Wikipedia:Reference desk/Archives/Science/2013 June 20

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June 20

Use of multiple transformers as a power bank

I'm wondering if and how it is possible to align multiple small transformers in series and parallel configuration (just as with batteries) to gain a higher output in amps and voltage without burning them out, starting with the weakest point. Would I need "flowback preventers" (don't remember the proper name but you sure know what I mean) [add: I guess I'm talking about a "foldback" or similar protection] on each transformer? Battery banks can not be compared to my intentioned "transformer bank", I know. That's why I'm asking for some professional input on how to achieve a working "transformer bank". Note: Transformers would have each an output of between 6 to 20 volts, with different output in amps of course. Note: a simple and cheap solution is preferred; Not that I'm cheap and simple myself but... :). Thanks.TMCk (talk) 03:01, 20 June 2013 (UTC)

You can do that but there's no point in doing it compared to having a bigger transformer with thicker wires. Batteries are put in series because the chemical process only generates a certain voltage and they are put in parallel because the manufacturers only produce certain sizes and the customers need to replace them. Neither of those is true for transformers. Dmcq (talk) 10:56, 20 June 2013 (UTC)

Actually, there *IS* a point to doing it and you'll occasionally see it done in practical circuits. Multiple physically-small transformers may fit into a space where a single large transformer won't because of "form factor" constraints. I have an inverter that uses four small high-frequency transformers operating together. Atlant (talk) 23:36, 20 June 2013 (UTC)

Are you talking about "naked" Transformers (i.e. AC) or a bunch of power bricks/PC power supplies (i.e. DC)? At any rate, yes, for transformers you would need some Rectifiers and Voltage_regulators. Most DC PSUs have some sort of Voltage_regulator built in. This can be very simple or quite complex as in an ATX power supply. In practice, these voltage correction circuits "fight" each other when a load is placed on the circuit. For example, if you needed a 600W PSU for your PC you could theoretically use 2x 350W PSUs. This is not a good idea for many reasons and is quite complicated to get right. See here: http://www.tomshardware.com/forum/298250-28-identical-power-supplies Just sell all the small ones on eBay and buy a big-ass one.196.214.78.114 (talk) 12:02, 20 June 2013 (UTC)

Sorry yes I'd read it as just straightforward transformers not switched mode power supplies which are another category of beast altogether and are more common nowadays. I wouldn't want to start sticking those together without a great deal of study, I think blue smoke if not a fire is altogether likely otherwise. Dmcq (talk) 16:20, 20 June 2013 (UTC)

Certainly transformers can be combined in series or in parallel, but if it is done haphazardly, some may be exposed to excess voltage or may have excess current drawn from them resulting in insulation failure or overloading, and the resulting in smoke, fire, and sparks. The transformer impedances must be considered, if they are not identical transformers, since a lower impedance transformer in parallel with a higher impedance one will "hog the load." The designer should make sure that there is adequate protection by means of fuses or circuit breakers for any condition where transformers or leads fail shorted or open. Many more things could go wrong with interconnected small transformers than with adequately large single transformers. Edison (talk) 19:17, 20 June 2013 (UTC)

• Thanks to all of you for your answers. A few comments in response:
  - Yes, Dmcq, I was thinking/talking about standard transformers that convert (120) AC current to DC. fluctuations in voltage are of no concern as they would be used to power non-sensitive equipment such as a low DC voltage but high amp power drill I.E., so the power source would be supervised at all times when in use besides being enclosed in a fireproof housing and protected by fuses for each single unit and a main fuse for the whole package. I might want to include a PC power supply I have laying around but most likely separated and to provide only power to a cooling fan for the unit.
  - The main question for me is (and Edison touched that issue in his comment), Is it certain that the smaller transformers will "hog the load" and shorten out and if so, is there some protection other than a fuse that would disconnect the weak point as it would render the whole unit useless? Is there some simple component that would limit the amps drawn from a single transformer?
  - Regarding rectifiers that I only know as converting AC to DC current: If I understood it correctly, it would also prevent backflow from higher rated units to lower ones. Is that a correct assumption?
  - BTW, Edison, I don't intend to do it the "haphazardly" way; That's why I'm educating myself by asking the experts here, experts like you ;)
  - Atlant, could you tell me in more detail about this "inverter that uses four small high-frequency transformers operating together?" I'd be truly appreciated :)
  To sum it up, the point of the whole thing is to use all those abandoned power supplies I have laying around and put them to some good use.
  Again, much appreciated for your input so far... and greedy as I am when it comes to knowledge, I'm still hoping for more :)) TMCk (talk) 01:28, 21 June 2013 (UTC)

