i would like to prove the quadratic formula in a cleaner way. perhaps if teachers see this approach they will be less reluctant to prove the quadratic formula. added : i have recently learned from the book sources in the development of mathematics : series and products from the fifteenth to the twenty - first century ( ranjan roy ) that the method described below was used by the ninth century mathematician sridhara. ( i highly recommend roy's book, which is much broader in its coverage than the title would suggest. ) we want to solve the equation $ $ ax ^ 2 + bx + c = 0, $ $ where $ a \ ne 0 $. the usual argument starts by dividing by $ a $. that is a strategic error, division is ugly, and produces formulas that are unpleasant to typeset. instead, multiply both sides by $ 4a $. we obtain the equivalent equation $ $ 4a ^ 2x ^ 2 + 4abx + 4ac = 0. \ tag { 1 } $ $ note that $ 4a ^ 2x ^ 2 + 4abx $ is almost the square of $ 2ax + b $. more precisely, $ $ 4a ^ 2x ^ 2 + 4abx = ( 2ax + b ) ^ 2 - b ^ 2. $ $ so our equation can be rewritten as $ $ ( 2ax + b ) ^ 2 - b ^ 2 + 4ac = 0 \ tag { 2 } $ $ or equivalently $ $ ( 2ax + b ) ^ 2 = b ^ 2 - 4ac. \ tag { 3 } $ $ now it's all over. we find that $ $ 2ax + b = \ pm \ sqrt { b ^ 2 - 4ac } \ tag { 4 } $ $ and therefore $ $ x = \ frac { - b \ pm \ sqrt { b ^ 2 - 4ac } } { 2a }. \ tag { 5 } $ $ no fractions until the very end! added : i have tried to show that initial division by $ a $, when followed by a completing the square procedure, is not a simplest strategy. one might remark additionally that if we first divide by $ a $, we end up needing a couple of additional " algebra " steps to partly undo the division in order to give the solutions their traditional form. division by $ a $ is definitely a right beginning if it is followed by an argument that develops the connection between the coefficients and the sum and product of the roots. ideally,


each type of proof should be presented, since each connects to an important family of ideas. and a twice proved theorem is twice as true.


i'm guessing the other frequencies it gets are harmonics of the fundamental? like you're playing 100 hz and it picks out 200 hz or 300 hz instead? first, you should limit your search space to the frequencies that a guitar is likely to be. find the highest fundamental you're likely to need and limit to that. autocorrelation will work better than fft at finding the fundamental, if the fundamental is lower in amplitude than the harmonics ( or missing altogether, but that's not an issue with guitar ) : you can also try weighting the lower frequencies to emphasize the fundamental and minimize harmonics, or use a peak - picking algorithm like this and then just choose the lowest in frequency. also, you should be windowing your signal before applying the fft. you just multiply it by a window function, which tapers off the beginning and end of the waveform to make the frequency spectrum cleaner. then you get tall narrow spikes for frequency components instead of broad ones. you can also use interpolation to get a more accurate peak. take the log of the spectrum, then fit a parabola to the peak and the two neighboring points, and find the parabola's true peak. you might not need this much accuracy, though. here is my example python code for all of this.


it's the largeness of the condition number $ \ kappa ( \ mathbf a ) $ that measures the nearness to singularity, not the tininess of the determinant. for instance, the diagonal matrix $ 10 ^ { - 50 } \ mathbf i $ has tiny determinant, but is well - conditioned. on the flip side, consider the following family of square upper triangular matrices, due to alexander ostrowski ( and also studied by jim wilkinson ) : $ $ \ mathbf u = \ begin { pmatrix } 1 & 2 & \ cdots & 2 \ \ & 1 & \ ddots & \ vdots \ \ & & \ ddots & 2 \ \ & & & 1 \ end { pmatrix } $ $ the determinant of the $ n \ times n $ matrix $ \ mathbf u $ is always $ 1 $, but the ratio of the largest to the smallest singular value ( i. e. the 2 - norm condition number $ \ kappa _ 2 ( \ mathbf u ) = \ dfrac { \ sigma _ 1 } { \ sigma _ n } $ ) was shown by ostrowski to be equal to $ \ cot ^ 2 \ dfrac { \ pi } { 4n } $, which can be seen to increase for increasing $ n $.


just looking at the video, it appears that the shape of the surface is varying quasi - periodically, as if the liquid is moving outward ( and upward ) toward the cup walls, then moving inward and rising in the center of the cup. this can be expected, if in the beginning the shape is not a perfect equilibrium shape ( e. g., like a parabolic surface in a rotating cup ). but when the the liquid moves toward the center, the rotation necessarily speeds up due to conservation of angular momentum ; and when it moves outward the opposite happens. a crude analogy : if you rolled a marble in a large wok with smooth spherical curvature, in such a way that it looped near the center / bottom, then out near the edge, you would see that its angular velocity increases when it approaches the center / bottom, and decreases when it recedes from the center / bottom. you can think of the volume of liquid doing the same thing as the surface shape changes from a shallow curve to a deep curve.


a microprocessor generally does not have ram, rom and io pins. it usually uses its pins as a bus to interface to peripherals such as ram, rom, serial ports, digital and analog io. it is expandable at the board level due to this. a microcontroller is'all in one ', the processor, ram, io all on the one chip, as such you cannot ( say ) increase the amount of ram available or the number of io ports. the controlling bus is internal and not available to the board designer. this means that a microprocessor is generally capable of being built into bigger general purpose applications than a microcontroller. the microcontroller is usually used for more dedicated applications. all of these are very general statements. there are chips available that blur the boundaries.


i'm going to go with a programmer metaphor for you. the mathematics ( including " a field is a function that returns a value for a point in space " ) are the interface : they define for you exactly what you can expect from this object. the " what is it, really, when you get right down to it " is the implementation. formally you don't care how it is implemented. in the case of fields they are not matter ( and i consider " substance " an unfortunate word to use in a definition, even though i am hard pressed to offer a better one ) but they are part of the universe and they are part of physics. what they are is the aggregate effect of the exchange of virtual particles governed by a quantum field theory ( in the case of e & m ) or the effect of the curvature of space - time ( in the case of gravity, and stay tuned to learn how this can be made to get along with quantum mechanics at the very small scale... ). alas i can't define how these things work unless you simply accept that fields do what the interface says and then study hard for a few years. now, it is very easy to get hung up on this " is it real or not " thing, and most people do for at least a while, but please just put it aside. when you peer really hard into the depth of the theory, it turns out that it is hard to say for sure that stuff is " stuff ". it is tempting to suggest that having a non - zero value of mass defines " stuffness ", but then how do you deal with the photo - electric effect ( which makes a pretty good argument that light comes in packets that have enough " stuffness " to bounce electrons around )? all the properties that you associate with stuff are actually explainable in terms of electro - magnetic fields and mass ( which in gr is described by a component of a tensor field! ). and round and round we go.


first, consider a turing machine as a model ( you can use other models too as long as they are turing equivalent ) of the algorithm at hand. when you provide an input of size $ n $, then you can think of the computation as a sequence of the machine's configuration after each step, i. e., $ c _ 0, c _ 1, \ ldots $. hopefully, the computation is finite, so there is some $ t $ such $ c _ 0, c _ 1, \ ldots, c _ t $. then $ t $ is the running time of the given algorithm for an input of size $ n $. an algorithm is polynomial ( has polynomial running time ) if for some $ k, c > 0 $, its running time on inputs of size $ n $ is at most $ cn ^ k $. equivalently, an algorithm is polynomial if for some $ k > 0 $, its running time on inputs of size $ n $ is $ o ( n ^ k ) $. this includes linear, quadratic, cubic and more. on the other hand, algorithms with exponential running times are not polynomial. there are things in between - for example, the best known algorithm for factoring runs in time $ o ( \ exp ( cn ^ { 1 / 3 } \ log ^ { 2 / 3 } n ) ) $ for some constant $ c > 0 $ ; such a running time is known as sub - exponential. other algorithms could run in time $ o ( \ exp ( a \ log ^ c n ) ) $ for some $ a > 0 $ and $ c > 1 $, and these are known as quasi - polynomial. such an algorithm has very recently been claimed for discrete log over small characteristics.


one big downside of kegg is the licensing issue. one big advantage of reactome are various crosslinks to other databases and data. ad 1, this depends on which pathway, they are both primary databases. sometimes other databases that for instance combine data of primary databases have better annotation of pathways ( there is an example in the review paper bellow ) ad 3, there is very extensive relatively new ( 2015 ) review on this topic focused on human pathways : comparison of human cell signaling pathway databases — evolution, drawbacks and challenges. however i could not find there which one is more complete...


