purely reactive, then the voltage and current are 90 degrees out of phase, There is no net energy flow over each half cycle. In this case, only reactive power flows, There is no net transfer of energy to the load, however electrical power does flow along the wires and returns by flowing in reverse along the same wires. During its travels both from the source to the reactive load and back to the power source, this purely reactive power flow loses energy to the line resistance. Practical loads have resistance as well as inductance, and/or capacitance, Power engineers analyse the apparent power as being the magnitude of the vector sum of active and reactive power. Apparent power is the product of the rms values of voltage, conductors, transformers and generators must be sized to carry the total current, not just the current that does useful work. Another consequence is that adding the apparent power for two loads will not accurately give the power unless they have the same phase difference between current and voltage. Conventionally, capacitors are treated as if they generate reactive power, if a capacitor and an inductor are placed in parallel, then the currents flowing through the capacitor and the inductor tend to cancel rather than add. The result of this is that capacitive and inductive circuit elements tend to each other out. Current lagging voltage, current leading voltage and these are all denoted in the diagram to the right. In the diagram, P is the power, Q is the reactive power, S is the complex power. Reactive power does not do any work, so it is represented as the axis of the vector diagram. Active power does do work, so it is the real axis, the unit for all forms of power is the watt, but this unit is generally reserved for active power

2.
Electrical network
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An electrical network is an interconnection of electrical components or a model of such an interconnection, consisting of electrical elements. An electrical circuit is a network consisting of a closed loop, linear electrical networks, a special type consisting only of sources, linear lumped elements, and linear distributed elements, have the property that signals are linearly superimposable. They are thus more easily analyzed, using powerful frequency domain methods such as Laplace transforms, to determine DC response, AC response, a resistive circuit is a circuit containing only resistors and ideal current and voltage sources. Analysis of resistive circuits is less complicated than analysis of circuits containing capacitors and inductors, if the sources are constant sources, the result is a DC circuit. A network that contains active components is known as an electronic circuit. Such networks are generally nonlinear and require more complex design and analysis tools, an active network is a network that contains an active source – either a voltage source or current source. A passive network is a network that does not contain an active source, a network is linear if its signals obey the principle of superposition, otherwise it is non-linear. Sources can be classified as independent sources and dependent sources Ideal Independent Source maintains same voltage or current regardless of the elements present in the circuit. Its value is either constant or sinusoidal, the strength of voltage or current is not changed by any variation in connected network. Dependent Sources depend upon a particular element of the circuit for delivering the power or voltage or current depending upon the type of source it is, a number of electrical laws apply to all electrical networks. These include, Kirchhoffs current law, The sum of all currents entering a node is equal to the sum of all currents leaving the node, Kirchhoffs voltage law, The directed sum of the electrical potential differences around a loop must be zero. Ohms law, The voltage across a resistor is equal to the product of the resistance, nortons theorem, Any network of voltage or current sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor. Thévenins theorem, Any network of voltage or current sources and resistors is electrically equivalent to a voltage source in series with a single resistor. Other more complex laws may be needed if the network contains nonlinear or reactive components, non-linear self-regenerative heterodyning systems can be approximated. Applying these laws results in a set of equations that can be solved either algebraically or numerically. To design any electrical circuit, either analog or digital, electrical engineers need to be able to predict the voltages, simple linear circuits can be analyzed by hand using complex number theory. In more complex cases the circuit may be analyzed with specialized programs or estimation techniques such as the piecewise-linear model. More complex circuits can be analyzed numerically with software such as SPICE or GNUCAP, once the steady state solution is found, the operating points of each element in the circuit are known