Radioactive decay energy distribution

When a radioactive substance decays. Most decays ought to be within a quite narrow set of decay energies. But given the stochastic nature some decays ought to deviate from what the Poisson distribution implies. So that if 99.9999% of the energy is of circa 40 keV, then perhaps some very rare decays are 800 keV ..? Electron9 (talk) 06:42, 20 June 2013 (UTC)

Do you have a question? 139.193.214.10 (talk) 10:29, 20 June 2013 (UTC)

Where do you suppose the extra energy is coming from? Energy is conserved, you know that right? Dauto (talk) 12:12, 20 June 2013 (UTC)

Not so fast. Radioactive decays, like other quantummechanical transitions have a finite natural linewidth. In fact, the decay energies should follow a Breit-Wigner distribution which extends to arbitrarily large energies. This implies that the 800 keV that Electron9 mentions are indeed possible, although very rare. This does not violate conservation of energy because of the uncertainty principle. --Wrongfilter (talk) 13:04, 20 June 2013 (UTC)

"Stochastic nature" refers to the time of the decay, not the energy. The actual decay energy most generally (even for high-energy phenomena like the decay of a Z boson) follows a relativistic Breit–Wigner distribution and e.g. the alpha particle kinetic energy and nucleus kinetic energy can be computed from conservation of momentum. The decay width is equal to ${\frac {\hbar }{\tau }}$, where $\hbar$ is the reduced Planck constant and $\tau$ is the mean lifetime of the radioactive parent nucleus; this mean lifetime has a simple relation to the the half-life, $\tau ={\frac {\tau _{1/2}}{log(2)}}$. Notice that the widths are often very narrow, e.g. for ²²⁶Ra with a half-life of 1601 years it's about $9\cdot 10^{-27}$ eV.

Apart from that, there are often several different decay energies, leading to a daughter nucleus in different energy states. Usually the daughter nucleus subsequently decays to its ground state by emission of gamma radiation.

Icek (talk) 13:11, 20 June 2013 (UTC)

The relativistic Breit–Wigner distribution is only relevant for resonances which happen when the particle's mass times its lifetime is of the order of Planck's constant or smaller. I don't mean to say that it would be wrong to use the Breit–Wigner distribution for long lived nuclei, but it's unnecessary. Due to the very sharp distributions obtained in those cases, you can simply replace the Breit–Wigner distribution with a Dirac's delta distribution. Dauto (talk) 13:56, 20 June 2013 (UTC)

So how does one calculate the probability that an energy above a certain level will occur?, ie how long time before an > 800 keV for substance x happens? or at least do an estimate if it's really complicated maths. Electron9 (talk) 14:29, 20 June 2013 (UTC)

The correct way to find this probabilities IS to use the Breit–Wigner distribution. My point is that for a long lived nuclei - say with life time longer than plank's constant divided by the decay energy, that probability can be safely set to zero. For example, if the decay energy is 40 keV, Than hbar/E = 6.6*10^(-16)/4*10^4=1.6*10^(-20) seconds. If the lifetime of the nuclei is much longer than 10^(-20) seconds, than the probability of a decay with an energy much different from the 40 keV becomes negligible. Dauto (talk) 14:54, 20 June 2013 (UTC)

How improbable is negligible? there's usually a lot of atoms around such that even low probability events occur. Let's say, how long time does it take for a substance of n mol of U-235 atoms to generate say 10 gamma photons with an energy of more than 800 keV ..? Electron9 (talk) 15:52, 20 June 2013 (UTC)

To answer that question, you must first re-derive the energy distribution to take into account the fact the system undergoes decoherence during it's lifetime. So, in the derivation of the Breit-Wigner distribution, it is assumed that you can describe the system as a superposition of the unstable particle and its decay products. That it will eventually interact with the environment is something that happens on a much longer timescale than the time scale for decay. In the case of an unstable long lived nucleus, the opposite is true, so you need to take that into account. What is clear is that the probability of having a decay with a significant different energy is exactly zero, and not just very small, because the mass of the unstable nucleus becomes well defined enough to eliminate that possibility entirely. Count Iblis (talk) 16:08, 20 June 2013 (UTC)

Below energies and above mean lifetimes for which the Breit-Wigner distribution is absolutely needed, one can use a Cauchy distribution (also known as Lorentz distribution).

Anyway, Count Iblis is correct in saying that for any practical measurements of long-lived isotopes, the measurement process introduces far more noise than the decay width. Analogous to Heisenberg's uncertainty principle there is a time-energy uncertainty; so one would definitely need longer than 1600 years in order to actually measure the decay width of ²²⁶Ra.