gpu hardware has two particular strengths : raw compute ( flops ) and memory bandwidth. most difficult computational problems fall into one of these two categories. for example, dense linear algebra ( a * b = c or solve [ ax = y ] or diagonalize [ a ], etc ) falls somewhere on the compute / memory bandwidth spectrum depending on system size. fast fourier transforms ( fft ) also fit this mold with high aggregate bandwidth needs. as do other transformations, grid / mesh - based algorithms, monte carlo, etc. if you look at the nvidia sdk code examples, you can get a feel for the sorts of problems that are most commonly addressed. i think the more instructive answer is to the question ` what kinds of problems are gpus really bad at?'most problems that don't fall into this category can be made to run on the gpu, though some take more effort than others. problems that don't map well are generally too small or too unpredictable. very small problems lack the parallelism needed to use all the threads on the gpu and / or could fit into a low - level cache on the cpu, substantially boosting cpu performance. unpredictable problems have too many meaningful branches, which can prevent data from efficiently streaming from gpu memory to the cores or reduce parallelism by breaking the simd paradigm ( see'divergent warps'). examples of these kinds of problems include : most graph algorithms ( too unpredictable, especially in memory - space ) sparse linear algebra ( but this is bad on the cpu too ) small signal processing problems ( ffts smaller than 1000 points, for example ) search sort


your question is asking about model verification. you can find numerous resources on methods and standards by searching for verification and validation ( roache 1997, 2002, 2004, oberkampf & trucano 2002, salari & knupp 2000, babuska & oden 2004 ), as well as the broader topic of uncertainty quantification. rather than elaborate on methods, i would like to highlight a community that took a firm stand on the issue. in 1986, roache, ghia, and white established the journal of fluids engineering editorial policy statement on the control of numerical accuracy which opens with a professional problem exists in the computational fluid dynamics community and also in the broader area of computational physics. namely, there is a need for higher standards on the control of numerical accuracy. [... ] the problem is certainly not unique to the jfe and came into even sharper focus at the 1980 - 81 afosrhttm - stanford conference on complex turbulent flows. it was a conclusion of that conference's evaluation committee that, in most of the submissions to that conference, it was impossible to evaluate and compare the accuracy of different turbulence models, since one could not distinguish physical modeling errors from numerical errors related to the algorithm and grid. this is especially the case for first - order accurate methods and hybrid methods. they conclude with very direct guidelines : the journal of fluids engineering will not accept for publication any paper reporting the numerical solution of a fluids engineering problem that fails to address the task of systematic truncation error testing and accuracy estimation. [... ] we must make it clear that a single calculation in a fixed grid will not be acceptable, since it is impossible to infer an accuracy estimate from such a calculation. also, the editors will not consider a reasonable agreement with experimental data to be sufficient proof of accuracy, especially if any adjustable parameters are involved, as in turbulence modeling. the current version contains a comprehensive set of criteria and represents a standard that, in my opinion, other fields should aspire to match. it is shameful that even today, awareness about the importance of model verification is absent in so many fields.


because a lot of really practical problems are the halting problem in disguise. a solution to them solves the halting problem. you want a compiler that finds the fastest possible machine code for a given program? actually the halting problem. you have javascript, with some variables at a high security level and some at a low security level. you want to make sure that an attacker can't get at the high security information. this is also just the halting problem. you have a parser for your programming language. you change it, but you want to make sure it still parses all the programs it used to. actually the halting problem. you have an anti - virus program, and you want to see if it ever executes a malicious instruction. actually just the halting problem. as for the wikipedia example, yes, you could model a modern computer as a finite - state machine. but there's two problems with this. every computer would be a different automaton, depending on the exact number of bits of ram. so this isn't useful for examining a particular piece of code, since the automaton is dependent on the machine on which it can run. you'd need $ 2 ^ n $ states if you have n bits of ram. so for your modern 8gb computer, that's $ 2 ^ { 32000000000 } $. this is a number so big that wolfram alpha doesn't even know how to interpret it. when i do $ 2 ^ { 10 ^ 9 } $ it says that it has $ 300000000 $ decimal digits. this is clearly much too large to store in a normal computer. the halting problem lets us reason about the relative difficulty of algorithms. it lets us know that, there are some algorithms that don't exist, that sometimes, all we can do is guess at a problem, and never know if we've solved it. if we didn't have the halting problem, we would still be searching for hilbert's magical algorithm which inputs theorems and outputs whether they're true or not. now we know we can stop looking, and we can put our efforts into finding heuristics and second - best methods for solving these problems. update : just to address a couple of issues raised in the comments. @ tyler fleming cloutier : the " nonsensical " problem arises in the proof that the halting problem is undecidable, but what's at the core


of undecidability is really having an infinite search space. you're searching for an object with a given property, and if one doesn't exist, there's no way to know when you're done. the difficulty of a problem can be related to the number of quantifiers it has. trying to show that there exists ( $ \ exists $ ) an object with an arbitrary property, you have to search until you find one. if none exists, there's no way ( in general ) to know this. proving that all objects ( $ \ forall $ ) have a property is hard, but you can search for an object without the property to disprove it. the more alternations there are between forall and exists, the harder a problem is. for more on this, see the arithmetic hierarchy. anything above $ \ sigma ^ 0 _ 0 = \ pi ^ 0 _ 0 $ is undecidable, though level 1 is semi - decidable. it's also possible to show that there are undecidable problems without using a nonsensical paradox like the halting problem or liar ’ s paradox. a turing machine can be encoded using a string of bits, i. e. an integer. but a problem can be encoded as a language, i. e. a subset of the integers. it's known that there is no bijection between the set of integers and the set of all subsets of the integers. so there must be some problems ( languages ) which don't have an associated turing machine ( algorithm ). @ brent : yes, this admits that this is decidable for modern computers. but it's decidable for a specific machine. if you add a usb drive with disk space, or the ability to store on a network, or anything else, then the machine has changed and the result doesn't still hold. it also has to be said that there are going to be many times where the algorithm says " this code will halt " because the code will fail and run out of memory, and that adding a single extra bit of memory would cause the code to succeed and give a different result. the thing is, turing machines don't have an infinite amount of memory. there's never a time where an infinite amount of symbols are written to the tape. instead, a turing machine has " unbounded " memory, meaning that you can keep getting more sources of memory when you need it. computers


are like this. you can add ram, or usb sticks, or hard drives, or network storage. yes, you run out of memory when you run out of atoms in the universe. but having unlimited memory is a much more useful model.


summary : you need a heatsink now!!!!! : - ) [ and having a series resistor as well wouldn't hurt : - ) ] well asked question your question is asked well - much better than usual. the circuit diagram and references are appreciated. this makes it much easier to give a good answer first time. hopefully this is one... : - ) it makes sense ( alas ) : the behavior is entirely expected. you are thermally overloading the regulator. you need to add a heat sink if you want to use it in this manner. you would benefit greatly from a proper understanding of what is happening. power = volts x current. for a linear regulator power total = power in load + power in regulator. regulator vdrop = vin - vload here vdrop in regulator = 24 - 5 = 19v. here power in = 24v x iload power in load = 5v x iload power in regulator = ( 24v - 5v ) x iload. for 100 ma of load current the regulator will dissipate vdrop x iload ( 24 - 5 ) x 0. 1 a = 19 x 0. 1 = 1. 9 watt. how hot? : page 2 of the data sheet says that the thermal resistance from junction to ambient ( = air ) is 50 degrees c per watt. this means that for every watt you dissipate you get 50 degrees c rise. at 100 ma you would have about 2 watts dissipation or about 2 x 50 = 100°c rise. water would boil happily on the ic. the hottest most people can hold onto long term is 55°c. yours is hotter than that. you didn't mention it boiling water ( wet finger sizzle test ). let's assume you have ~ ~ 80°c case temperature. let's assume 20°c air temperature ( because its easy - a few degrees either way makes little difference. trise = tcase - tambient = 80°c - 20°c = 60°c. dissipation = trise / rth = 60 / 50 ~ = 1. 2 watt. at 19v drop 1. 2 w = 1. 2 / 19 a = 0. 0632 a or about 60 ma. ie if you are drawing about 50 ma you will get a case temperature of 70°c - 80°c degrees range. you need a heatsink. fixing it : the data sheet page 2 says rt


##hj - case = thermal resistance from junction to case is 5c / w = 10 % of junction to air. if you use a say 10 c / w heatsink then total rth will be r _ jc + rc _ amb ( add junction to case to case to air ). = 5 + 10 = 15°c / watt. for 50 ma you will get 0. 050a x 19v = 0. 95w or a rise of 15°c / watt x 0. 95 ~ = 14°c rise. even with say 20°c rise and a 25v ambient you will get 20 + 25 = 45°c heatsink temperature. the heatsink will be hot but you will be able to hold it without ( too much ) pain. beating the heat : as above, heat dissipation in a linear regulator in this situation is 1. 9 watt per 100 ma or 19 watt at 1a. that's a lot of heat. at 1a, to keep temperature under the temperature of boiling water ( 100°c ) when ambient temperature was 25°c you'd need an overall thermal resistance of no more than ( 100°c - 25°c ) / 19 watt = 3. 9°c / w. as the junction to case rthjc is already greater than 3. 9 at 5°c / w you cannot keep the junction under 100°c in these conditions. junction to case alone at 19v and 1a will add 19v x 1a x 5°c / w = 95°c rise. while the ic is rated to allow temperatures as high as 150°c, this is not good for reliability and should be avoided if at all possible. just as an exercise, to just get it under 150°c in the above case the external heatsink would need to be ( 150 - 95 ) °c / 19w = 2. 9°c / w. that's attainable but is a larger heatsink than you'd hope to use. an alternative is to reduce the energy dissipated and thus the temperature rise. the ways of reducing heat dissipation in the regulator are : ( 1 ) use a switching regulator such as the natsemi simple switchers series. a performance switching regulator with even only 70 % efficiency will reduce the heat dissipation dramatically as only 2 watt is dissipated in the regulator!. ie energy in = 7. 1 watts. energy out = 70 % = 5 watts. current at 5 watts at 5v = 1a.


