Electric power is defined as the rate at which electrical energy Electric potential energy aka "electrostatic potential energy" is a potential energy associated with the conservative Coulomb forces within a defined system of point charges. The term "electrostatic potential energy" is preferred here because it seems less likely to be misunderstood. The reference zero is usually taken to be a is transferred by an electric circuit An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources, and switches. The SI The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science unit of power is the watt The watt is a derived unit of power in the International System of Units , named after the 18th-century Scottish engineer James Watt. Its unit symbol is W. The unit measures the rate of energy conversion.
Electrical power is transmitted with overhead lines on pylons like these in Brisbane Brisbane is the capital and most populous city in the Australian state of Queensland and the third most populous city in Australia. Brisbane's metropolitan area has an approximate population of 2 million. A resident of Brisbane is commonly known as a "Brisbanite", Australia For at least 40,000 years before European settlement in the late 18th century, Australia was inhabited by indigenous Australians, who belonged to one or more of the roughly 250 language groups. After sporadic visits by fishermen from the immediate north and discovery by Dutch explorers in 1606, Australia's eastern half was claimed by the British. For underground transmission see high voltage cables A high voltage cable - also called HV cable - is used for electric power transmission at high voltage. High voltage cables of differing types have a variety of applications in instruments, ignition systems, AC and DC power transmission. In all applications, the insulation of the cable must not deteriorate due to the high voltage stress, ozone.When electric current flows in a circuit, it can transfer energy In physics, energy is a quantity that can be assigned to every particle, object, and system of objects as a consequence of the state of that particle, object or system of objects. Different forms of energy include kinetic, potential, thermal, gravitational, sound, elastic, light, and electromagnetic energy. The forms of energy are often named to do mechanical In physics, mechanical work is the amount of energy transferred by a force acting through a distance. Like energy, it is a scalar quantity, with SI units of joules. The term work was first coined in 1826 by the French mathematician Gaspard-Gustave Coriolis or thermodynamic work In thermodynamics, work performed by a system is the quantity of energy transferred by the system to another that is accounted for in a particular way; namely, by changes in the external generalized mechanical constraints on the system. Devices convert electrical energy into many useful forms, such as heat In physics and thermodynamics, heat is the process of energy transfer from one body or system to another due to thermal contact, which in turn is defined as an energy transfer to a body in any other way than due to work performed on the body (electric heaters An electric heater is an electrical appliance that converts electrical energy into heat. The heating element inside every electric heater is simply an electrical resistor, and works on the principle of Joule heating: an electric current through a resistor converts electrical energy into heat energy), light Light is electromagnetic radiation of a wavelength that is visible to the human eye . In physics, the term light sometimes refers to electromagnetic radiation of any wavelength, whether visible or not (light bulbs The incandescent light bulb, incandescent lamp or incandescent light globe is a source of electric light that works by incandescence . An electric current passes through a thin filament, heating it to a temperature that produces light. The enclosing glass bulb contains either a vacuum or an inert gas to prevent oxidation of the hot filament), motion The kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. Negative work of the same magnitude (electric motors An electric motor uses electrical energy to produce mechanical energy, very typically through the interaction of magnetic fields and current-carrying conductors. The reverse process, producing electrical energy from mechanical energy, is accomplished by a generator or dynamo. Many types of electric motors can be run as generators, and vice versa), sound Sound is a travelling wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations (loudspeaker A loudspeaker is an electroacoustic transducer that converts an electrical signal into sound. The speaker moves in accordance with the variations of an electrical signal and causes sound waves to propagate through a medium such as air or water) or chemical changes In chemistry and manufacturing, electrolysis is a method of using an electric current to drive an otherwise non-spontaneous chemical reaction. Electrolysis is commercially highly important as a stage in the separation of elements from naturally occurring sources such as ores using an electrolytic cell. Electricity can be produced mechanically by generation The fundamental principles of electricity generation were discovered during the 1820s and early 1830s by the British scientist Michael Faraday. His basic method is still used today: electricity is generated by the movement of a loop of wire, or disc of copper between the poles of a magnet, or chemically, or by direct conversion from light in photovoltaic cells A solar cell or photovoltaic cell is a device that converts sunlight directly into electricity by the photovoltaic effect. Sometimes the term solar cell is reserved for devices intended specifically to capture energy from sunlight, while the term photovoltaic cell is used when the light source is unspecified. Assemblies of cells are used to make, also it can be stored Grid energy storage refers to the methods used to large-scale store electricity within an electrical power grid. Electrical energy is stored during times when production (from power plants) exceeds consumption and the stores are utilized at times when consumption exceeds production. In this way, electricity production need not be drastically chemically in batteries An electrical battery is a combination of one or more electrochemical cells, used to convert stored chemical energy into electrical energy. Since the invention of the first Voltaic pile in 1800 by Alessandro Volta, the battery has become a common power source for many household and industrial applications. According to a 2005 estimate, the.
