# Transient analysis time constant help please

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

1. ### jcb19 Thread Starter New Member

Feb 20, 2013
14
0
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
12,652
3,460
The time constant is defined as t when e^-15t = e^-1

3. ### WBahn Moderator

Mar 31, 2012
18,093
4,918
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
18,093
4,918
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.