another option is a pre - made drop - in replacement for a 3 terminal regulator. the following image and link are from the part referred to in a comment by jay kominek. oki - 78sr 1. 5a, 5v drop in switching regulator replacement for an lm7805. 7v - 36v in. at 36 volts in, 5v out, 1. 5a efficiency is 80 %. as pout = 5v x 1. 5a = 7. 5w = 80 %, the power dissipated in the regulator is 20 % / 80 % x 7. 5w = 1. 9 watts. very tolerable. no heatsink required and can provide 1. 5a out at 85 degrees c. [ [ errata : just noticed the curve below is at 3. 3v. the 5v part manages 85 % at 1. 5a so is better than the above. ] ] ( 2 ) reduce the voltage ( 3 ) reduce the current ( 4 ) dissipate some energy external to the regulator. option 1 is the best technically. if this is not acceptable and if 2 & 3 are fixed then option 4 is needed. the easiest and ( probably best ) external dissipation system is a resistor. a series power resistor which drops from 24v to a voltage that the regulator will accept at max current will do the job well. note that you will want a filter capacitor at the input to the regulator due to the resistance making the supply high impedance. say about 0. 33uf, more won't hurt. a 1 uf ceramic should do. even a larger cap such as a 10 uf to 100 uf aluminum electrolytic should be good. assume vin = 24 v. vregulator in min = 8v ( headroom / dropout. check data sheet. selected reg says 8v at < 1a. ) iin = 1 a. required drop at 1a = 24 - 8 = 16v. say 15v to be " safe ". r = v / i = 15 / 1 = 15 ohms. power = i2 * r = 1 x 15 = 15 watts. a 20 watt resistor would be marginal. a 25w + resistor would be better. here's a 25w 15r resistor priced at $ 3. 30 / 1 in stock lead free with datasheet here. note that this also needs a heat sink!!! you can buy free air rated resistors


up to 100's of watts. what you use is your choice but this would work well. note that it is rated at 25 watt commercial or 20 watt military so at 15w it is " doing well ". another option is a suitable length of properly rated resistance wire mounted appropriately. odds are a resistor manufacturer already does this better than you do. with this arrangement : total power = 24w resistor power = 15 watt load power = 5 watt regulator power = 3 watt regulator junction rise will be 5°c / w x 3 = 15°c above the case. you will need to provide a heatsink to keep regulator and heatsink happy but that is now " just a matter of engineering ". heatsink examples : 21 degrees °c ( or °k ) per watt 7. 8°c / w digikey - many heatsink examples including this 5. 3 c / w heatsink 2. 5°c / w 0. 48°c / w!!! 119mm wide x 300mm long x 65 mm tall. 1 foot long x 4. 7 " wide x 2. 6 " tall good article on heatsink selection forced convection heatsink thermal resistance reducing linear regulator dissipation with a series input resistor : as noted above, using a series resistor to drop voltage prior to a linear regulator can greatly reduce dissipation in the regulator. while cooling a regulator usually requires heatsinks, air - cooled resistors can be obtained cheaply that are able to dissipate 10 or more watts without needing a heatsink. it is not usually a good idea to solve high input voltage problems in this manner but it can have its place. in the example below an lm317 5v output 1a supply operated from 12v. adding a resistor can more than halve the power dissipation in the lm317 under worst case conditions by adding a cheap air cooled wire mounted series input resistor. the lm317 needs 2 to 2. 5v headroom at lower currents or say 2. 75v under extreme load and temperature conditions. ( see fig 3 in the datasheet, - copied below ). lm317 headroom or dropout voltage rin has to be sized such that it does not drop excessive voltage when v _ 12v is at its minimum, vdropout is worst case for the conditions and the series diode drop and output voltage are allowed for. voltage across resistor must always be less than = minimum vin less


maximum vdiode drop less worst case dropout relevant to situation less output voltage so rin < = ( v _ 12 - vd - 2. 75 - 5 ) / imax. for 12v minimum vin, and say 0. 8v diode drop and say 1 amp out that's ( 12 - 0. 8 - 2. 75 - 5 ) / 1 = 3. 45 / 1 = 3r45 = say 3r3. power in r = i ^ 2r = 3. 3w so a 5w part would be marginally acceptable and 10w would be better. dissipation in the lm317 falls from > 6 watt to < 3 watt. an excellent example of a suitable wire lead mounted air - cooled resistor would be a member of this nicely specified yageo family of wire - wound resistors with members rated from 2w to 40w air cooled. a 10 watt units is in stock at digikey at $ us0. 63 / 1. resistor ambient temperature ratings and temperature rise : nice to have are these two graphs from the datasheet above which allow real world results to be estimated. the left hand graph shows that a 10 watt resistor operated at 3w3 = 33 % of its rate wattage has an allowable ambient temperature of up to 150 c ( actually about 180 c if you plot the operating point in the graph but the manufacturer says 150 c max is allowed. the second graph shows that temperature rise for a 10 w resistor operated at 3w3 will be about 100°c above ambient. a 5 w resistor from the same family would be operating at 66 % of rating and have a temperature rise of 140°c above ambient. ( a 40 w would have about 75°c rise but 2 x 10 w = under 50°c and 10 x 2 w only about 25°c!!!. the decreasing temperature rise with an increasing number of resistors with the same combined wattage rating in each case is presumably related to " square cubed law " action as there is less cooling surface area per volume as size increases. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ added august 2015 - case study : somebody asked the reasonable question : isn't a more likely explanation the relatively high capacitive load ( 220 µf )? e. g. causing the


regulator to become unstable, oscillations causing a lot of heat dissipated in the regulator. in the datasheet, all of the circuits for normal operation only have a 100 nf capacitor on the output. i answered in comments, but they may be deleted in due course and this is a worthwhile addition to the subject, so here are the comments edited into the answer. in some cases oscillation and instability of the regulator certainly is an issue but, in this case and many like it, the most likely reason is excess dissipation. the 78xxx family are very old and predate both the modern low dropout regulators and the series powered ( lm317 style ) ones. the 78xxx family are essentially unconditionally stable with respect to cout. they in fact need none for proper operation and the 0. 1uf often shown is to provide a reservoir to provide extra surge or spike handling. in some of the related data sheets they actually say that cout can be " increased without limit " but i do not see such a note here - but also ( as i'd expect ) there is no note suggesting instability at high cout. in fig 33 on page 31 of the datasheet they show the use of a reverse diode to " protect against " high capacitance loads " - i. e., capacitors with high enough energy to cause damage if discharged into the output - i. e., far more than 0. 1 uf. dissipation : at 24 vin and 5 vout the regulator dissipates 19 mw per ma. rthja is 50 c / w for the to220 package so you'd get about 1°c rise per ma of current. so with say 1 watt dissipation in 20 c ambient air the case would be at about 65°c ( and could be more depending how the case is oriented and located ). 65°c is somewhat above the lower limit of " burn my finger " temperature. at 19 mw / ma it would take 50 ma to dissipate 1 watt. the actual load in the example given is unknown - he shows an indicator led at about 8 or 9 ma ( if red ) plus a load of the regulator internal current used ( under 10 ma ) + " pic18fxxxx ), a few leds... " that total could reach or exceed 50 ma depending on the pic circuit, or may be much less. |


overall given regulator family, differential voltage, actual cooling uncertainty, tambient uncertainty, c / w typical figure and more it seems like sheer dissipation is a reasonable reason for what he sees in this case - and for what many people using linear regulators will experience in similar cases. there is a chance that it's instability for reasons less obvious, and such should never be rejected without good reason, but i'd start on dissipation. in this case a series input resistor ( say 5w rated with air cooling ) would move much of the dissipation into a component better suited to deal with it. and / or a modest heatsink should work marvels.


in regression, it is often recommended to center the variables so that the predictors have mean $ 0 $. this makes it easier to interpret the intercept term as the expected value of $ y _ i $ when the predictor values are set to their means. otherwise, the intercept is interpreted as the expected value of $ y _ i $ when the predictors are set to 0, which may not be a realistic or interpretable situation ( e. g. what if the predictors were height and weight? ). another practical reason for scaling in regression is when one variable has a very large scale, e. g. if you were using population size of a country as a predictor. in that case, the regression coefficients may be on a very small order of magnitude ( e. g. $ 10 ^ { - 6 } $ ) which can be a little annoying when you're reading computer output, so you may convert the variable to, for example, population size in millions. the convention that you standardize predictions primarily exists so that the units of the regression coefficients are the same. as @ gung alludes to and @ manst shows explicitly ( + 1 to both, btw ), centering / scaling does not affect your statistical inference in regression models - the estimates are adjusted appropriately and the $ p $ - values will be the same. other situations where centering and / or scaling may be useful : when you're trying to sum or average variables that are on different scales, perhaps to create a composite score of some kind. without scaling, it may be the case that one variable has a larger impact on the sum due purely to its scale, which may be undesirable. to simplify calculations and notation. for example, the sample covariance matrix of a matrix of values centered by their sample means is simply $ x'x $. similarly, if a univariate random variable $ x $ has been mean centered, then $ { \ rm var } ( x ) = e ( x ^ 2 ) $ and the variance can be estimated from a sample by looking at the sample mean of the squares of the observed values. related to aforementioned, pca can only be interpreted as the singular value decomposition of a data matrix when the columns have first been centered by their means. note that scaling is not necessary in the last two bullet points i mentioned and centering may not be necessary in the first bullet i mentioned, so the two do not need to go hand and hand at all times.


the first thing you have to understand is that notes are not uniquely defined. everything depends on what tuning you use. i'll assume we're talking about equal temperament here. in equal temperament, a half - step is the same as a frequency ratio of $ \ sqrt [ 12 ] { 2 } $ ; that way, twelve half - steps makes up an octave. why twelve? at the end of the day, what we want out of our musical frequencies are nice ratios of small integers. for example, a perfect fifth is supposed to correspond to a frequency ratio of $ 3 : 2 $, or $ 1. 5 : 1 $, but in equal temperament it doesn't ; instead, it corresponds to a ratio of $ 2 ^ { \ frac { 7 } { 12 } } : 1 \ approx 1. 498 : 1 $. as you can see, this is not a fifth ; however, it is quite close. similarly, a perfect fourth is supposed to correspond to a frequency ratio of $ 4 : 3 $, or $ 1. 333... : 1 $, but in equal temperament it corresponds to a ratio of $ 2 ^ { \ frac { 5 } { 12 } } : 1 \ approx 1. 335 : 1 $. again, this is not a perfect fourth, but is quite close. and so on. what's going on here is a massively convenient mathematical coincidence : several of the powers of $ \ sqrt [ 12 ] { 2 } $ happen to be good approximations to ratios of small integers, and there are enough of these to play western music. here's how this coincidence works. you get the white keys from $ c $ using ( part of ) the circle of fifths. start with $ c $ and go up a fifth to get $ g $, then $ d $, then $ a $, then $ e $, then $ b $. then go down a fifth to get $ f $. these are the " neighbors " of $ c $ in the circle of fifths. you get the black keys from here using the rest of the circle of fifths. after you've gone up a " perfect " perfect fifth twelve times, you get a frequency ratio of $ 3 ^ { 12 } : 2 ^ { 12 } \ approx 129. 7 : 1 $. this happens to be rather close to $ 2 ^ 7 : 1 $, or seven octaves! and if we replace $ 3 : 2 $ by $