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Mathematics of electric power
Circuits
Electric power, like mechanical power, is represented by the letter P in electrical equations. The term wattage is used colloquially to mean "electric power in watts."
Direct current
In direct current resistive The electrical resistance of an object is a measure of its attraction to the passage of a steady electric current. An object of uniform cross section will have a resistance proportional to its length and inversely proportional to its cross-sectional area, and proportional to the resistivity of the material circuits, electrical power is calculated using Joule's law Joule's first law, also known as the Joule effect, is a physical law expressing the relationship between the heat generated by the current flowing through a conductor. It is named for James Prescott Joule who studied the phenomenon in the 1840s. It is expressed as::
where P is the electric power, V the potential difference The voltage between two points is a short name for the electrical force that would drive an electric current between those points. Specifically, voltage is equal to energy per unit charge. In the case of static electric fields, the voltage between two points is equal to the electrical potential difference between those points. In the more general, and I the electric current Electric current means, depending on the context, a flow of electric charge or the rate of flow of electric charge (a quantity). This flowing electric charge is typically carried by moving electrons, in a conductor such as wire; in an electrolyte, it is instead carried by ions, and, in a plasma, by both.
In the case of resistive The electrical resistance of an object is a measure of its opposition to the passage of a steady electric current. An object of uniform cross section will have a resistance proportional to its length and inversely proportional to its cross-sectional area, and proportional to the resistivity of the material (Ohmic, or linear) loads, Joule's law can be combined with Ohm's law In electrical circuits, Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points, and inversely proportional to the resistance between them, provided that the temperature remains constant (I = V/R) to produce alternative expressions for the dissipated power:
Alternating current
Main article: AC power 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 elements such as inductance and capacitance may result in periodic reversals of the direction of energy flow. The portion of power that, averaged over a complete cycle of the AC waveform, results in netIn alternating current 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 elements such as inductance and capacitance may result in periodic reversals of the direction of energy flow. The portion of power that, averaged over a complete cycle of the AC waveform, results in net circuits, energy storage elements such as inductance Inductance is the property in an electrical circuit where a change in the electric current through that circuit induces an electromotive force that opposes the change in current (See Induced EMF) and capacitance In electromagnetism and electronics, capacitance is the ability of a body to hold an electrical charge. Capacitance is also a measure of the amount of electrical energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor. In a parallel plate capacitor, capacitance is directly proportional to may result in periodic reversals of the direction of energy flow. The portion of power flow that, averaged over a complete cycle of the AC waveform, results in net transfer of energy in one direction is known as real power 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 elements such as inductance and capacitance may result in periodic reversals of the direction of energy flow. The portion of power that, averaged over a complete cycle of the AC waveform, results in net (also referred to as active power). That portion of power flow due to stored energy, that returns to the source in each cycle, is known as reactive power 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 elements such as inductance and capacitance may result in periodic reversals of the direction of energy flow. The portion of power that, averaged over a complete cycle of the AC waveform, results in net.
Power triangle The components of AC power 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 elements such as inductance and capacitance may result in periodic reversals of the direction of energy flow. The portion of power that, averaged over a complete cycle of the AC waveform, results in netThe relationship between real power, reactive power and apparent power can be expressed by representing the quantities as vectors. Real power is represented as a horizontal vector and reactive power is represented as a vertical vector. The apparent power vector is the hypotenuse of a right triangle formed by connecting the real and reactive power vectors. This representation is often called the power triangle. Using the Pythagorean Theorem In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle . In terms of areas, it states:, the relationship among real, reactive and apparent power is:
- (apparent power)2 = (real power)2 + (reactive power)2
Real and reactive powers can also be calculated directly from the apparent power, when the current and voltage are both sinusoids The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields. Its most basic form as a function of time is: with a known phase angle between them:
- (real power) = (apparent power)cos(θ)
- (reactive power) = (apparent power)sin(θ)
The ratio of real power to apparent power is called power factor The power factor of an AC electric power system is defined as the ratio of the real power flowing to the load to the apparent power, and is a dimensionless number between 0 and 1 . Real power is the capacity of the circuit for performing work in a particular time. Apparent power is the product of the current and voltage of the circuit. Due to and is a number always between 0 and 1.
