common usage. reality, the amount of charge entering the battery during this containing a supply of jewels. In other words, I prefer to use conventional current throughout. You can increase the power generated by the waterwheel in two ways. q The angle formed between real and apparent power would approach zero. 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. resistance is represented by rough (bumpy) road. The voltage between two points is a short name for the electrical force that would drive an electric current between those points. Well potential difference ($V$) is defined as the energy transferred in an electrical circuit per coulomb of charge that passes through the circuit. Chan, Shu-Park, "Circuits: Introduction", pp. Figure 1: As the charges go (chemistry) or holes (transistors). This approach is especially useful in the design of mechanical filtersâthese use mechanical devices to implement an electrical function. The concept of thermal resistance is based on this analogy. [19], Even after the mechanical fundamental variables have been chosen, there is still not a unique set of analogs. There is no one, unique way of doing this; numerous analogies are theoretically possible, but there are two analogies that are widely used: the impedance analogy and the mobility analogy. 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. example the unfortunate phrase “charging a battery” which should jewels to fall off the cars. be more accurately described as “energizing a battery.” In [33], The mobility analogy is characterised by admittance in the same way that the impedance analogy is characterised by impedance. when one car moves, they all move. [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. [30] The acoustical impedance analogy gives rise to the idea of acoustic impedance. Using our garden hose analogy, the voltage of electricity is akin to the pressure in a garden hose. 191â196 in Hohmann, D. (ed). entities with which the charges are associated are irrelevant. Mechanicalâelectrical analogies are developed by finding relationships between variables in one domain that have a mathematical form identical to variables in the other domain. 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. = nicely avoids getting hung up on the unimportant detail that as a bulb or resistor.” Figure 1 illustrates the essence of this According to it electric current is analogous to the rate of flow of water, potential difference is analogous to pressure applied across the pipe and electric charge is equivalent to quantity of water. Resistance: In the analogy, What the mechanical analogs of these elements are depends on what variables are chosen to be the fundamental variables. The impedance analogy makes force and voltage analogous while the mobility analogy makes force and current analogous. The speedometer can quickly go from zero to sixty and back to zero, but the odometer only slowly counts up: faster if your speed is faster. symbol with the number of cells equal to the number of vaults. In this analogy, the water system is showing only the flow of charges (you can think of them as electrons). They are often reversible, but are rarely used in that way. making a second flow redundant. I do my best to avoid this, but will Twist the faucet open and you have a stream of water that creates pressure inside the hose. The voltage in this case represents the number of jewels carried by each car. On the By itself, that is not enough to fully define the analogy, a second variable must be chosen. [23] The Hamiltonian variables are also called the energy variables. The heavier the weight and/or the higher it is lifted, the more work has been done. But it was a required condition to allow the electrical MW to flow through the system and do real work. The ratio of voltage to current is electrical resistance (Ohm's law). the number of squiggles equalling the number of bumps. One such phenomenon is the presence of different types of power in ac electrical systems. ampere = one coulomb/second. Doing so will force it to dissipate 4 times as much power and almost certainly cause it to burn out. We now have the basic conceptual A mechanical system by itself can be so represented, but analogies are of greatest use in electromechanical systems where there is a connection between mechanical and electrical parts. cars/second corresponding to the unit of electrical current: one understand simple direct-current (DC) circuits. process equals the charge leaving. associating the jewels with the fuel that powers the car. The expression “current flowing” is ... Wattage is a measure of electrical power. Firestone introduced the concept of across and through variables in this paper and presented a structure for extending the analogy into other energy domains. [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. Drawing battery cells is tedious so we'll just use a representative battery symbol from now on and label it as to the number of vaults. reality, the amount of charge entering the battery during this thereby doubling the violence of their interaction with the two bumps. Electric circuits analogy to water pipes. Joines, William T.; Palmer, W. Devereux; Bernhard, Jennifer T.. Lenk, Arno; G. Ballas, Rüdiger; Werthschützky, Roland; Pfeifer, Günther. with a car underneath, and zero or more jewels on top. cars travelling through pick up one jewel from each vault. For most students, the least understood of … Doing so cars/second corresponding to the unit of electrical current: one [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. Impedance can be thought of as an extension to the concept of resistance. coulomb. This reluctance model is sometimes called the reluctance-resistance model since it makes these two quantities analogous. 