2 ^ { \ frac { 7 } { 12 } } : 1 $, then we get exactly seven octaves. in other words, the reason you can afford to identify these intervals is because $ 3 ^ { 12 } $ happens to be rather close to $ 2 ^ { 19 } $. said another way, $ $ \ log _ 2 3 \ approx \ frac { 19 } { 12 } $ $ happens to be a good rational approximation, and this is the main basis of equal temperament. ( the other main coincidence here is that $ \ log _ 2 \ frac { 5 } { 4 } \ approx \ frac { 4 } { 12 } $ ; this is what allows us to squeeze major thirds into equal temperament as well. ) it is a fundamental fact of mathematics that $ \ log _ 2 3 $ is irrational, so it is impossible for any kind of equal temperament to have " perfect " perfect fifths regardless of how many notes you use. however, you can write down good rational approximations by looking at the continued fraction of $ \ log _ 2 3 $ and writing down convergents, and these will correspond to equal - tempered scales with more notes. of course, you can use other types of temperament, such as well temperament ; if you stick to $ 12 $ notes ( which not everybody does! ), you will be forced to make some intervals sound better and some intervals sound worse. in particular, if you don't use equal temperament then different keys sound different. this is a major reason many western composers composed in different keys ; during their time, this actually made a difference. as a result when you're playing certain sufficiently old pieces you aren't actually playing them as they were intended to be heard - you're using the wrong tuning. edit : i suppose it is also good to say something about why we care about frequency ratios which are ratios of small integers. this has to do with the physics of sound, and i'm not particularly knowledgeable here, but this is my understanding of the situation. you probably know that sound is a wave. more precisely, sound is a longitudinal wave carried by air molecules. you might think that there is a simple equation for the sound created by a single note, perhaps $ \ sin 2 \ pi f t $ if the corresponding tone has frequency $ f $. actually this only occurs for tones which are produced electronically ; any tone you produce in nature carries with it overtones and has a fourier series $ $ \ sum \ left (


a _ n \ sin 2 \ pi n f t + b _ n \ cos 2 \ pi n f t \ right ) $ $ where the coefficients $ a _ n, b _ n $ determine the timbre of the sound ; this is why different instruments sound different even when they play the same notes, and has to do with the physics of vibration, which i don't understand too well. so any tone which you hear at frequency $ f $ almost certainly also has components at frequency $ 2f, 3f, 4f,... $. if you play two notes of frequencies $ f, f'$ together, then the resulting sound corresponds to what you get when you add their fourier series. now it's not hard to see that if $ \ frac { f } { f'} $ is a ratio of small integers, then many ( but not all ) of the overtones will match in frequency with each other ; the result sounds a more complex note with certain overtones. otherwise, you get dissonance as you hear both types of overtones simultaneously and their frequencies will be similar, but not similar enough. edit : you should probably check out david benson's " music : a mathematical offering ", the book rahul narain recommended in the comments for the full story. there was a lot i didn't know, and i'm only in the introduction!


these answers require way too much machinery. by definition, the characteristic polynomial of an $ n \ times n $ matrix $ a $ is given by $ $ p ( t ) = \ det ( a - ti ) = ( - 1 ) ^ n \ big ( t ^ n - ( \ text { tr } a ) \, t ^ { n - 1 } + \ dots + ( - 1 ) ^ n \ det a \ big ) \,. $ $ on the other hand, $ p ( t ) = ( - 1 ) ^ n ( t - \ lambda _ 1 ) \ dots ( t - \ lambda _ n ) $, where the $ \ lambda _ j $ are the eigenvalues of $ a $. so, comparing coefficients, we have $ \ text { tr } a = \ lambda _ 1 + \ dots + \ lambda _ n $.


the main advantage, in my opinion, of using cloud - based resources is flexibility, i. e. if you have a fluctuating workload, you only pay for what you need. if this is not the case in your application, i. e. you know you will have a quantifiable and constant workload, then you're probably better - off building your own cluster. in the cloud, you pay for flexibility, and if you don't need flexibility, you would be paying for something you don't need. if your workload is flexible but somewhat intense and relies on certain hardware features ( see aeismail's answer ), you may want to try sharing a cluster with other people in your university to amortize the idle cycles. my old university runs such a shared cluster with a " shareholder model " in which every group is guaranteed a share of the computing power proportional to their investment in the hardware and idle cycles can be used by anyone. the only difficulty is centralizing the cluster administration.


as i understand this, there are basically two effects at work here. when you populate an $ \ mathrm { s } $ - orbital, you add a significant amount of electron density close to the nucleus. this screens the attractive charge of the nucleus from the $ \ mathrm { d } $ - orbitals, making them higher in energy ( and more radially diffuse ). the difference in energy between putting all the electrons in $ \ mathrm { d } $ - orbitals and putting one in an $ \ mathrm { s } $ - orbital increases as you fill the $ \ mathrm { d } $ - orbitals. additionally, pairing electrons in one orbital ( so, adding the second $ \ mathrm { s } $ electron ) carries a significant energy cost in terms of coulombic repulsion because you're adding an electron essentially in exactly the same space as there's already an electron. i'm assuming that the effect isn't strong enough to avert fluorine having a $ \ mathrm { 2s ^ 2 } $ occupation, and if you look at gadolinium, the effect there isn't strong enough to stop the $ \ mathrm { s } $ from filling ( large nuclear charge and orbital extent at the nucleus is a good combination energy - wise ), it does manage to make it more favourable to add the electron into the $ \ mathrm { 5d } $ instead of the $ \ mathrm { 4f } $ orbitals. also, if you take a look at tungsten vs gold, there the effect isn't strong enough for tungsten to avoid a $ \ mathrm { 6s ^ 2 } $ occupation, but is for gold - more $ \ mathrm { d } $ electrons making the screening effect overcome the strong nuclear charge and enhanced nuclear penetration of an $ \ mathrm { s } $ - orbital.


perhaps the examiner intended the students to notice the square is determined by a $ ( 3, 4, 5 ) $ triangle, because $ 3 + 5 = 4 + 4 $ (! ) : consequently, as several others have noted, $ $ \ frac { \ text { perimeter of the circle } } { \ text { perimeter of the square } } = \ frac { 5 \ cdot 2 \ pi } { 4 \ cdot 8 } = \ frac { \ pi } { 3. 2 } < 1. $ $ for an approach less dependent on inspiration, taking the origin of the coordinate system at the center of the circle seems easier than placing the origin at the center of the square. without loss of generality, assume the circle has unit radius : equating the lengths of the horizontal and vertical sides of the square in this diagram, we read off $ $ x + 1 = 2y \ quad \ text { ( or $ x = 2y - 1 $ ). } $ $ invoking the pythagorean theorem and substituting the preceding line, \ begin { align * } 0 & = x ^ { 2 } + y ^ { 2 } - 1 \ \ & = ( 2y - 1 ) ^ { 2 } + y ^ { 2 } - 1 \ \ & = 5y ^ { 2 } - 4y \ \ & = y ( 5y - 4 ). \ end { align * } clearly $ y \ neq 0 $, so $ y = 4 / 5 $, $ x = 3 / 5 $, and we notice the examiner's favorite triangle.


ohm's law states that the electric current through a conductor between two points is directly proportional to the voltage across the two points. it is represented by the equation v = ri, where v is the voltage, r is the resistance, and i is the current.


a transformer works on the principle of electromagnetic induction and is used to change the voltage level of alternating current ( ac ). it consists of two coils : the primary and secondary, which are not electrically connected but linked by a magnetic field. when ac flows through the primary coil, it creates a varying magnetic field, inducing a voltage in the secondary coil. the voltage change between the primary and secondary coils depends on the ratio of the number of turns in each coil.


ac ( alternating current ) and dc ( direct current ) are two types of electrical currents. ac current changes direction periodically, whereas dc current flows in one direction only. ac is commonly used for power distribution because it is less costly to transmit over long distances and can easily be transformed to different voltages. dc is often used in batteries, electronics, and solar power systems, as it provides a constant voltage or current.


a capacitor in a circuit is used for storing electrical energy temporarily in an electric field. it consists of two conductive plates separated by an insulating material or dielectric. capacitors are commonly used for filtering unwanted frequency components from signals, for power smoothing in power supplies, in timing circuits, and for energy storage in pulsing laser applications. they play a crucial role in both analog and digital electronic devices.


a diode is a semiconductor device that allows current to flow in one direction only. it has two terminals, an anode and a cathode. diodes are commonly used for rectification ( converting ac to dc ), in voltage regulation, and as protection devices in circuits.


a dc motor operates on the principle that a current - carrying conductor, placed in a magnetic field, experiences a mechanical force. the direction of this force is given by fleming ’ s left - hand rule and is the basis for the movement in dc motors.


a relay is an electrically operated switch. it consists of a coil that, when energized, creates a magnetic field which attracts a lever and changes the switch contacts. relays are used to control a high - power circuit with a low - power signal, often in safety - critical applications.


a fuse and a circuit breaker are both overcurrent protection devices. a fuse melts and breaks the circuit when excessive current flows through it, whereas a circuit breaker trips to interrupt the circuit. circuit breakers can be reset, but fuses must be replaced after they blow.


an inductor is a passive electrical component that stores energy in a magnetic field when electric current flows through it. it typically consists of a coil of wire and is used to control the flow of current in circuits, often in filtering applications or in creating magnetic fields.


