Analogies between the mechanical and acoustical domain in the through and across analogy have a dual relationship with both the impedance analogy and mobility analogy. This may seem Minute LecturesAnalogies to explain reactive power (part 2)Round-up Another four analogies represent the idea of active and reactive power in an electric system: • The beer analogy • The marble-in-a-tube analogy • The cash flow analogy • The water tower analogy Some people prefer one or another analogy We hope they will increase the reader’s insight in the phenomenon, or help explaining the phenomenon … [2], Electrical analogies of mechanical systems can be used just as a teaching aid, to help understand the behaviour of the mechanical system. Each vault supplies one This process equals the charge leaving. It must be understood that neither voltage nor current by themselves constitute power. In former times, up to about the early 20th century, it was more likely that the reverse analogy would be used; mechanical analogies were formed of the then little understood electrical phenomena. But the main Transducers have many uses and there are many kinds, in electromechanical systems they can be used as actuators and sensors. The second diagram in figure 5 suggests that we just have two simple circuits supplied from a common 12 vault bank. However, the representation of a passive transducer converting between analogous variables (for instance an effort variable to another effort variable in the impedance analogy) can be simplified by replacing the dependent generators with a transformer. The potential energy of the water at a higher location (which drives the stream) can be compared to the voltage or potential difference in the … The flow of water can be analogous to the amperage of current, which is the rate of flow of charge. but in this article, I will extend the basic idea to provide a i.e. understand simple direct-current (DC) circuits. is the ratio of Working Power to Apparent Power. Speedometer Odometer Analogy You can imagine that power (W) is like your speedometer (current speed), while energy (kWh) is like your odometer. Electrically speaking this means that the resistance. q = number of bumps, the rate of flow is one car/second. The electric current and water flow can be calculated using the same Ohms Law formula: I=V/R. Each vault supplies one One deficiency in this analogy is that it only works easily for capacitors that are grounded. The same circuit has been redrawn underneath "folded open" to clarify the fact that each half can be treated independently. For most students, the least understood of … Electrical A physical analogy for ac electrical power Electricity cannot be seen physically; only its effects can be seen or felt. 2â4, in Dorf, Richard C. (ed). Imagine a 1 inch hose with a little bit of water flowing through it. [56], In 1933 Floyd A. Firestone proposed a new analogy, the mobility analogy, in which force is analogous to current instead of voltage. destroys the analogy. The important relationship when converting from a circuit to the Mechanical 1 analog is that between Kirchoff's Current Law and D'Alemberts Law (with inertial forces included). Analogies between all three domains â electrical, mechanical and acoustical â are required to fully represent electromechanical audio systems. = [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 example in they would only lose 2 of the 4 jewels they are now carrying. The mountain analogy in this article will help you to understand these properties. number of jewels carried by each car. [24], There are two principle classes of analogy in use. Power conjugate variables in the analog domain are chosen that bear some resemblance to force and velocity.[27]. This is to be compared to the elements discussed so far which are all one-ports. The usual choice for a translational mechanical system is force (F) and velocity (u) but it is not the only choice. around the circuit, energy is transported from the battery to the jewel/car corresponding to the unit for electrical potential: one Fukazawa, Tatsuya; Tanaka, Yasuo, "Evoked otoacoustic emissions in a cochlear model", pp. This explains why it is a bad idea to connect a bulb designed to operate on a 6 volt supply to a 12 volt supply. “What is electricity?” should be, “Electricity is a means for Take a hose and point it at a waterwheel like the ones that were used to turn grinding stones in watermills. A large pipe offers very little resistance to flow, as shown by Poiseuille's law. The teaching of electricity probably admit that consistency on this point is difficult to achieve given p There are six canonical forms of these representations: impedance parameters, chain parameters, hybrid parameters and their inverses. proceed onto a roadway where the traffic is always bumper-to-bumper, Power Equivalent in the Electricity-Water Analogy Kirt's Cogitations™ #321 " Factoids ," " Kirt's Cogitations , " and " Tech Topics Smorgasbord " are all manifestations of my rantings on various subjects relevant (usually) to the overall RF Cafe theme. [1], Mechanicalâelectrical analogies are useful in general where the system includes transducers between different energy domains. On the right we see the equivalent circuit showing the single 5 bump road that would cause the same 2 cars/sec. This is the useful stuff we want and need, this is what does the work. Analogies are especially useful in analysing mechanical filters. Thus, in the through and across analogy the mechanical domain is analogous to the electrical domain like the mobility analogy, but the acoustical domain is analogous to the electrical domain like the impedance analogy. t is the time in seconds (s). The expression “current flowing” is when one car moves, they all move. The On the Current-Flowrate Analogy. [17] An analog of this in mechanical systems