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. On the right, cars carrying 4 jewels each arrive at the rate of 2 per sec. Rather, power is the combination of both voltage and current in a circuit. ∂ They can be treated independently assuming that the bank has an infinite supply of jewels and no "internal resistance." 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. Two-port networks can be represented as a 2Ã2 matrix, or equivalently, as a network of two dependent generators and two impedances or admittances. The integrand of a power conjugate variable with respect to a Hamiltonian variable is a measure of energy. Rather, it was to explain electrical phenomena in more familiar mechanical terms. For instance, a coil intended for use as an inductor has resistance as well as inductance. The terms electrical potential and However, these are not power conjugate variables and are not fully compatible with the other variables in the table. Voltage: The word vault is a number of bumps, the rate of flow is one car/second. This is the useful stuff we want and need, this is what does the work. Relating to AC power systems, the portion of the current that is delivered by the generators to create the magnetic fields “disappears” if the system is turned off, i.e., it did no work. The impedance analogy gives rise to the concept of impedance in other energy domains (but measured in different units). To get to the flow of energy, I’ve introduced a grain mill, powered by water (representing an electrical … Electrical current. refers only to the pressure reduction process obtained by the control valve. analogy and not a model. These are network diagrams that describe the topology of the electrical system using a specialised graph notation. Current-Flowrate Analogy. Acoustical analogies have also been included in the descriptions as a third variant. From about 1920 the electrical analogy became a standard analysis tool. However, as electrical network analysis matured it was found that certain mechanical problems could more easily be solved through an electrical analogy. destroys the analogy. Figure 3: On the left, a two must travel through the bank. However, the technique can be used to solve purely mechanical problems, and can also be extended into other, unrelated, energy domains. The usual choice for a translational mechanical system is force (F) and velocity (u) but it is not the only choice. Electrical power, or the wattage of an electrical system, is always equal to the voltage multiplied by the current. At the high school level, the best answer to the question, This leads to two classes of analogies, the impedance analogies and the mobility analogies. Nowadays, analysis by analogy is a standard design tool wherever more than one energy domain is involved. The The transducer provides the link between the mechanical and electrical domains and thus a network representation is required for it in order to develop a unified electrical analogy. is defined as the resistance which causes one coulomb/second to flow This is because the much higher propagation speeds in the electrical domain lead to longer wavelengths (mechanical vibrations in steel propagate at about 6,000 m/s,[9] electromagnetic waves in common cable types propagate at about 2 x 108 m/s[10]). topic. The circuits illustrated in figure 3, According to Warren P. Mason the efficiency of ship electric foghorns grew from less than one per cent to 50 per cent. [39], It is perhaps more common in the thermal domain to choose temperature and thermal power as the fundamental variables because, unlike entropy, they can be measured directly. The top part shows a typical parallel circuit. Consider for In the translational mechanical domain the Hamiltonian variables are distance displacement (x) and momentum (p) because. The variable pair mmf and magnetic flux is not a power conjugate pair. vault bank supplies energy to cars encountering two bumps. proceed onto a roadway where the traffic is always bumper-to-bumper, H [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. Remember that voltage is the … H right, the two vault bank is replaced by a four vault bank. In force voltage analogy, the mathematical equations of translational mechanical system are compared with mesh equations of the electrical system. Unlike the water pump in our river analogy, however, the power plant automatically adjusts to meet the demands of the consumer at the end of the wires. Electricity was originally understood to be a kind of fluid, and the names of certain electric quantities are derived from hydraulic … Remarkably, the conversion efficiency was improved at the same time (the usual situation with amplifying systems is that gain can be traded for bandwidth such that the gain-bandwidth product remains constant). This is interesting: doubling the number of vaults. 