electromagnetic induction is the process of generating electric current with a changing magnetic field. it's based on two key principles : first, a changing magnetic field within a coil of wire induces a voltage across the ends of the coil ; second, if the coil is closed through an electrical load, this induced voltage generates an electric current. this principle is the fundamental operating mechanism behind generators, transformers, induction motors, and many types of electrical sensors.


inductors and capacitors are both passive electronic components but serve different functions. an inductor stores energy in a magnetic field when electric current flows through it and opposes changes in current flow. a capacitor, on the other hand, stores energy in an electric field between its plates and opposes changes in voltage. inductors are often used in filtering and tuning circuits, whereas capacitors are used for energy storage, power conditioning, and signal filtering.


a semiconductor is a material with electrical conductivity intermediate between a conductor and an insulator. this property allows it to control electrical current, making it essential in modern electronics, including diodes, transistors, and integrated circuits.


photovoltaic cells convert sunlight into electricity using the photovoltaic effect. when light photons hit a solar cell, they can excite electrons, freeing them from atoms and allowing them to flow through the material to produce electricity.


a resistor is a passive component in a circuit that opposes the flow of electric current, which can be used to adjust signal levels, divide voltages, limit current, and dissipate power as heat.


electrical impedance is a measure of the opposition that a circuit presents to the passage of a current when a voltage is applied. it generalizes the concept of resistance to ac circuits, and includes both resistance and reactance ( capacitive and inductive effects ).


a ground wire is a safety feature in electrical systems that provides a path for electrical current to flow safely into the earth in the event of a short circuit or electrical fault, reducing the risk of electric shock or fire.


an inverter is a device that converts dc ( direct current ) to ac ( alternating current ). it uses electronic circuits to change the voltage, frequency, and waveform of the input power. inverters are commonly used in solar power systems and for power backup systems.


circuit breakers are protective devices that automatically stop the flow of current in an electrical circuit as a safety measure. they trip, or open the circuit, when they detect an overload or short circuit, preventing damage and potential fires.


analog signals represent data in continuous waves, varying smoothly over time, whereas digital signals represent data in discrete binary format ( 0s and 1s ). digital signals are less susceptible to interference and noise than analog signals.


transformers in a power grid are used to step up the voltage for efficient transmission over long distances and then step it down for safe use in homes and businesses. this process minimizes the power loss during transmission.


superconductors are materials that conduct electricity with zero resistance when cooled below a certain temperature. this property is significant for creating highly efficient electrical systems and for applications like magnetic resonance imaging ( mri ) and maglev trains.


ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. it is significant because it lays the foundational understanding of how voltage, current, and resistance interact in an electrical circuit.


the power factor in electrical systems is a measure of the efficiency of power usage. it is the ratio of the real power that is used to do work and the apparent power that is supplied to the circuit. a high power factor indicates efficient utilization of electrical power.


ac ( alternating current ) power is a type of electrical current where the direction of flow reverses periodically, while dc ( direct current ) power flows in a constant direction. ac is used for power distribution grids due to its ease of transforming voltage levels, while dc is often used in battery - powered devices.


a microcontroller is a compact integrated circuit designed to govern a specific operation in an embedded system. they are used in automatically controlled devices and products, such as automobile engine control systems, implantable medical devices, remote controls, office machines, and appliances.


a capacitor stores energy in an electric field, created between two conductive plates separated by an insulating material ( dielectric ). when voltage is applied across the plates, an electric field is established, allowing energy to be stored and released as needed.


a diode is a semiconductor device that primarily functions as a one - way switch for current. it allows current to flow easily in one direction but significantly restricts flow in the opposite direction. diodes are commonly used for rectification, signal modulation, and voltage regulation.


electromagnetic interference ( emi ) is a disturbance generated by external sources that affects an electrical circuit, leading to poor performance or failure. it can be mitigated through shielding, grounding, using filters, and designing circuits to minimize interference susceptibility.


an electric motor operates on the principle of electromagnetic induction. when an electric current passes through a coil within a magnetic field, it creates a force that causes the coil to rotate. this rotation can then be harnessed to do mechanical work.


a power supply unit typically includes a transformer for voltage regulation, a rectifier to convert ac to dc, a filter to smooth the output from the rectifier, and a regulator to provide a stable voltage output regardless of variations in load or input voltage.


operational amplifiers, or op - amps, are versatile components used in electronic circuits. they amplify voltage signals and are key in applications such as signal conditioning, filtering, or performing mathematical operations like addition, subtraction, integration, and differentiation.


a relay is an electrically operated switch that uses an electromagnet to mechanically operate a switching mechanism. it is used in electrical circuits to control a high - power circuit with a low - power signal, often in safety - critical applications like switching off machinery.


wireless charging works using the principle of magnetic resonance or inductive charging, where an electromagnetic field transfers energy between two coils - a transmitter coil in the charging device and a receiver coil in the device being charged.


there are mainly two types of electrical circuits : series circuits, where components are connected end - to - end and the same current flows through all components ; and parallel circuits, where components are connected across the same voltage source, allowing current to divide among them.


a fuse is a safety device in electrical circuits that protects against excessive current. it contains a metal wire or strip that melts when too much current flows through it, thereby interrupting the circuit and preventing damage or fire.


a variable frequency drive ( vfd ) is a type of motor controller that drives an electric motor by varying the frequency and voltage of its power supply. it's commonly used to control the speed of motors in various applications like pumps, fans, and conveyor systems.


an electrical ground is a reference point in an electrical circuit from which voltages are measured, a common return path for electric current, or a direct physical connection to the earth. it's important for safety, preventing electric shock, and ensuring proper functioning of electrical systems.


solar inverters convert the variable direct current ( dc ) output of a photovoltaic ( pv ) solar panel into a utility frequency alternating current ( ac ) that can be fed into a commercial electrical grid or used by a local, off - grid electrical network.


led lighting offers several advantages : energy efficiency ( lower power consumption ), longer operational life, improved physical robustness, smaller size, faster switching, and environmental friendliness by being free of toxic chemicals and recyclable.


a snubber circuit is used in power electronics to protect switching components from voltage spikes caused by inductive loads. it achieves this by dampening or'snubbing'excessive voltage and absorbing energy from the spikes, thus extending the life of the switching device.


a hall effect sensor detects magnetic fields by measuring the voltage that develops across an electrical conductor through which an electric current is flowing, in the presence of a perpendicular magnetic field. this voltage is known as the hall voltage and is proportional to the strength of the magnetic field.


a bleeder resistor in a high - voltage power supply is used to discharge the capacitors safely when the power is turned off. it helps to prevent electric shocks and damage by slowly draining residual charge from the capacitors over time.


a mosfet ( metal - oxide - semiconductor field - effect transistor ) operates by varying the width of a channel along which charge carriers ( electrons or holes ) flow. the width of the channel is controlled by the voltage on an electrode called the gate, which is insulated from the channel, controlling the electrical conductivity of the device.


a synchronous motor runs at a speed equal to its synchronous speed, which is directly proportional to the frequency of the power supply. an asynchronous motor, also known as an induction motor, runs at a speed less than its synchronous speed. the difference in speed is due to'slip ', which is necessary for torque production in asynchronous motors.


pulse - width modulation ( pwm ) controls motor speed by varying the duration of'on'pulses to adjust the average voltage sent to the motor. by increasing or decreasing the pulse width, pwm can effectively control the speed of the motor without losing efficiency.


the skin effect in electrical conductors is the phenomenon where alternating current ( ac ) tends to flow near the surface of the conductor, rather than uniformly throughout its cross - section. this effect increases the effective resistance of the conductor at higher frequencies, impacting the design and performance of high - frequency circuits.


optical fiber communication uses light pulses to transmit data through strands of fiber made of glass or plastic. the light signals represent digital data, which are transmitted over long distances with low loss and high bandwidth capabilities, making it ideal for high - speed data communication.


a varistor, or voltage - dependent resistor, is used in circuits for protection against excessive transient voltages. it changes resistance with the voltage applied and clamps high - voltage surges, thus protecting sensitive electronic components.


frequency converters in adjustable - speed drives work by converting the fixed frequency and voltage of the power supply into a variable frequency and voltage output. this allows control over the speed of ac motors, as their speed depends on the frequency of the power supply.


a phase - locked loop ( pll ) is an electronic circuit that synchronizes an output oscillator signal with a reference signal in phase and frequency. it's widely used in telecommunications for frequency synthesis, modulation, demodulation, and signal recovery.


a lithium - ion battery operates based on the movement of lithium ions between the anode and cathode. during discharge, lithium ions move from the anode to the cathode through an electrolyte, releasing energy. charging reverses this process, storing energy in the battery.


reactive power in ac circuits is the portion of electricity that establishes and sustains the electric and magnetic fields of ac equipment. unlike active power, which does work, reactive power oscillates between the source and load, being essential for the functioning of ac systems but not consumed as usable power.


in coaxial cables, electromagnetic waves propagate along the length of the cable between the central conductor and the outer conductor. the outer conductor shields the inner conductor from external electromagnetic interference, ensuring signal integrity, especially at high frequencies.


the fourier transform is significant in signal processing as it converts a signal from its original time or spatial domain into the frequency domain. it reveals the frequency components of a time - based signal, aiding in analysis, filtering, and modulation of signals.


a heat sink in electronic components dissipates heat away from the components, such as processors or power transistors, to prevent overheating. it increases the surface area in contact with the air, enhancing heat dissipation through convection and radiation.


mems are miniaturized mechanical and electromechanical devices that integrate mechanical components, sensors, actuators, and electronics on a single silicon chip. they find applications in diverse fields like consumer electronics, automotive systems, biomedical devices, and environmental monitoring.


an induction generator produces electricity by converting mechanical energy into electrical energy using electromagnetic induction. unlike a synchronous generator, it doesn ’ t require a separate dc excitation source and starts generating power when its rotor is spun faster than the synchronous speed.


