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∂ The flow variable in an energy domain is the variable analogous to velocity in the mechanical domain. Electric current flow in coulombs/sec = amperes. Two things flow in an operating electrical circuit— charges and energy. The electric power P is equal to the energy consumption E divided by the consumption time t: P is the electric power in watt (W). Impedance can be thought of as an extension to the concept of resistance. [51] The idea of complex impedance was introduced by Arthur E. Kennelly in 1893, and the concept of impedance was not extended into the mechanical domain until 1920 by Kennelly and Arthur Gordon Webster. right, the two vault bank is replaced by a four vault bank. But using water as an analogy offers an easy way to gain a basic understanding. [25], Different fundamental variables are chosen for mechanical translation and rotational systems leading to two variants for each of the analogies. Therefore, $IV$ (which gives the power), will be the energy transferred per charge, times the charge that passes through a component … By 1900 the electrical analogy of the mechanical domain was becoming commonplace. The two-port element in the electrical domain that does this is called a gyrator. electrical circuit without explaining why. resistance is represented by rough (bumpy) road. There is a wide choice of variables that can be used, but most commonly used are a power conjugate pair of variables (described below) and the pair of Hamiltonian variables derived from these. The variable pair mmf and magnetic flux is not a power conjugate pair. [15] Another condition required of electrical systems for the application of the lumped element model is that no significant fields exist outside the component since these can couple to other unrelated components. [49] This was the earliest mechanical–electrical analogy. resistance is represented by rough (bumpy) road. Thus jewels arrive at the rate of 2 jewels/sec. At the high school level, the best answer to the question, reality, the amount of charge entering the battery during this Mechanical Analogy I: Intuitive Probably the first analogy that comes to mind between electrical and mechanical systems is that current is kind of like velocity—both are motion of some kind. Some authors discourage this terminology because it is not domain neutral. In the absence of a resistor, like in the water analogy, an uncontrolled amount of electricity can pass through the circuit if the power (positive terminal) is … tedious, so as we continue, banks will be drawn using the battery A different pair may be more appropriate for a system with a different geometry, such as a rotational system. The This is to be compared to the elements discussed so far which are all one-ports. example the unfortunate phrase “charging a battery” which should Rather, power is the combination of both voltage and current in a circuit. jewels to fall off the cars. Seely, Samuel; Tarnoff, Norman H.; Holstein, David, This page was last edited on 23 November 2020, at 11:56. Indeed, the lumped element abstract topology of electrical analysis has much to offer problems in the mechanical domain, and other energy domains for that matter. We now have the basic conceptual ampere = one coulomb/second. In the ideal horse pulling the railcar analogy, if the reactive power (kVAr) is near zero, then real power (kW) and apparent power (kVA) would almost be equal, which means the horse would not waste as much energy pulling the car. This is almost always the assumption when analyzing DC circuits though not often stated. the three vault bank, each vault supplies one jewel to each car i.e. By itself, that is not enough to fully define the analogy, a second variable must be chosen. Thus, for a given KVA: The more foam you have (the higher the percentage of KVAR), the lower your ratio of KW (beer) to KVA (beer plus foam). vault bank supplies energy to cars encountering two bumps. Power is a measure of how much work can be performed in a given amount of time. For this reason domain-neutral terminology is preferred when developing network diagrams for control systems. Power Factor (P.F.) play on the word volt. For instance the associations F with v and u with i can be made. coulomb. Forces act through an element; a rod with a force applied to the top will transmit the same force to an element connected to its bottom. t three bumps. [52], Maxwell's purpose in constructing this analogy was not to represent mechanical systems in terms of electrical networks. Electrically speaking this means that the resistance equivalent to a pair of resistors in series is the sum of the individual resistances. In this case, where the number of vaults matches the To ensure that all 4 jewels are lost, the cars must travel at, Let's now examine the rate at which energy is transferred to the bumpy road. d Thus, the power conjugate variables in the mechanical domain are analogs. The analogous pairs are voltage and pressure; electrical charge and fluid volume; current and fluid