3.
Root mean square
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In statistics and its applications, the root mean square is defined as the square root of mean square. The RMS is also known as the mean and is a particular case of the generalized mean with exponent 2. RMS can also be defined for a continuously varying function in terms of an integral of the squares of the values during a cycle. For a cyclically alternating electric current, RMS is equal to the value of the current that would produce the same average power dissipation in a resistive load. In Estimation theory the mean square error of an estimator is a measure of the imperfection of the fit of the estimator to the data. The RMS value of a set of values is the root of the arithmetic mean of the squares of the values. In Physics, the RMS current is the value of the current that dissipates power in a resistor. In the case of a set of n values, the RMS x r m s =1 n, the RMS over all time of a periodic function is equal to the RMS of one period of the function. The RMS value of a function or signal can be approximated by taking the RMS of a sequence of equally spaced samples. Additionally, the RMS value of various waveforms can also be determined without calculus, in the case of the RMS statistic of a random process, the expected value is used instead of the mean. If the waveform is a sine wave, the relationships between amplitudes and RMS are fixed and known, as they are for any continuous periodic wave. However, this is not true for a waveform which may or may not be periodic or continuous. For a zero-mean sine wave, the relationship between RMS and peak-to-peak amplitude is, Peak-to-peak =22 × R M S ≈2.8 × R M S, for other waveforms the relationships are not the same as they are for sine waves. Waveforms made by summing known simple waveforms have an RMS that is the root of the sum of squares of the component RMS values, if the component waveforms are orthogonal. R M S Total = R M S12 + R M S22 + ⋯ + R M S n 2 A special case of this, another special case, useful in statistics, is given in #Relationship to other statistics. Electrical engineers often need to know the power, P, dissipated by an electrical resistance and it is easy to do the calculation when there is a constant current, I, through the resistance. Average power can also be using the same method that in the case of a time-varying voltage, V, with RMS value VRMS. This equation can be used for any waveform, such as a sinusoidal or sawtooth waveform

4.
Voltage
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Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential energy between two points per unit electric charge. The voltage between two points is equal to the work done per unit of charge against an electric field to move the test charge between two points. This is measured in units of volts, voltage can be caused by static electric fields, by electric current through a magnetic field, by time-varying magnetic fields, or some combination of these three. A voltmeter can be used to measure the voltage between two points in a system, often a reference potential such as the ground of the system is used as one of the points. A voltage may represent either a source of energy or lost, used, given two points in space, x A and x B, voltage is the difference in electric potential between those two points. Electric potential must be distinguished from electric energy by noting that the potential is a per-unit-charge quantity. Like mechanical potential energy, the zero of electric potential can be chosen at any point, so the difference in potential, i. e. the voltage, is the quantity which is physically meaningful. The voltage between point A to point B is equal to the work which would have to be done, per unit charge, against or by the electric field to move the charge from A to B. The voltage between the two ends of a path is the energy required to move a small electric charge along that path. Mathematically this is expressed as the integral of the electric field. In the general case, both an electric field and a dynamic electromagnetic field must be included in determining the voltage between two points. Historically this quantity has also called tension and pressure. Pressure is now obsolete but tension is used, for example within the phrase high tension which is commonly used in thermionic valve based electronics. Voltage is defined so that negatively charged objects are pulled towards higher voltages, therefore, the conventional current in a wire or resistor always flows from higher voltage to lower voltage. Current can flow from lower voltage to higher voltage, but only when a source of energy is present to push it against the electric field. This is the case within any electric power source, for example, inside a battery, chemical reactions provide the energy needed for ion current to flow from the negative to the positive terminal. The electric field is not the only factor determining charge flow in a material, the electric potential of a material is not even a well defined quantity, since it varies on the subatomic scale. A more convenient definition of voltage can be found instead in the concept of Fermi level, in this case the voltage between two bodies is the thermodynamic work required to move a unit of charge between them

5.
Electric current
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An electric current is a flow of electric charge. In electric circuits this charge is carried by moving electrons in a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in an ionised gas. The SI unit for measuring a current is the ampere. Electric current is measured using a device called an ammeter, electric currents cause Joule heating, which creates light in incandescent light bulbs. They also create magnetic fields, which are used in motors, inductors and generators, the particles that carry the charge in an electric current are called charge carriers. In metals, one or more electrons from each atom are loosely bound to the atom and these conduction electrons are the charge carriers in metal conductors. The conventional symbol for current is I, which originates from the French phrase intensité de courant, current intensity is often referred to simply as current. The I symbol was used by André-Marie Ampère, after whom the unit of current is named, in formulating the eponymous Ampères force law. The notation travelled from France to Great Britain, where it became standard, in a conductive material, the moving charged particles which constitute the electric current are called charge carriers. In other materials, notably the semiconductors, the carriers can be positive or negative. Positive and negative charge carriers may even be present at the same time, a flow of positive charges gives the same electric current, and has the same effect in a circuit, as an equal flow of negative charges in the opposite direction. Since current can be the flow of positive or negative charges. The direction of current is arbitrarily defined as the same direction as positive charges flow. This is called the direction of current I. If the current flows in the direction, the variable I has a negative value. When analyzing electrical circuits, the direction of current through a specific circuit element is usually unknown. Consequently, the directions of currents are often assigned arbitrarily

