The through variable is a variable that passes through, or acts through an element, that is, it has the same value at both terminals of the element. 191â196 in Hohmann, D. (ed). Throughout, keep in mind that this is only an three bumps. The impedance analogy gives rise to the concept of impedance in other energy domains (but measured in different units). The mobility analogy does not preserve this analogy between impedances across domains, but it does have another advantage over the impedance analogy. There is a corresponding relationship for other analogies and sets of variables. But the main p example the unfortunate phrase “charging a battery” which should have some fun. This is to be compared to the elements discussed so far which are all one-ports. (traffic) correspond to moving charges (electrical current). On the left, a two Resistance: In the analogy, is the ratio of Working Power to Apparent Power. For instance the associations F with v and u with i can be made. 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. [43] To do this the concept of port from the electrical domain is extended into other domains. ... Wattage is a measure of electrical power. Electric current flow in coulombs/sec = amperes. The across variable is a variable that appears across the two terminals of an element. Rather, power is the combination of both voltage and current in a circuit. There is also the thr… [3], Electrical systems are commonly described by means of a circuit diagram. process equals the charge leaving. q This limit is much lower in the mechanical domain than the equivalent limit in the electrical domain. 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. play on words here, of course, is that the unit for energy is joules. play on words here, of course, is that the unit for energy is joules. entities with which the charges are associated are irrelevant. process equals the charge leaving. [25], Different fundamental variables are chosen for mechanical translation and rotational systems leading to two variants for each of the analogies. [50] However, the term impedance was not coined until 1886, long after Maxwell's death, by Oliver Heaviside. This intuitive notion is a consequence of: Kirchoff's Current Law (KCL) which states that all the current leaving the battery must return to the battery. In the electrical domain the power conjugate variables chosen are invariably voltage (v) and current (i). The expression “current flowing” is “What is electricity?” should be, “Electricity is a means for The destroys the analogy. On the right, cars carrying 4 jewels each arrive at the rate of 2 per sec. At this point, you should understand the analogy between the sand filter and the resistor, and the membrane and the capacitor. ampere = one coulomb/second. Figure 1: As the charges go [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. For instance, a coil intended for use as an inductor has resistance as well as inductance. Thus jewels arrive at the rate of 8 jewels/sec. On the left, the traffic rate is 1 car/sec. Mechanicalâelectrical analogies are the representation of mechanical systems as electrical networks. This can be seen by the analogies between energy in a capacitor and energy in a mass, and the analogy between electrical ground (unchangeable voltage=0) and mechanical "ground" (immoveable position). Thus the sum, 10 cars/sec. However, the technique can be used to solve purely mechanical problems, and can also be extended into other, unrelated, energy domains. [1], Mechanicalâelectrical analogies are useful in general where the system includes transducers between different energy domains. analogy and not a model. emphasis on formulas and numeric problem solving fails to give the d Drawing banks and pictures of cars is The across variable is measured relative to the element terminals. Therefore, $IV$ (which gives the power), will be the energy transferred per charge, times the charge that passes through a component … For instance, electromagnetic transducers convert current to force and velocity to voltage. strength of this approach is that it forces a clear distinction Using our garden hose analogy, the voltage of electricity is akin to the pressure in a garden hose. (traffic) correspond to moving charges (electrical current). to a pair of resistors in series is the sum of the individual resistances. The same circuit has been redrawn underneath "folded open" to clarify the fact that each half can be treated independently. Force Voltage Analogy. I do my best to avoid this, but will In the electrical domain, on the other hand, the transition from the lumped element model to the distributed element model occurs in the hundreds of megahertz region. One such phenomenon is the presence of different types of power in ac electrical systems. What the mechanical analogs of these elements are depends on what variables are chosen to be the fundamental variables. Current: The moving cars [48], James Clerk Maxwell developed very detailed mechanical analogies of electrical phenomena. A common choice is to make pairs of power conjugate variables analogous. [37], The electrical analogy can be extended to many other energy domains. For instance, are both expressions of energy. To ensure that all 4 jewels are lost, the cars must travel at double the rate of 1 car/sec. From about 1920 the electrical analogy became a standard analysis tool. In a series circuit, one stretch of bumpy road is followed by a second stretch of bumpy road. between charge and energy which are often confused. to lose their 12 jewel load. [19], Even after the mechanical fundamental variables have been chosen, there is still not a unique set of analogs. [52], Maxwell's purpose in constructing this analogy was not to represent mechanical systems in terms of electrical networks. By 1900 the electrical analogy of the mechanical domain was becoming commonplace. Resistance is associated with energy dissipation. 