is vibration in one component being coupled to an unrelated component. [3], Electrical systems are commonly described by means of a circuit diagram. It is energy that accumulates. number of bumps, the rate of flow is one car/second. nicely avoids getting hung up on the unimportant detail that to leave the bank. (traffic) correspond to moving charges (electrical current). H 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. Acoustical analogies have also been included in the descriptions as a third variant. play on words here, of course, is that the unit for energy is joules. Resistance as seen in the flow of electricity: Similarly in a circuit, a resistor is like the valve. Another variation is required for acoustical systems; here pressure and voltage are made analogous (impedance analogy). [note 2] The mechanical analogs of these elements can be used to construct a mechanical network diagram. This limit is much lower in the mechanical domain than the equivalent limit in the electrical domain. The unit of acoustic impedance is the acoustic ohm; in SI units this is N-s/m5. (The ohm Well potential difference ($V$) is defined as the energy transferred in an electrical circuit per coulomb of charge that passes through the circuit. In the more general case with electric and magnetic fields that vary with time, the terms are no longer synonymous. Therefore, $IV$ (which gives the power), will be the energy transferred per charge, times the charge that passes through a component … This is interesting: doubling the number of vaults. Solution: Electric circuits analogy to water pipes. This is possible because the electrical components are represented as ideal lumped elements, that is, the element is treated as if it is occupying a single point (lumped at that point). The impedance analogy (also called the Maxwell analogy) preserves the analogy between mechanical, acoustical and electrical impedance but does not preserve the topology of networks. reality, the amount of charge entering the battery during this d They then [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. leads to more misconceptions than any other topic in science. Energy: A bank represents the But it was a required condition to allow the electrical MW to flow through the system and do real work. vault bank supplies energy to cars encountering two bumps. Two things flow in an operating electrical circuit— charges and energy. arbitrary but it follows from associating bumps with ohms. On the right, cars carrying 4 jewels each arrive at the rate of 2 per sec. It is thus not analogous to force which is a through variable, even though pressure is in units of force per area. It has the major advantage that the entire system can be represented in a unified, coherent way. Current ($I$) is defined as the rate of flow of charge, so the amount of charge that passes through a given component per second. [57] A variation of the force-current analogy was proposed by Horace M. Trent in 1955 and it is this version that is generally meant by the through and across analogy. [47] Whether a transducer is a gyrator or a transformer is analogy related; the same electromagnetic transducer in the mobility analogy is a transformer because it is converting between analogous variables. coulomb. cars/second corresponding to the unit of electrical current: one also problematic. [36] In the acoustic system, pressure is an across variable because pressure is measured relative to the two terminals of an element, not as an absolute pressure. between charge and energy which are often confused. q The flow variable in an energy domain is the variable analogous to velocity in the mechanical domain. The mobility analogy (also called the Firestone analogy) preserves network topologies at the expense of losing the analogy between impedances across energy domains. the three vault bank, each vault supplies one jewel to each car [42], A transducer is a device that takes energy from one domain as input and converts it to another energy domain as output. On the right we see the equivalent circuit showing the single 5 bump road that would cause the same 2 cars/sec. This can be represented on the circuit diagram as a resistor in series with an inductor. Doing so will force it to dissipate 4 times as much power and almost certainly cause it to burn out. coulomb. must travel through the bank. James Clerk Maxwell introduced analogies of this sort in the 19th century. reality, the amount of charge entering the battery during this The At times, some aspects of electricity can be difficult to understand. In other words, I prefer to use conventional current throughout. The variable pair mmf and magnetic flux is not a power conjugate pair. That is, the effort variable in the mechanical domain is analogous to current (the flow variable) in the electrical domain, and the flow variable in the mechanical domain is analogous to voltage (the effort variable) in the electrical domain. The effort variable in an energy domain is the variable analogous to force in the mechanical domain. Chan, Shu-Park, "Circuits: Introduction", pp. The cars traveling over the 3 bump road must travel at the rate of 4 cars/sec. The cars then return to the bank where There is also the thr… The top part shows a typical parallel circuit. It is perfectly possible that both versions of the analogy are needed in, say, a system that includes rotating and reciprocating parts, in which case a force-torque analogy is required within the mechanical domain and a force-torque-voltage analogy to the electrical domain. [55], The application of electrical network analysis, most especially the newly developed field of filter theory, to mechanical and acoustic systems led to huge improvements in performance. 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. 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