6.
Direct current
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Direct current is a flow of electrical charge carriers that always takes place in the same direction. The current need not always have the magnitude, but if it is to be defined as dc. This contrasts with alternating current which varies the direction of flow, sources of direct current include power supplies, electrochemical cells and batteries, and photovoltaic cells and panels. The intensity, or amplitude, of a direct current might fluctuate with time, in some such cases the dc has an ac component superimposed on it. An example of this is the output of a cell that receives a modulated light communications signal. A source of dc is sometimes called a dc generator, batteries and various other sources of dc produce a constant voltage. This is called pure dc and can be represented by a straight, the peak and effective values are the same. The peak to peak value is zero because the instantaneous amplitude never changes, in some instances the value of a dc voltage pulsates or oscillates rapidly with time, in a manner similar to the changes in an ac wave. The unfiltered output of a wave or a full wave rectifier. In 1820, Hans Christian Orsted discovered that electrical current creates a magnetic field and this discovery made scientists relate magnetism to the electric phenomena. In 1879, Thomas Edison invented the light bulb. He improved a 50-year-old idea using lower current electricity, a vacuum inside the globe and a small carbonized filament. At that time, the idea of lightning was not new. Edison not only invented an incandescent electric light, but an electric lighting system contained all the necessary elements to make the incandescent light safe, economical. Prior to 1879, direct current electricity had been used in lighting for the outdoors and it was in the 1880s when the modern electric utility industry began. It was an evolution from street lighting systems and from gas and it was located in Lower Manhattan, on Pearl Street. This station provided light and electricity to customers in a one square mile range, the station was called Thomas Edisons Pearl Street Electricity Generating Station. This station introduced four elements of an electric utility system, Efficient distribution, competitive price, reliable central generation

7.
Alternating current
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Alternating current, is an electric current which periodically reverses direction, whereas direct current flows only in one direction. A common source of DC power is a cell in a flashlight. The abbreviations AC and DC are often used to mean simply alternating and direct, the usual waveform of alternating current in most electric power circuits is a sine wave. In certain applications, different waveforms are used, such as triangular or square waves, audio and radio signals carried on electrical wires are also examples of alternating current. These types of alternating current carry information encoded onto the AC signal and these currents typically alternate at higher frequencies than those used in power transmission. Electrical energy is distributed as alternating current because AC voltage may be increased or decreased with a transformer, use of a higher voltage leads to significantly more efficient transmission of power. The power losses in a conductor are a product of the square of the current and this means that when transmitting a fixed power on a given wire, if the current is halved, the power loss will be four times less. Power is often transmitted at hundreds of kilovolts, and transformed to 100–240 volts for domestic use, high voltages have disadvantages, such as the increased insulation required, and generally increased difficulty in their safe handling. In a power plant, energy is generated at a convenient voltage for the design of a generator, near the loads, the transmission voltage is stepped down to the voltages used by equipment. Consumer voltages vary somewhat depending on the country and size of load, the voltage delivered to equipment such as lighting and motor loads is standardized, with an allowable range of voltage over which equipment is expected to operate. Standard power utilization voltages and percentage tolerance vary in the different mains power systems found in the world, high-voltage direct-current electric power transmission systems have become more viable as technology has provided efficient means of changing the voltage of DC power. HVDC systems, however, tend to be expensive and less efficient over shorter distances than transformers. Three-phase electrical generation is very common, the simplest way is to use three separate coils in the generator stator, physically offset by an angle of 120° to each other. Three current waveforms are produced that are equal in magnitude and 120° out of phase to each other, if coils are added opposite to these, they generate the same phases with reverse polarity and so can be simply wired together. In practice, higher pole orders are commonly used, for example, a 12-pole machine would have 36 coils. The advantage is that lower rotational speeds can be used to generate the same frequency, for example, a 2-pole machine running at 3600 rpm and a 12-pole machine running at 600 rpm produce the same frequency, the lower speed is preferable for larger machines. If the load on a system is balanced equally among the phases. Even in the worst-case unbalanced load, the current will not exceed the highest of the phase currents