But if one would measure with a long enough time of observation, and sufficiently sensitive instruments, then I can give you a simple formula for the probability of the decay energy being higher than some energy E₁:

${\frac {\Gamma }{2\pi (E_{1}-E_{0})}}$

$\Gamma$ is the decay width ($9\cdot 10^{-27}$ eV in the example I posted above) and $E_{0}$ is the decay energy (40 keV in your example). The formula is only valid as long as the energy difference is much larger than the decay width.

Icek (talk) 18:16, 20 June 2013 (UTC)

Neglecting for a moment that, as Count Iblis correctly pointed out, that probability really is zero, and assuming you are talking about perfectly isolated atoms so that coherence could be preserved, plugging in the data for U-235 in Icek's formula, the answer to the OP's question is that 1 in 3.7*10^37. That's about 6*10^13 moles of U-235 or 1.45 * 10^13 kg of U-235 or 1.45* 10^7 kilotonnes of U-235. That's about 3000 times the size of the world supply of U-235. (Or may be I'm confusing the supply of U-235 with the supply of Uranium in general in which case multiply by another factor of 140). In any case, it's clearly that the only sensible answer to the OP's question is "Not a snow ball's chance in hell". Dauto (talk) 21:51, 20 June 2013 (UTC)

I'm talking of a solid block of some decaying material, say 1 cm³ and if it's possible to use the emission of low probability, high energy photons, neutrons etc to detect such substance. The high energy would make detection through other materials and distance possible. Electron9 (talk) 23:22, 20 June 2013 (UTC)

Count Iblis and Dauto are not correct in claiming that the probability is really zero: Not with respect to the situation when one really has a sufficiently long observation time; and even less when talking about measuring within shorter times and possibly with some other interactions (because these things broaden the decay width). Even less so when one thinks about physics more generally: We don't know everything, and there could be some rare decay (e.g. proton decay) that results in the emission of the right particle at the right energy.

Electron9, it is in principle possible to do it with e.g. gamma rays (high energy photons) emitted from a solid block, and you can just plug the data for your particular isotope into the formula. But for anything but very short-lived isotopes it's pretty hopeless to really measure it, and it's difficult to produce solid blocks of 1 cm³ of very short-lived isotopes. And needless to say you have to care about a lot of other things like contaminants (other radioactive isotopes) in your block and broadening of the decay width by e.g. Compton scattering.

Icek (talk) 10:59, 21 June 2013 (UTC)

I agree that saying that something is "exactly" zero is shady. But the probability for what the OP is asking for is so incredibly small that for any practical purpose imaginable it can be effectively considered to be exactly zero. Dauto (talk) 14:08, 21 June 2013 (UTC)

It seems to me an artifact of pretending that one cannot identify the initial state of the system accurately enough for the decay with large energies of the decay propducts to be possible (in principle) at all. If you take this serious, then the effect is due to not having the initial nucleus in the state you thought you had. But nothing would stop one from preparing the correct initial state (within the available time limits) which then cannot decay with the decay products having such high energies. Count Iblis (talk) 14:31, 21 June 2013 (UTC)

Mailing list regarding Rodentia

Hello, could you please point me out a mailing list regarding Rodentia? --194.95.30.128 (talk) 10:59, 20 June 2013 (UTC)

Have you tried using Google? A quick search turned up some results... — Preceding unsigned comment added by 217.158.236.14 (talk) 11:24, 20 June 2013 (UTC)

What aspects of rodents in particular are you interested in - e.g. their physiology, their ecology, keeping them as pets or eradicating them as pests? This may help us narrow our replies. Equisetum (talk | contributions) 11:27, 20 June 2013 (UTC)

Here is a listserv for pet rats, hosted by Yahoo [1]. Using the key word "listserv" gives decent google results for many similar topics. SemanticMantis (talk) 12:39, 20 June 2013 (UTC)

Thanks everybody for the help. I already made some Google search, but I did not find anything useful. I am searching for a list focused on Rodentia on a mere biological basis (not for pest control or for pet keeping, sorry for giving this for granted). The main aspects I am interested in are taxonomy and ecology. Using Using "listserv" as a keyword improves the quality of Google results (still I need to find a suitable one, but I will keep searching). --194.95.30.128 (talk) 17:37, 20 June 2013 (UTC)

Here's a nice list of bio/eco lists [2]. There is one for shrews, and one for animal behavior, but not one for all things rodent. You could also join the very popular list ECOLOG, and ask there for good rodent science lists. Another key phrase for searches would be "small mammal ecology." SemanticMantis (talk) 18:43, 20 June 2013 (UTC)

Thanks for the hints. I am considering subscribing to ECOLOG, but first I will try to refine my Google searches, also on the basis of your indications. Strange anyway, I would have expected to find such a list much more easily! --194.95.30.128 (talk) 11:56, 21 June 2013 (UTC)