a zener diode is used to provide voltage regulation in circuits. it allows current to flow in the forward direction like a normal diode, but also in the reverse direction if the voltage is greater than the zener breakdown voltage. it's commonly used for stabilizing and clipping circuits.


a piezoelectric transducer works on the piezoelectric effect, where certain materials produce an electric charge when mechanically stressed. conversely, when an electric field is applied, these materials change shape. this property is utilized in sensors and actuators.


gauss's law in electromagnetism states that the total electric flux through a closed surface is equal to the charge enclosed divided by the permittivity of the medium. it's important for understanding electric fields in terms of charge distribution, and for calculating electric fields in symmetric charge configurations.


a rectifier in an ac to dc conversion circuit converts alternating current ( ac ), which reverses direction periodically, into direct current ( dc ), which flows in only one direction. this is achieved by using diodes or thyristors which allow current to pass only in one direction.


a synchronous rectifier works by replacing the diodes in a rectifier circuit with actively controlled switches, like mosfets, which are turned on and off in sync with the ac input. this reduces power losses compared to traditional diode rectifiers, especially in low - voltage applications.


a differential amplifier amplifies the difference between two input voltages while rejecting any voltage common to both inputs. it is widely used in instrumentation and operational amplifiers for its high common - mode rejection ratio, making it ideal for noise reduction in signal processing.


switched - mode power supplies ( smps ) work by switching the input power on and off rapidly with a high frequency through power transistors, converting the voltage and current characteristics. the power is then smoothed and regulated using capacitors and inductors.


electrical hysteresis in magnetic materials refers to the lag between the magnetization of the material and the magnetic field applied to it. this phenomenon results in a hysteresis loop in the magnetization versus field graph, crucial in understanding magnetic properties for memory storage and transformers.


an optocoupler, or optical isolator, uses light to transfer an electrical signal between two isolated circuits, thereby providing electrical isolation. it's used to protect sensitive components from high voltages and to prevent ground loops in digital communication systems.


ferrite beads suppress high - frequency noise in electronic circuits by absorbing unwanted high - frequency signals and dissipating them as heat. they act as a low - pass filter, allowing low - frequency signals to pass while attenuating the amplitude of high - frequency noise.


a voltage regulator in a power supply circuit maintains a constant output voltage level despite variations in input voltage and load conditions. it ensures that electronic devices receive a steady, reliable voltage, which is crucial for proper functioning and longevity.


a flyback diode in a circuit with an inductive load is used to protect other components from voltage spikes caused by the collapsing magnetic field when the current to the inductor is switched off. the diode does this by providing a safe path for the inductive kickback current.


in an lc filter circuit, an inductor works with a capacitor to filter out certain frequencies from a signal. the inductor resists changes in current, helping to smooth the output and filter out high - frequency noise, while the capacitor filters out low - frequency noise.


a wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit. one leg includes the unknown component, while the other leg includes known resistances. it's widely used in strain gauges and temperature sensors.


a supercapacitor differs from a traditional capacitor in its higher capacity and energy density. it stores energy via electrostatic and electrochemical processes, allowing for faster charge / discharge times, longer life cycles, and a higher power capacity than typical electrolytic capacitors.


a phototransistor is a light - sensitive transistor. it works similarly to a normal transistor but has a light - sensitive base region. incoming photons increase the current flow between the collector and emitter, making phototransistors useful in light detection and photonic circuits.


a darlington transistor pair is a configuration where two bipolar transistors are connected such that the current amplified by the first is amplified further by the second. this provides high current gain and is used in applications requiring high amplification from a low input current.


a voltage multiplier is an electrical circuit that converts ac or pulsing dc electrical power from a lower voltage to a higher dc voltage. it uses a network of capacitors and diodes to successively store and transfer charge, effectively increasing the voltage.


the seebeck effect is significant in thermoelectrics as it describes the conversion of temperature differences directly into electricity. it is the basis for thermocouples and thermoelectric generators, which can convert heat from sources like industrial waste heat or solar heat into electrical power.


a buck converter reduces voltage in a power supply using a series of controlled switches and energy storage components ( inductors and capacitors ). it efficiently steps down voltage by switching on and off at high frequency, storing energy in the inductor during'on'phases and releasing it during'off'phases.


a schmitt trigger in digital circuits is used to convert varying or noisy input signals into clean, stable digital output signals. it has a hysteresis loop that provides different threshold voltages for high - to - low and low - to - high transitions, which is essential for debouncing switches and creating stable square waves.


a band - pass filter is an electronic circuit that allows signals within a certain frequency range to pass while attenuating signals outside this range. it's commonly used in wireless communication systems, audio processing, and instrumentation to isolate specific frequency bands.


a current transformer operates on the principle of magnetic induction. it is used to measure alternating current ( ac ), transforming a high current from a primary conductor to a lower current in the secondary circuit. the secondary current is proportional to the primary current, allowing for safe monitoring and measurement.


an opto - isolator, also known as an optical isolator, functions by using a light source ( led ) and a light sensor ( phototransistor ) to transmit an electrical signal between two isolated circuits. the isolation prevents high voltages from affecting the system receiving the signal.


a digital multimeter measures resistance by passing a small, known current through the resistor and measuring the voltage across it. the resistance is then calculated using ohm's law ( resistance = voltage / current ). this method provides an accurate measurement of resistance.


a balun in rf ( radio frequency ) circuits is used to convert between balanced and unbalanced signals. it matches the impedance between these types of circuits and minimizes signal loss and interference, which is critical in antenna and transmission line applications.


the time constant in rc circuits, denoted as τ ( tau ), is the time it takes for the voltage across the capacitor to charge to about 63. 2 % of its maximum value or to decay to 36. 8 % if discharging. it's calculated as the product of the resistance and capacitance ( τ = r × c ).


synchronous counters have all their flip - flops clocked at the same time by a common clock signal, ensuring precise and simultaneous state changes. asynchronous counters, on the other hand, have flip - flops that are clocked by the output of the preceding flip - flop, causing a slight delay in state change propagation.


a choke is an inductor designed to block high - frequency alternating current ( ac ) in an electrical circuit while allowing lower frequencies or direct current ( dc ) to pass. it's used for filtering and power conditioning, preventing electromagnetic interference ( emi ) from affecting sensitive components.


a gate driver in power electronics is a circuit that provides the proper voltage and current to switch power devices, like mosfets and igbts, on and off effectively. it ensures fast switching, minimizes power loss, and protects the device from damage due to improper driving.


an rf ( radio frequency ) amplifier enhances signal transmission by increasing the amplitude of a radio frequency signal. this amplification is crucial for boosting the signal strength before transmission, ensuring that it can travel longer distances without significant loss of quality.


a silicon - controlled rectifier ( scr ) is a four - layer solid - state current - controlling device. it functions as an electrically controlled switch that remains off until a certain threshold gate current is applied. once triggered, it conducts until the current falls below a certain holding level. it's widely used in power control and switching applications.


phase shift oscillators are used to generate sine wave outputs at audio frequencies. they are commonly employed in music instruments, signal generators, and as rf oscillators in transceivers, where precise control of the frequency and phase of the output signal is required.


in a bjt used as a switch, applying a small current to the base terminal allows a larger current to flow between the collector and emitter terminals. when the base current is removed, the switch is'off ', and no current flows through the collector - emitter path. this on - off action enables bjts to control and amplify electronic signals in a circuit.


a thermistor functions in temperature sensing by exhibiting a change in its electrical resistance with temperature variation. depending on the type, its resistance either decreases ( negative temperature coefficient - ntc ) or increases ( positive temperature coefficient - ptc ) with rising temperature. this property makes thermistors suitable for precise temperature measurements and control.


a surge protector safeguards electrical devices from voltage spikes in power lines. it diverts the excess voltage to the ground, thereby protecting connected devices from potential damage. this is crucial for maintaining the longevity and reliability of electronic equipment, especially those sensitive to high voltage.


an igbt combines the high - current capability of a bipolar transistor with the high - voltage switching of a mosfet, making it ideal for handling large power loads. it's widely used in variable - frequency drives, electric vehicle motor controllers, and power amplifiers.


electromagnetic compatibility ( emc ) in electronic design is the ability of electrical equipment to function satisfactorily in its electromagnetic environment without introducing intolerable electromagnetic disturbance to other equipment. this involves managing emissions of electromagnetic energy and improving immunity to external electromagnetic interference.


the smith chart is a graphical tool used in rf engineering for solving problems related to transmission lines and matching circuits. it allows engineers to visualize complex impedance, reflection coefficients, and s - parameters, simplifying the design and analysis of rf systems.


a digital - to - analog converter ( dac ) functions by converting digital signals, usually binary codes, into proportional analog voltages or currents. this conversion is essential in systems where digital data needs to be presented in an analog form, like in audio amplifiers, and in control and measurement systems.


fiber optics offer several advantages for data transmission : they have a much higher bandwidth than metal cables, resulting in faster data transfer rates ; they are less susceptible to electromagnetic interference ; they provide greater security ; and they are lighter and less bulky.


a varactor diode operates as a variable capacitor under the influence of a reverse bias voltage. its capacitance varies with the applied voltage, making it useful in tuning circuits, such as voltage - controlled oscillators ( vcos ) and rf filters, especially in frequency modulation and phase - locked loops.


a synchronous demodulator, also known as a coherent detector, works by multiplying an incoming modulated signal with a reference signal that is synchronized with the carrier wave of the modulated signal. this process extracts the original information signal from the modulated carrier wave, commonly used in digital communication systems for efficient signal demodulation.


a waveguide in microwave transmission is a structure that guides electromagnetic waves, particularly microwaves, from one point to another. it confines and directs the waves in a particular direction, minimizing power loss and maintaining signal integrity over the transmission path.


a gunn diode operates based on the gunn effect, where applying a strong electric field causes the diode to oscillate and emit microwaves. it doesn't have a p - n junction like other diodes. gunn diodes are used in radar systems, oscillators, and microwave frequency signal generators due to their ability to generate high frequencies.