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. 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. d The rough road is represented by the resistor symbol with The teaching of electricity probably “What is electricity?” should be, “Electricity is a means for Doubling the number of vaults has two effects. Resistance is associated with energy dissipation. Figure 3 uses Over the 2 bump road, the rate is 6 cars/sec. [49] This was the earliest mechanicalâelectrical analogy. The mechanical network is arranged differently to its analogous electrical network. 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. to leave the bank. three bumps. The Hamiltonian variables in the electrical domain are charge (q) and flux linkage (λ) because. There is a corresponding relationship for other analogies and sets of variables. Transducers have many uses and there are many kinds, in electromechanical systems they can be used as actuators and sensors. Current ($I$) is defined as the rate of flow of charge, so the amount of charge that passes through a given component per second. A different pair may be more appropriate for a system with a different geometry, such as a rotational system. This limit is much lower in the mechanical domain than the equivalent limit in the electrical domain. Thus, the power conjugate variables in the mechanical domain are analogs. [7], There is a limit to the applicability of this lumped element model. Thus jewels arrive at the rate of 2 jewels/sec. I therefore tend to ∂ Firestone, Floyd A., "A new analogy between mechanical and electrical system elements". [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. I do my best to avoid this, but will To ensure that all 4 jewels are lost, the cars must travel at double the rate of 1 car/sec. A wire offers very little resistance to charge flow according to Ohm's law. when one volt is placed across it.). understand simple direct-current (DC) circuits. The across variable is measured relative to the element terminals. Throughout, keep in mind that this is only an Imagine a bank with one or more vaults, each (traffic) correspond to moving charges (electrical current). this notation. The electrical analogy steady-state model of a GPRMS published in Ref. transporting energy from a source, such as a battery, to a load, such bulb where it is converted into heat and light. The two-port element in the electrical domain that does this is called a gyrator. 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. In the more general case with electric and magnetic fields that vary with time, the terms are no longer synonymous. These are variables which when multiplied together have units of power. + between charge and energy which are often confused. There is also the through and across analogy, also called the Trent analogy. [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. Solution: In the impedance analogy, the ratio of the power conjugate variables is always a quantity analogous to electrical impedance. We are now in a position to do some This can be represented on the circuit diagram as a resistor in series with an inductor. 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. For instance, are both expressions of energy. process equals the charge leaving. By 1900 the electrical analogy of the mechanical domain was becoming commonplace. Early phonographs suffered badly from unwanted resonances in the mechanical parts. [37], The electrical analogy can be extended to many other energy domains. In reality there are many limitations of such approach as operating temperatures, power dissipation and power limits. The bandwidth of mechanical phonographs grew from three to five octaves when the mechanical parts of the sound transmission were designed as if they were the elements of an electric filter ( see also Mechanical filter § Sound reproduction). (traffic) correspond to moving charges (electrical current). conceptual framework for all the quantities needed to [3], Electrical systems are commonly described by means of a circuit diagram. q 2â4, in Dorf, Richard C. (ed). The In the analogy, Variations of these analogies are used for rotating mechanical systems, such as in electric motors. [48], James Clerk Maxwell developed very detailed mechanical analogies of electrical phenomena. mention electrons only in passing when teaching current electricity be more accurately described as “energizing a battery.” In In the mechanical domain the analogous variables are velocity and force, as in the mobility analogy. By analogy, a transducer that converts non-analogous variables between energy domains is also called a gyrator. In the case of static electric fields, the voltage between two points is equal to the electrical potential difference between those points. On the left, each car carries two jewels and they arrive at the rate of 1 per sec. Those are force voltage analogy and force current analogy. passing by. Mechanical systems can make use of this electrical theory in mechanical designs through a mechanicalâelectrical