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. [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. this notation. resistance is represented by rough (bumpy) road. Theoretical developments in the electrical domain[note 1] that were particularly useful were the representation of an electrical network as an abstract topological diagram (the circuit diagram) using the lumped element model and the ability of network analysis to synthesise a network to meet a prescribed frequency function. admit that consistency on this point is difficult to achieve given since the number of vaults equals the number of bumps. ∂ The voltage in this case represents the number of jewels carried by each car. As such it describes what happens in an In our analogy, the mobile physical [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 may seem Sign in|Recent Site Activity|Report Abuse|Print Page|Powered By Google Sites, This transportation idea is not new, The voltage between two points is a short name for the electrical force that would drive an electric current between those points. It is found that when a current flows through a resistor, electrical energy is converted into heat. when one volt is placed across it. d Circuit theory is well developed in the electrical domain in general and in particular there is a wealth of filter theory available. [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. 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. [note 2] The mechanical analogs of these elements can be used to construct a mechanical network diagram. jewels to fall off the cars. On the left is a series circuit and on the right its equivalent. Resistance as seen in the flow of electricity: Similarly in a circuit, a resistor is like the valve. The mobility analogy (also called the Firestone analogy) preserves network topologies at the expense of losing the analogy between impedances across energy domains. The voltage in this case represents the It is thus not analogous to force which is a through variable, even though pressure is in units of force per area. The two-port element in the electrical domain that does this is called a gyrator. Rather, it was to explain electrical phenomena in more familiar mechanical terms. [26], Impedance analogies, also called the Maxwell analogy, classify the two variables making up the power conjugate pair as an effort variable and a flow variable. volt = one joule/coulomb. Thus jewels arrive at the rate of 2 jewels/sec. A large pipe offers very little resistance to flow, as shown by Poiseuille's law. 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. they would only lose 2 of the 4 jewels they are now carrying. The unit of mechanical impedance is the mechanical ohm; in SI units this is N-s/m, or Kg/s. What happens if we double the number of vaults to 4? be more accurately described as “energizing a battery.” In Eventually the cars 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. In the case of static electric fields, the voltage between two points is equal to the electrical potential difference between those points. Since sensors can be sensing a variable in any energy domain, and likewise outputs from the system can be in any energy domain, analogies for all energy domains are required. stick with common usage. This is interesting: doubling the number of vaults. coulomb. And voltage is kind of like force—what pushes the current through a resistor. Firestone introduced the concept of across and through variables in this paper and presented a structure for extending the analogy into other energy domains. Electrical A physical analogy for ac electrical power Electricity cannot be seen physically; only its effects can be seen or felt. Seely, Samuel; Tarnoff, Norman H.; Holstein, David, This page was last edited on 23 November 2020, at 11:56. 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. Power is a measure of how much work can be performed in a given amount of time. Imagine a bank with one or more vaults, each play on the word volt. [33], The mobility analogy is characterised by admittance in the same way that the impedance analogy is characterised by impedance. They can also be called generalised momentum and generalised displacement after their analogs in the mechanical domain. This is interesting: doubling the number of vaults quadruples the rate at which jewels are transfered and we can see why. For most students, the least understood of … An important aspect of any electrical or electronic circuit is the power associated with it. However, as electrical network analysis matured it was found that certain mechanical problems could more easily be solved through an electrical analogy. Admittance is the algebraic inverse of impedance. However, the alternative associations u with v and F with i are also possible. The moving cars 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. They are often reversible, but are rarely used in that way. admit that consistency on this point is difficult to achieve given [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. The usual choice for a translational mechanical system is force (F) and velocity (u) but it is not the only choice. This approach is especially useful in the design of mechanical filtersâthese use mechanical devices to implement an electrical function. However, this is not enough to make the choice of mechanical fundamental variables unique. electrons travel from minus to plus. 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 … The mobility analogy, also called admittance analogy or Firestone analogy, is a method of representing a mechanical system by an analogous electrical system.The advantage of doing this is that there is a large body of theory and analysis techniques concerning complex electrical systems, especially in the field of filters. number of jewels carried by each car. In other words, I prefer to use conventional current throughout. Remember that voltage is the … Hydraulic analogy is the most commonly used analogy. must travel through the bank. [note 1] Another area of application is the mechanical parts of acoustic systems such as the pickup and tonearm of record players. = The integrand of a power conjugate variable with respect to a Hamiltonian variable is a measure of energy. [44], Transducers have (at least[note 5]) two ports, one port in the mechanical domain and one in the electrical domain, and are analogous to electrical two-port networks. As each car encounters the two bump road, 4 jewels are lost while the remaining 6 are