optical encoders work by emitting a light beam through a rotating disk with transparent and opaque segments. the light is detected by a photodiode array, which generates a digital signal corresponding to the rotation. this allows for precise measurement of the angular position and speed of a rotating shaft.


ultrasonic sensing technology operates on the principle of emitting high - frequency sound waves and detecting their reflections from objects. the time taken for the sound waves to return is measured to determine the distance to an object. it is widely used in level sensing, obstacle detection, and range finding applications.


a digital phase - locked loop ( dpll ) maintains synchronization of a digital output signal with a reference signal. it uses a digital or software - based approach to lock onto the phase and frequency of the input signal, often used in digital communication systems for clock recovery and frequency synthesis.


a planar transformer uses flat windings, often etched onto a printed circuit board, instead of traditional wire - wound coils. this design allows for a lower profile, reduced leakage inductance, and better heat dissipation. planar transformers are used in high - frequency applications like switch - mode power supplies.


a piezoelectric accelerometer measures vibration by exploiting the piezoelectric effect. it contains piezoelectric materials that generate an electric charge when subjected to mechanical stress from vibrations. the generated charge is proportional to the vibration's acceleration, enabling precise measurement.


a pulse transformer is designed to transfer rectangular electrical pulses between circuits while isolating the input side from the output. it's used for applications requiring impedance matching and signal isolation, such as driving power switches in solid - state relays or igbts.


signal integrity in high - speed digital design refers to the quality and reliability of electrical signals as they travel through a circuit. it involves managing issues like noise, distortion, and signal loss, ensuring that signals are transmitted and received accurately, which is crucial in high - speed digital communication and processing.


load flow analysis in power systems is essential for determining the voltage at various points of the system and the flow of electrical power through the network. it helps in planning and operating a power system efficiently, ensuring stability and reliability, and is critical for optimizing system performance under different load conditions.


a cryotron is a superconducting device that operates at cryogenic temperatures, functioning as a switch or a gate in digital circuits. it utilizes the property of superconductivity, where resistance drops to zero below a certain temperature. cryotrons are used in superconducting circuits for their high speed and low energy dissipation.


an anechoic chamber, lined with material that absorbs electromagnetic waves, creates a space free of reflections and external noise. it's used in electromagnetic testing to accurately measure antenna patterns, radar cross - sections, and emissions without interference from external signals or reflections.


a magnetic amplifier uses the saturation properties of a magnetic core to control the flow of an ac current. by varying the degree of saturation of the core with a control dc current, it modulates the impedance of the ac circuit, thus amplifying the ac signal. it's used in power control and signal processing applications.


a quantum dot laser operates on the principle of quantum confinement in semiconductor quantum dots. electrons and holes are confined in these nanometer - sized dots, leading to discrete energy levels. this results in efficient electron - hole recombination and laser light emission at specific wavelengths, used in high - performance optical devices.


an interferometric modulator display ( imod ) works on the principle of interference of light. it uses microscopic cavities that reflect specific wavelengths of light when an electric field is applied, creating colors. this technology is used in displays for its low power consumption and high visibility in ambient light.


a regenerative braking system in electric vehicles captures the kinetic energy typically lost during braking and converts it into electrical energy, which is then stored in the vehicle ’ s battery. this improves the overall efficiency of the vehicle and extends the driving range.


a duplexer in communication systems is a device that allows simultaneous transmission and reception of signals through the same antenna while preventing the transmitter ’ s output from overloading the receiver. it's essential in radar and radio communication systems for efficient use of the frequency spectrum.


phase - change memory ( pcm ) operates by exploiting the reversible phase change in chalcogenide materials ( e. g., gst ) between crystalline and amorphous states with the application of heat. this change in phase alters the material's resistance, allowing data to be stored as binary information. pcm is known for its high speed, endurance, and non - volatility.


a vector signal analyzer not only measures the magnitude of a signal, like a traditional spectrum analyzer, but also its phase information across a wide frequency range. this allows for more detailed analysis of complex modulated signals, crucial in modern communication systems for signal characterization and troubleshooting.


a virtual ground in op - amp circuits is a point within the circuit that is maintained at a constant voltage, typically half the supply voltage, but without a direct physical connection to the ground terminal. it allows for bipolar operation of the op - amp using a single power supply and simplifies the design of analog circuits.


a squid operates based on the quantum phenomenon of superconductivity and the josephson effect. it is extremely sensitive to magnetic fields, even to the quantum level. squids are used in various applications requiring high sensitivity measurements, such as in medical imaging ( mri ) and in geological survey equipment.


a mems gyroscope measures angular velocity using the coriolis effect. when the sensor rotates, the vibration of the mems structure causes a measurable change due to the coriolis force. this change is proportional to the rate of rotation, allowing the gyroscope to accurately measure angular velocity.


gan transistors in power electronics offer several advantages : higher efficiency due to lower on - resistance and faster switching speeds ; reduced size and weight because of high power density ; and better thermal performance, allowing for smaller heat sinks and overall system size reduction.


a smart grid in power distribution is an electricity network that uses digital technology to monitor and manage the transport of electricity from all generation sources to meet the varying electricity demands of end users. it enhances efficiency, reliability, economics, and sustainability of electricity services.


a silicon photomultiplier ( sipm ) is a highly sensitive semiconductor device designed to detect and amplify light signals. it consists of an array of avalanche photodiodes operated in geiger mode. each photon incident on the device can trigger a measurable avalanche, making sipms extremely sensitive to low light levels.


a dielectric resonator in microwave circuits is used to create resonant circuits with high quality factor ( q - factor ). it employs a dielectric material with low loss at microwave frequencies to confine electromagnetic fields, which is crucial in applications like filters, oscillators, and antennas.


a microwave monolithic integrated circuit ( mmic ) is a type of integrated circuit ( ic ) designed to operate at microwave frequencies ( 300 mhz to 300 ghz ). it integrates active and passive components, like transistors, diodes, resistors, capacitors, on a single semiconductor substrate, commonly used in radar systems, satellite communications, and mobile phone technology.


power line communication ( plc ) is a technology that enables sending data over electrical power lines. it uses the existing power infrastructure to transmit data, eliminating the need for separate data transmission lines. plc is used for applications like smart grid management, home automation, and internet access.


a laser diode in optical communication is significant for its ability to generate coherent light of a narrow spectral width. this allows for high data rate transmission over long distances with minimal signal loss, making laser diodes indispensable in fiber optic communication systems.


a digital signal processor ( dsp ) in audio processing manipulates audio signals to improve quality, add effects, or extract information. it performs operations like filtering, equalization, noise reduction, and compression in real - time, making it essential in audio systems, musical instruments, and communication devices.


a solid - state relay ( ssr ) operates using electronic components without moving parts, unlike mechanical relays. it uses semiconductors, like thyristors, triacs, or mosfets, to switch the circuit. ssrs provide faster switching, longer lifespan, and are more reliable as they are not prone to mechanical failures.


a strain gauge measures mechanical deformation by changing its electrical resistance as it stretches or compresses. when a material deforms, the strain gauge deforms along with it, altering the resistance in a manner proportional to the level of strain, allowing for precise measurement of stress and strain in materials.


an electromagnetic pulse ( emp ) is a burst of electromagnetic radiation that can result from a high - energy explosion or a suddenly fluctuating magnetic field. emp can disrupt or damage electronic systems and data, making it a significant concern in military, communication, and infrastructure security.


carbon nanotube transistors utilize carbon nanotubes'unique electrical properties, offering high electron mobility, mechanical strength, and thermal conductivity. they are used in developing high - speed and energy - efficient electronic devices, including flexible electronics, sensors, and advanced computing systems.


a frequency synthesizer in communication systems generates a range of frequencies from a single fixed timebase or reference frequency. it is essential for tuning to different frequencies in radios, telecommunication networks, and signal generators, allowing for versatile and precise frequency generation.


electrochromic materials in smart windows change their color or opacity when an electrical voltage is applied. this property is used to control the amount of light and heat passing through the window, enhancing energy efficiency and comfort in buildings and vehicles.


a band - stop filter, or notch filter, in electronic circuits is designed to block or attenuate frequencies within a specific range while allowing frequencies outside that range to pass. it's used in applications like noise reduction, suppression of interfering signals, and in audio processing to eliminate unwanted frequencies.


in frequency modulation, a phase - locked loop ( pll ) maintains a constant phase relationship between the output of the loop and the input frequency. it dynamically adjusts to changes in the input frequency, making it ideal for demodulating frequency modulated signals by tracking and locking onto the carrier frequency.


mems mirrors are tiny mirrors controlled by microelectromechanical elements. they can be precisely tilted and moved to reflect light beams in specific directions. these mirrors are used in optical applications like projection systems, fiber optic switches, and in advanced imaging systems for precise beam steering.


a superheterodyne receiver works by converting a higher frequency signal to a lower intermediate frequency ( if ) using a process called heterodyning. it involves mixing the incoming signal with a signal from a local oscillator to produce the if, which is then amplified and processed. this method improves selectivity and sensitivity in radio receivers.


a faraday cage is used for electromagnetic shielding to block external static and non - static electric fields. it is made of conductive materials that distribute charge or radiation around the cage's exterior, protecting whatever is inside from external electromagnetic interference.


a photodiode works on the principle of the photoelectric effect, where it converts light into an electrical current. when photons are absorbed by the photodiode, they generate electron - hole pairs, leading to a flow of current in the external circuit. photodiodes are used for light detection and photometry due to their sensitivity to light.


switched reluctance motors have several advantages : simple and rugged construction, high efficiency, and good torque - to - weight ratio. they are reliable, have a low manufacturing cost, and are capable of operating in high - temperature environments, making them suitable for industrial and automotive applications.


a delta - sigma modulator enhances analog - to - digital conversion by oversampling the analog signal at a much higher rate than the nyquist rate and then using noise shaping to push quantization noise out of the frequency band of interest. this results in high - resolution digital output with improved signal - to - noise ratio.


