Transient analysis time constant help please

Discussion in 'Math' started by jcb19, Mar 11, 2013.

  1. jcb19

    Thread Starter New Member

    Feb 20, 2013
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    Can someone show me how to derive the time constant in milliseconds from the following equations please:
    v=150e^-15t and i=10e^-15t
     
  2. MrChips

    Moderator

    Oct 2, 2009
    12,449
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    The time constant is defined as t when e^-15t = e^-1
     
  3. WBahn

    Moderator

    Mar 31, 2012
    17,765
    4,801
    Given those equations you can't, because your parameters don't have units.

    It's like asking how fast I am going in mph if the equation for my position is

    x = 75t

    You can't answer it because you haven't been given enough in formation.

    In your equations, what are the units of 't' that go along with your equation? It is likely either in seconds or milliseconds, but it very much makes a difference as to which!

    You also need units on the '150' and the '10', but those are separate from the question of the time constant.
     
  4. thatoneguy

    AAC Fanatic!

    Feb 19, 2009
    6,357
    718
    I understand the need for units, but this is the "normal" way questions are stated.

    Unless otherwise stated, V is volts, I is Amperes, t is time in seconds, unless all the books I have on the topic are also leaving out units.

    Once the details get beyond the basic level, where units aren't implicit/standard, then carrying the units with the numbers makes sense.

    Example would be Ohm's law: V=IR

    No units required as it is self explanatory at that level. Once non base numbers are used, such as mA and mV, they need to be included.
     
  5. WBahn

    Moderator

    Mar 31, 2012
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    I disagree, regardless of how many textbook authors disregard units. And I fully admit that many of them do, with math books being by far the worst offenders. Then again, many textbook authors have never worked outside of acadamia and ignoring units, in their world, might cost someone a few points on an assignment.

    But, then again, I am a self-confessed and completely unapologetic units nazi.

    Taking the Ohm's Law example, I will always maintain that it is wrong to say something like

    V=10*3=30

    Even if you tack a V onto the final answer.

    Aside from the risk associated with assuming that anyone reading it is going to implicitly apply the same units that the person that wrote it assumed, it leads to sloppiness of thought that is insidious and can be downright deadly.

    The majority of mistakes that people make when working a problem (and we all make them and we will all continue to make them) affect the units. If the units are religiously applied and tracked throughout the work from start to end, then those mistakes get caught, usually very early on when the cost of tracking them down and fixing them is small. But if people just use the numbers only because the units are implied, then those mistakes frequently don't get caught until "bad things" happen.

    But if you develop the habit of always tracking your units and always asking if the answer makes sense, then you make far fewer mistakes to begin with and a huge fraction of the mistakes you do make get caught almost immediately. One example of the mindset that gets established is the engrained realization that arguments to transcendental functions, such as sin(), log() and exp(), absolutely must be dimensionless. So you immediately redflag situations in which sloppiness at some point resulted in something like sin(x) or e^t and you resolve it. Or when a scaling constant has been overlooked or dropped along the way. You also get tripped up a lot less frequently because of sloppiness associated with radian frequency and cyclical frequency because they don't have the same units and therefore if one is used when the other should have been it causes a units fault that gets resolved instead of overlooked.

    In many countries if a surgeon were to be sloppy and not take simple, proven precautions such as counting all of the gauze pads (and everything else) before suturing to ensure that nothing got left in the patient and the patient died or suffered a severe injury as a result, the doctor (and probably several others up the line) would be facing serious malpractice charges and possibly even charges for criminal negligence. What's more, few people would argue that such charges weren't warranted because, after all, a surgeon that can't be bothered to observe the most basic and simple procedures to ensure their patient's safety can kill someone and shouldn't be practicing.

    Well, I feel the same way about engineers that can't be bothered to follow what is arguably the most powerful error detection and correction process available to them, especially when doing so costs nothing. I don't believe they should be practicing engineering and if someone dies or is severely injured as a result of them not tracking their units (and many, many people have died as a result of this) then they should face criminal negligence charges.

    People will hold a surgeon to a high expectation in terms of their diligence because, if they make a mistake, someone could die. Well, a surgeon is generally limited to killing people one at a time while engineers kill people in job lots.

    The sad thing is that instilling that engrained, automatic use of units is surprisingly easy to achieve. I had a class about ten years ago that really faught against my units policy (and a couple of other policies, including my awarding of negative points for the employment of magical methods). They complained enough to other instructors that the dean got wind of it and found out that a handful of students were trying to get a petition up to have me removed as the instructor, so he asked to have some time to talk to the class. This was about midway through the semester. After talking to them he was going over their grievances with me and said that things had calmed down and no one wanted any action taken anymore. He explained how the students really resented me taking off points for not tracking units early in the semester but that it was okay now because I wasn't doing that any more. I actually laughed out loud. Not only was I still taking off points for not tracking units, but the penalties were triple what they had been at the beginning. But it was true that I wasn't taking off points any more -- because the students were tracking their units properly! And, making far fewer mistakes and getting much better homework grades. Yet, surprisingly, they didn't even realize that they were -- they thought I had changed and softened when, in actuality, they had changed and risen to the expectations that had been set for them. I ended up with an extremely strong reporte with that group of students and several of them (including the three that had tried to start the petition) stayed in touch with me for several years after they graduated and many of them (self-selected, to be sure) made a point of telling me that the single most valuable thing they walked away from that class with was the habit of tracking their units.

    I also ended up with the Part Time Instructor of the Year Award for the College, which just shows that it can pay to **** off your students! :D
     
    Last edited: Mar 13, 2013
  6. MrChips

    Moderator

    Oct 2, 2009
    12,449
    3,364
    The first story of confused units that comes to mind is this one about the emergency landing of Air Canada flight 147, a Boeing 767 which ran out of fuel near Gimli, Manitoba. Ground crew miscalculated the amount of fuel because they used the wrong units. Some interesting coincidences allowed the plane to land safely on an unused airstrip. The pilot was an experienced glider pilot and was familiar with the airstrip at Gimli.

    http://www.cbc.ca/archives/categori...o-metric/gimli-glider-lands-without-fuel.html
     
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