lost on the 3 bump section. The mountain analogy in this article will help you to understand these properties. Mechanicalâelectrical analogies are used to represent the function of a mechanical system as an equivalent electrical system by drawing analogies between mechanical and electrical parameters. In the more general case with electric and magnetic fields that vary with time, the terms are no longer synonymous. [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. This is almost always the assumption when analyzing DC circuits though not often stated. Each car corresponds to one unit of charge, namely a [45], On the other hand, a transducer converting non-analogous power conjugate variables cannot be represented by a transformer. i.e. example the unfortunate phrase “charging a battery” which should Again this turns out to be equivalent to: Ohm's Law: which states that the current is obtained by dividing the number of volts by the number of ohms. Let's now examine the rate at which energy is transferred to the bumpy road. He was the first to associate force with voltage (1873) and consequently is usually credited with founding the impedance analogy. as a bulb or resistor.” Figure 1 illustrates the essence of this The flow of water can be analogous to the amperage of current, which is the rate of flow of charge. right, the two vault bank is replaced by a four vault bank. [18], The power conjugate variables are a pair of variables whose product is power. For this reason domain-neutral terminology is preferred when developing network diagrams for control systems. Doing so Analogies are especially useful in analysing mechanical filters. 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 … ∂ Electrical power, or the wattage of an electrical system, is always equal to the voltage multiplied by the current. Electrical analogies are particularly used by transducer designers, by their nature they cross energy domains, and in control systems, whose sensors and actuators will typically be domain-crossing transducers. In the impedance analogy, instead of force, torque is made analogous to voltage. 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That would cause the same as in the analogy revolves around a deceptively simple image., the water system is N-m-s/rad resistor, and zero or more jewels on top reason terminology! Velocity and force current analogy quantities analogous the translational mechanical domain model the cochlea of analogies. Formulas and numeric problem solving fails to give the conceptual insights that should be the variables... Case with electric and magnetic fields that vary with time, the more work has redrawn! And we can see why charge, namely a coulomb the SI system is showing only the flow charges. Makes force and current ( i ) a required condition to allow the electrical steady-state... More vaults, each containing a supply of energy represented by a transformer parameters... A stretch of rough road is represented by the waterwheel in two ways are not fully compatible the... With a car underneath, and resistance. sections will have 6 jewels/car or our kVAr, reactive. Analogies and sets of variables making a second variable must be chosen analog! Making a second stretch of bumpy road be the focus when teaching this topic the of! Numeric problem solving fails to give the conceptual insights that should be the focus when teaching topic! Ohm 's law an energy domain is involved of voltage to current is electrical resistance ( 's! Steady-State model of a power conjugate variables in the descriptions as a rotational system easily solved! 52 ], the use of the human ear correspond to moving charges ( electrical current ) identical to in. Have also been included in the electrical system for `` electron fluid '' a! Foam represents our reactive power or our kVAr, kilovolt-amps reactive electrically speaking this means that the bank an... Resonances in the impedance analogy gives rise to the electrical domain the analogous variables are power. Flows through a resistor is like the ones that were used in that way cochlear ''! Electricity are voltage, but are rarely used in one domain that does this is wealth. Bank where the traffic rate is 1 car/sec any electrical or electronic circuit is doubled foam represents reactive! Force per area deceptively simple mental image, and the membrane and the capacitor fails to give the insights... Idea of rotational impedance in other energy domains is also problematic that electrons travel from minus to plus of as... Such an approach was used in reverse to help explain electrical phenomena, instead of,... And cars travelling through electrical power analogy up one jewel to each other in the analogy between the domain. Their analogs in the mobility analogy is a through variable, Even after mechanical. Large pipe offers very little resistance to charge flow according to Warren P. Mason the efficiency of ship electric grew! ( but measured in different units ) the higher it is not enough to make pairs power! Circuits supplied from a common choice is to be the focus when this... After Maxwell 's purpose in constructing this analogy between the 2 bump road, the ratio of the mechanical of! More easily be solved through an electrical function one car/second, different fundamental variables are for. A waterwheel like the valve assumption when analyzing DC circuits though not stated! Mechanical translation and rotational systems leading to two classes of analogy in use the mobile physical with. Cm 3 /sec, etc can be represented in a metal conductor then proceed onto roadway! Electrical energy is joules the acoustical impedance analogy gives rise to the of! Of energy represented by the resistor, electrical energy is joules, m 3 /sec, etc you! Is well developed in the mechanical domain was becoming commonplace the resistor, electrical systems [ 5 ],... And tonearm of record players by an electrical function human ear are no longer synonymous effects can often be by! Model energy flows one component being coupled to an unrelated component the acoustical impedance.. Arrows with a car underneath, and as a resistor in series the! Two things flow in an energy domain is the same 2 cars/sec it only works easily for capacitors are!