in electric motor control, a hall effect sensor detects the rotor's position relative to the stator. this information is crucial for precise timing of current flow through the motor windings, ensuring efficient motor operation and control, particularly in brushless dc motors.


a varactor diode in voltage - controlled oscillators ( vcos ) acts as a variable capacitor controlled by voltage. changing the reverse bias voltage changes its capacitance, which in turn adjusts the resonant frequency of the oscillator. this property makes varactor diodes essential in frequency tuning applications.


a piezoelectric sensor in pressure measurement uses the piezoelectric effect, where certain materials generate an electric charge in response to applied mechanical stress. when pressure is applied to the sensor, it produces a voltage proportional to the pressure, enabling precise measurements.


wavelength division multiplexing in fiber optics is a technique where multiple light wavelengths ( colors ) are used to transmit data over the same fiber. each wavelength carries a separate data channel, allowing for increased bandwidth and data capacity over a single optical fiber.


a wheatstone bridge is significant in strain gauge measurements as it precisely measures the small changes in resistance that occur when a strain gauge is deformed. the bridge circuit allows for high sensitivity and accuracy in detecting these changes, which correlate to the strain


a breadboard is a device for constructing a temporary prototype of an electronic circuit and for experimenting with circuit designs. it consists of a grid of holes into which electronic components can be inserted and interconnected with jumper wires, without soldering.


resistors are used in led circuits to limit the amount of current flowing through the led to prevent it from burning out. they ensure that the led operates at the correct voltage and current levels.


solar panels generate electricity by converting sunlight into electrical energy through the photovoltaic effect. when sunlight hits the solar cells, it excites electrons, creating an electric current which is then used as a power source.


a rheostat is a variable resistor used to control current, whereas a potentiometer is a variable resistor used to control voltage. both are used to adjust levels in circuits, but their applications and operational methods differ.


copper wires are commonly used in electrical wiring due to their high electrical conductivity, flexibility, durability, and resistance to corrosion, making them highly efficient for transmitting electrical current.


a multimeter is a versatile instrument used to measure electrical properties such as voltage, current, and resistance. it is an essential tool for diagnosing and troubleshooting electrical circuits and devices.


a rechargeable battery operates on the principle of reversible chemical reactions that allow it to store energy and release it when needed. it can be recharged by applying external electrical power, which reverses the chemical reactions.


a heat sink in a computer's cpu dissipates heat generated by the cpu, maintaining an optimal operating temperature. it prevents overheating which can cause reduced performance or damage.


a basic remote control works by sending a coded signal ( usually infrared ) to a receiver device, which then performs the corresponding action. this allows for wireless operation of devices such as tvs and dvd players.


a diode bridge, also known as a bridge rectifier, converts alternating current ( ac ) into direct current ( dc ). it consists of four diodes arranged in a bridge circuit that efficiently converts the ac input into dc output.


a relay is an electrically operated switch used in electrical circuits. it allows a low - power signal to control a higher - power circuit, providing a means of controlling larger loads with smaller control signals, often used in automation and control applications.


leds ( light emitting diodes ) differ from traditional incandescent bulbs in their operation and efficiency. leds are more energy - efficient, have a longer lifespan, and work by passing current through a semiconductor, whereas incandescent bulbs produce light by heating a filament until it glows.


the basic principles of wireless charging involve the transfer of energy between two objects through electromagnetic fields, typically using inductive or resonant charging methods. it allows for charging of devices without the need for direct electrical connections.


in a camera flash circuit, a capacitor stores electrical energy and then rapidly releases it to produce a bright burst of light. it is used to accumulate charge and discharge it quickly to generate the necessary power for the flash.


a basic thermostat regulates temperature by switching heating or cooling devices on or off to maintain the desired setpoint. it senses the ambient temperature and activates the heating or cooling system to adjust the room temperature accordingly.


in a power supply, an inductor is used to store energy in a magnetic field when current flows through it. it helps in filtering out noise, smoothing the output voltage, and in some designs, aids in converting voltage levels.


solar - powered calculators work by using photovoltaic cells to convert light energy into electrical energy. this energy powers the calculator, eliminating the need for traditional batteries and allowing the device to operate in well - lit conditions.


an analog signal represents information in a continuous form, often resembling a wave, while a digital signal represents information in a discrete or binary form, using a series of ones and zeros. digital signals are typically more resistant to interference and easier to process with modern electronics.


transformers are used in long - distance power transmission to step up the voltage for efficient transmission over power lines, reducing energy loss due to resistance in the wires. at the destination, transformers step down the voltage for safe usage in homes and businesses.


a circuit breaker is a safety device used to protect an electrical circuit from damage caused by excess current or overload. it automatically interrupts the current flow when it detects an overload or fault condition, preventing damage to the circuit and potential fire hazards.


a voltage divider is a simple circuit that turns a large voltage into a smaller one. using just two resistors, it divides the input voltage into smaller voltages based on the ratio of the resistors. this is useful in many applications where specific voltage levels are needed.


an electric kettle uses a thermostat to regulate the water temperature. when the water reaches the boiling point, the thermostat detects the temperature rise and automatically shuts off the power to prevent overheating and save energy.


in a series circuit, components are connected end - to - end, so the same current flows through each component. in a parallel circuit, components are connected across the same voltage source, so each component has the same voltage across it but the current can vary.


surge protectors safeguard electronic devices by detecting excess voltage and diverting the extra current into the grounding wire, thereby preventing it from flowing through the devices and potentially causing damage.


an oscillator in electronic circuits generates a continuous, oscillating electrical signal, usually in the form of a sine wave or square wave. it's used in many devices like clocks, radios, and computers to provide a steady signal.


insulation is important in electrical wiring to prevent accidental contact with the conductive material, thereby reducing the risk of electric shock or short circuits, which can lead to fires or damage to equipment.


a diode allows current to flow in only one direction, effectively preventing backflow. this is crucial in protecting sensitive components in a circuit from potential damage due to reverse current.


leds produce different colors by using various semiconductor materials that determine the color of the light emitted. the specific wavelength of the light, which corresponds to color, is a result of the band gap of the semiconductor material used in the led.


a wind turbine generator operates by converting kinetic energy from wind into mechanical energy. when the wind turns the turbine's blades, it spins a rotor connected to a generator, producing electricity.


a simple thermostat maintains room temperature by turning the heating or cooling system on and off based on the temperature setting. it senses the ambient temperature and activates or deactivates the system to keep the temperature within the set range.


a current limiter in a power supply protects the circuit from excessive current draw. it restricts the amount of current that can flow through the circuit, preventing damage to components and reducing the risk of overheating or electrical fires.


an rc ( resistor - capacitor ) circuit functions as a filter by allowing certain frequencies to pass while blocking others. it can act as a low - pass filter, letting lower frequencies through and attenuating higher frequencies, or as a high - pass filter, doing the opposite.


a thermocouple works on the seebeck effect, where a voltage is generated at the junction of two different metals when exposed to temperature differences. this voltage change is proportional to the temperature change, allowing the thermocouple to measure temperature accurately.


varistors protect circuits from voltage spikes by changing their resistance based on the voltage level. when a spike occurs, the varistor's resistance drops significantly, allowing the excess current to pass through it, away from sensitive components, thus shielding them from damage.


a snubber circuit in power electronics is used to dampen voltage spikes and oscillations, particularly in inductive loads. it absorbs or redirects energy from these spikes, preventing damage to switching components like transistors and thyristors.


a zener diode is used for voltage regulation by maintaining a constant voltage across its terminals within a specified tolerance when the voltage exceeds a certain breakdown threshold. this makes it ideal for protecting circuits by limiting the maximum voltage to a safe level.


a buck converter in power supply circuits steps down voltage efficiently from a higher input voltage to a lower output voltage. it uses a switch, inductor, and capacitor to transfer energy stored in the inductor to the load at a regulated voltage level.


a unijunction transistor has a single junction and three terminals. it works by controlling the flow of current through one of its terminals ( the emitter ) until it reaches a certain peak voltage. beyond this point, the resistance drops, allowing current to flow more freely.


an optoisolator, or optical isolator, is used in circuit design to transfer a signal between different parts of a system while maintaining electrical isolation. this is crucial for protecting sensitive electronics from high voltages and for preventing ground loops.


a charge controller in solar power systems regulates the voltage and current coming from the solar panels to the battery. it prevents overcharging and over - discharging of the battery, thereby enhancing battery life and ensuring efficient operation of the solar power system.


an isolation transformer is used to transfer electrical power from a source of alternating current ( ac ) power to a device while isolating the device from the power source for safety. it provides galvanic isolation, which is important for protecting against electric shock and reducing noise in sensitive devices.


a gfci outlet monitors the amount of current flowing from hot to neutral and quickly switches off the power if it detects a ground fault or a leakage current to ground, such as through a person. this helps to prevent electric shocks and is commonly used in bathrooms and kitchens.


the basic function of an inverter is to convert direct current ( dc ) into alternating current ( ac ). this is useful in applications where ac power is needed but only dc power is available, such as in solar power systems or for running ac devices from a car battery.


capacitive touch screens work by sensing the electrical properties of the human body. when a finger touches the screen, it changes the screen's electrostatic field at that point. sensors detect this change and convert it into a signal that the device can process.


a magnetic circuit breaker operates using an electromagnet. in the event of a high current or short circuit, the magnetic field in the electromagnet strengthens, pulling a lever to open the circuit and stop the current flow, thus protecting against electrical damage.


silver is used in high - end electrical contacts because it has the highest electrical conductivity of all metals. it ensures minimal resistance and efficient conductance in electrical connections, although it's more expensive and less durable than other materials like copper.


a bimetallic strip in a thermostat consists of two different metals bonded together that expand at different rates when heated. the strip bends as the temperature changes, breaking or making an electrical connection, and thereby controlling the activation of heating or cooling systems.