flow; electrical resistance and hydraulic resistance; electrical conductivity and hydraulic conductivity; and power in the two energy transmission media. [4] Thus, the first step in forming an analogy of a mechanical system is to describe it as a mechanical network in a similar way, that is, as a topological graph of ideal elements. This device converts voltages to currents and currents to voltages. Drawing banks and pictures of cars is In force voltage analogy, the mathematical equations of translational mechanical system are compared with mesh equations of the electrical system. topic. An important aspect of any electrical or electronic circuit is the power associated with it. [note 1] Another area of application is the mechanical parts of acoustic systems such as the pickup and tonearm of record players. I do my best to avoid this, but will stick with common usage. Since electric current is invisible and the processes in play in electronics are often difficult to demonstrate, the various electronic components are represented by hydraulic equivalents. By now it must be clear that what we are really talking about is: Power: the rate at which energy is transferred measured in watts = joules/sec. A classic example, as pointed out by Giovanni Gavetti and Jan W. Rivkin in a Harvard Business Review article titled “How Strategists Really Think: Tapping the Power of Analogy“: The experience of Enron shows how a seductive but bad analogy can lead to flawed decisions. t [31], Mobility analogies, also called the Firestone analogy, are the electrical duals of impedance analogies. [6], In an electrical network diagram, limited to linear systems, there are three passive elements: resistance, inductance, and capacitance; and two active elements: the voltage generator, and the current generator. [53] When George Ashley Campbell first demonstrated the use of loading coils to improve telephone lines in 1899, he calculated the distance needed between coils by analogy with the work of Charles Godfrey on mechanical lines loaded with periodic weights. In the electrical domain, a transmission line, a basic distributed element component, can be included in the model with the introduction of the additional element of electrical length. [18], The power conjugate variables are a pair of variables whose product is power. Electricity 101 – Voltage, Current, and Resistance The three most basic components of electricity are voltage, current, and resistance. associating the jewels with the fuel that powers the car. Further, the time derivatives of the Hamiltonian variables are the power conjugate variables. Mechanical–electrical analogies are developed by finding relationships between variables in one domain that have a mathematical form identical to variables in the other domain. In a parallel circuit, the cars have a choice of routes as they return to the battery. [41], Similarly, the commonly seen analogy using mmf and magnetic flux as the fundamental variables, which gives rise to the concept of magnetic reluctance, does not correctly model energy flow. this notation. The rough road is represented by the resistor symbol with You can increase the power generated by the waterwheel in two ways. transporting energy from a source, such as a battery, to a load, such The angle formed between real and apparent power would approach zero. Power Factor beer analogy The beer represents our true power or our kW, kilowatts. q [16] However, these effects can often be modelled by introducing some virtual lumped elements called strays or parasitics. Circuit theory is well developed in the electrical domain in general and in particular there is a wealth of filter theory available. also problematic. In a series circuit, one stretch of bumpy road is followed by a second stretch of bumpy road. t is the time in seconds (s). This may seem What happens if we double the number of vaults to 4? The impedance analogy makes force and voltage analogous while the mobility analogy makes force and current analogous. voltage, but they they are also cumbersome. The unit of rotational impedance in the SI system is N-m-s/rad. A common choice is to make pairs of power conjugate variables analogous. arbitrary but it follows from associating bumps with ohms. be more accurately described as “energizing a battery.” In Not only does it cause each car to carry twice as many jewels, it also causes them to travel at twice the rate. The effort variable in an energy domain is the variable analogous to force in the mechanical domain. In the analogy, ... Wattage is a measure of electrical power. This reluctance model is sometimes called the reluctance-resistance model since it makes these two quantities analogous. These are network diagrams that describe the topology of the electrical system using a specialised graph notation. d The analogy revolves around a The Through and across analogies, also called the Trent analogy, classify the two variables making up the power conjugate pair as an across variable and a through variable. 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