analogy. jewel/car corresponding to the unit for electrical potential: one The mobility analogy does not preserve this analogy between impedances across domains, but it does have another advantage over the impedance analogy. to a pair of resistors in series is the sum of the individual resistances. strength of this approach is that it forces a clear distinction Eventually the cars They can also be called generalised momentum and generalised displacement after their analogs in the mechanical domain. On the left, each car carries two jewels and they arrive at the rate of 1 per sec. example the unfortunate phrase “charging a battery” which should The analogy shown in the table, which does use a power conjugate pair, is sometimes called the gyratorâcapacitor model. common usage. [21], The Hamiltonian variables, also called the energy variables, are those variables r = (q, p), which are conjugate according to Hamilton's equations:[22], d A common choice is to make pairs of power conjugate variables analogous. number of jewels carried by each car. could be electrons (metals), positrons (particle physics), ions {\displaystyle {\frac {\mathrm {d} {\boldsymbol {p}}}{\mathrm {d} t}}=-{\frac {\partial {\mathcal {H}}}{\partial {\boldsymbol {q}}}}\quad ,\quad {\frac {\mathrm {d} {\boldsymbol {q}}}{\mathrm {d} t}}=+{\frac {\partial {\mathcal {H}}}{\partial {\boldsymbol {p}}}}}. In fact, my preference is to number of bumps, the rate of flow is one car/second. The moving cars [29] The rotational impedance analogy describes rotating mechanical systems and gives rise to the idea of rotational impedance. Thus jewels arrive at the rate of 8 jewels/sec. , Analogies are especially useful in analysing mechanical filters. should be avoided. Any of them can be used. If the cars continued to travel at 1 car/sec. It is thus not analogous to force which is a through variable, even though pressure is in units of force per area. An important aspect of any electrical or electronic circuit is the power associated with it. In the field of sensors and actuators, and for control systems using them, it is a common method of analysis to develop an electrical analogy of the entire system. The analogy revolves around a On the left is a series circuit and on the right its equivalent. Electrically speaking this means that the resistance. and to always talk about positive charges and their movement. Vannevar Bush was a pioneer of this kind of modelling in his development of analogue computers, and a coherent presentation of this method was presented in a 1925 paper by Clifford A. [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. leads to more misconceptions than any other topic in science. In the impedance analogy, instead of force, torque is made analogous to voltage. play on words here, of course, is that the unit for energy is joules. they would only lose 2 of the 4 jewels they are now carrying. [12], In some cases it is possible to continue using a topological network diagram even when components needing a distributed element analysis are present. 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 flow of water can be analogous to the amperage of current, which is the rate of flow of charge. [note 1] Another area of application is the mechanical parts of acoustic systems such as the pickup and tonearm of record players. (The ohm the flow of charges the process is repeated. Circuit theory is well developed in the electrical domain in general and in particular there is a wealth of filter theory available. The voltage in this case represents the 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. Power conjugate variables in the analog domain are chosen that bear some resemblance to force and velocity.[27]. They i.e. electrons travel from minus to plus. since the number of vaults equals the number of bumps. 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. 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. Thus jewels arrive at the rate of 2 jewels/sec. However, the term amperage for current This Physics video explains how the electric current flows using the analogy of water flow. Admittance is the algebraic inverse of impedance. For instance, electromagnetic transducers convert current to force and velocity to voltage. Since the energy of the mass in a Mechani… Nickle. The circuit diagram does not try to represent the true physical dimensions of the electrical components or their actual spatial relationship to each other. However, the alternative associations u with v and F with i are also possible. play on the word volt. Resistor can be considered as a constricted pipe opposing the water flow. the three vault bank, each vault supplies one jewel to each car It has the major advantage that the entire system can be represented in a unified, coherent way. [24], There are two principle classes of analogy in use. Likewise, the use of the terms I-type and V-type (after current and voltage) is also discouraged. There is also the thr… In this case, where the number of vaults matches the (The ohm [43] To do this the concept of port from the electrical domain is extended into other domains. The best analogy is usually the stream of water. vault bank supplies energy to cars encountering two bumps.