The above theory of reactive power and the power triangle is true only when both the voltage and current is strictly sinusoidal. Therefore is more or less abandoned for low voltage distribution applications where the current normally is rather distorted. It can still be used for high voltage tranmission applications and, with some care, for medium voltage applications where the current normally is less distorted.
In space
Electrical power flows wherever electric and magnetic fields exist together and fluctuate in the same place. The simplest example of this is in electrical circuits, as the preceding section showed. In the general case, however, the simple equation P = IV must be replaced by a more complex calculation, the integral Integration is an important concept in mathematics and, together with differentiation, is one of the two main operations in calculus. Given a function ƒ of a real variable x and an interval [a, b] of the real line, the definite integral of the vector In elementary mathematics, physics, and engineering, a Euclidean vector is a geometric object that has both a magnitude (or length) and direction. A Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B, and denoted by cross-product In mathematics, the cross product, vector product or Gibbs vector product is a binary operation on two vectors in three-dimensional space. It has a vector result, a vector which is always perpendicular to both of the vectors being multiplied and the plane containing them. It has many applications in mathematics, engineering and physics of the electrical and magnetic fields over a specified area, thus:
The result is a scalar since it is the surface integral In mathematics, a surface integral is a definite integral taken over a surface ; it can be thought of as the double integral analog of the line integral. Given a surface, one may integrate over its scalar fields (that is, functions which return numbers as values), and vector fields (that is, functions which return vectors as values) of the Poynting vector In physics, the Poynting vector can be thought of as representing the energy flux of an electromagnetic field. It is named after its inventor John Henry Poynting. Oliver Heaviside and Nikolay Umov independently co-invented the Poynting vector. In Poynting's original paper and in many textbooks it is defined as.
See also
- High voltage cable A high voltage cable - also called HV cable - is used for electric power transmission at high voltage. High voltage cables of differing types have a variety of applications in instruments, ignition systems, AC and DC power transmission. In all applications, the insulation of the cable must not deteriorate due to the high voltage stress, ozone
- AC power 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 elements such as inductance and capacitance may result in periodic reversals of the direction of energy flow. The portion of power that, averaged over a complete cycle of the AC waveform, results in net
- EGRID
- World energy resources and consumption In 2008, total worldwide energy consumption was 474 exajoules with 80 to 90 percent derived from the combustion of fossil fuels. This is equivalent to an average power consumption rate of 15 terawatts (1.504×1013 W). Not all of the world's economies track their energy consumption with the same rigor, and the exact energy content of a barrel of
- Rural electricity Rural electrification is the process of bringing electrical power to rural and remote areas. Electricity is used not only for lighting and household purposes, but it also allows for mechanization of many farming operations, such as threshing, milking, and hoisting grain for storage; in areas facing labor shortages, this allows for greater
Power generation
References
- Reports on August 2003 Blackout, North American Electric Reliability Council website
- Croft, Terrell; Summers, Wilford I. (1987). American Electricans' Handbook (Eleventh Edition ed.). New York: McGraw Hill. ISBN 0-070-13932-6. http://books.mcgraw-hill.com/getbook.php?isbn=0071377352.
- Fink, Donald G.; Beaty, H. Wayne (1978). Standard Handbook for Electrical Engineers (Eleventh Edition ed.). New York: McGraw Hill. ISBN 0-070-20974-X. http://books.mcgraw-hill.com/getbook.php?isbn=0070220050.
Categories: Electric power | Electromagnetism
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Q. A certain airplane has tow independent alternator to provide electrical power. The probablity that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? Neither will fail? One or the other will fail? Show all steps carefully.
Asked by roberto m - Wed Jun 11 20:42:42 2008 - - 4 Answers - 0 Comments
A. Let X be the number of alternators that fail. X has the binomial distribution with n = 2 trials and success probability p = 0.02 In general, if X has the binomial distribution with n trials and a success probability of p then P[X = x] = n!/(x!(n-x)!) * p^x * (1-p)^(n-x) for values of x = 0, 1, 2, ..., n P[X = x] = 0 for any other value of x. The probability mass function is derived by looking at the number of combination of x objects chosen from n objects and then a total of x success and n - x failures. Or, in other words, the binomial is the sum of n independent and identically distributed Bernoulli trials. X ~ Binomial( n = 2 , p = 0.02 ) the mean of the binomial distribution is n * p = 0.04 the variance of the binomial… [cont.]
Answered by Merlyn - Thu Jun 12 14:19:18 2008