8.
Sine wave
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A sine wave or sinusoid is a mathematical curve that describes a smooth repetitive oscillation. It is named after the sine, of which it is the graph. It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time is, y = A sin = A sin where, A = the amplitude, F = the ordinary frequency, the number of oscillations that occur each second of time. ω = 2πf, the frequency, the rate of change of the function argument in units of radians per second φ = the phase. When φ is non-zero, the entire waveform appears to be shifted in time by the amount φ /ω seconds, a negative value represents a delay, and a positive value represents an advance. The sine wave is important in physics because it retains its shape when added to another sine wave of the same frequency and arbitrary phase. It is the only periodic waveform that has this property and this property leads to its importance in Fourier analysis and makes it acoustically unique. The wavenumber is related to the frequency by. K = ω v =2 π f v =2 π λ where λ is the wavelength, f is the frequency, and v is the linear speed. This equation gives a wave for a single dimension, thus the generalized equation given above gives the displacement of the wave at a position x at time t along a single line. This could, for example, be considered the value of a wave along a wire, in two or three spatial dimensions, the same equation describes a travelling plane wave if position x and wavenumber k are interpreted as vectors, and their product as a dot product. For more complex such as the height of a water wave in a pond after a stone has been dropped in. This wave pattern occurs often in nature, including wind waves, sound waves, a cosine wave is said to be sinusoidal, because cos = sin , which is also a sine wave with a phase-shift of π/2 radians. Because of this start, it is often said that the cosine function leads the sine function or the sine lags the cosine. The human ear can recognize single sine waves as sounding clear because sine waves are representations of a frequency with no harmonics. Presence of higher harmonics in addition to the fundamental causes variation in the timbre, on the other hand, if the sound contains aperiodic waves along with sine waves, then the sound will be perceived noisy as noise is characterized as being aperiodic or having a non-repetitive pattern. In 1822, French mathematician Joseph Fourier discovered that sinusoidal waves can be used as building blocks to describe and approximate any periodic waveform

9.
Uninterruptible power supply
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The on-battery runtime of most uninterruptible power sources is relatively short but sufficient to start a standby power source or properly shut down the protected equipment. UPS units range in size from units designed to protect a computer without a video monitor to large units powering entire data centers or buildings. The worlds largest UPS, the 46-megawatt Battery Electric Storage System, in Fairbanks, Alaska, powers the entire city, the primary role of any UPS is to provide short-term power when the input power source fails. The three general categories of modern UPS systems are on-line, line-interactive and standby, a line-interactive UPS maintains the inverter in line and redirects the batterys DC current path from the normal charging mode to supplying current when power is lost. In a standby system the load is powered directly by the input power, most UPS below 1 kVA are of the line-interactive or standby variety which are usually less expensive. For large power units, Dynamic Uninterruptible Power Supplies are sometimes used, a synchronous motor/alternator is connected on the mains via a choke. Energy is stored in a flywheel, when the mains power fails, an eddy-current regulation maintains the power on the load as long as the flywheels energy is not exhausted. DUPS are sometimes combined or integrated with a generator that is turned on after a brief delay. A fuel cell UPS has been developed in recent years using hydrogen, the offline/standby UPS offers only the most basic features, providing surge protection and battery backup. The protected equipment is connected directly to incoming utility power. When the incoming voltage falls below or rises above a level the SPS turns on its internal DC-AC inverter circuitry. The UPS then mechanically switches the connected equipment on to its DC-AC inverter output, the switchover time can be as long as 25 milliseconds depending on the amount of time it takes the standby UPS to detect the lost utility voltage. The UPS will be designed to power equipment, such as a personal computer. The line-interactive UPS is similar in operation to a standby UPS and this is a special type of transformer that can add or subtract powered coils of wire, thereby increasing or decreasing the magnetic field and the output voltage of the transformer. This may also be performed by a buck–boost transformer which is distinct from an autotransformer and this type of UPS is able to tolerate continuous undervoltage brownouts and overvoltage surges without consuming the limited reserve battery power. It instead compensates by automatically selecting different power taps on the autotransformer, depending on the design, changing the autotransformer tap can cause a very brief output power disruption, which may cause UPSs equipped with a power-loss alarm to chirp for a moment. This has become popular even in the cheapest UPSs because it takes advantage of components already included, the difference between the two voltages is because charging a battery requires a delta voltage. Furthermore, it is easier to do the switching on the side of the transformer because of the lower currents on that side