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Spikeman197
1 year ago

There’s a s to cut the unity of time out. A unit in the exponent, or for example a logarithm, has no meaning.

Lutz28213
1 year ago
Reply to  Spikeman197

That’s wrong! This is the time constant – in this case T=5 seconds

Spikeman197
1 year ago
Reply to  Lutz28213

Aha…and what is e^(-5 s)?

isohypse
1 year ago

that’s second (s)

Lutz28213
1 year ago
Reply to  isohypse

Wrong (see my contribution)

isohypse
1 year ago
Reply to  Lutz28213

see my answer to your contribution.

Doktorelektrik
1 year ago

To your unit question:

  • Is the function e high (-…..) dimensionless?

or otherwise asked:

  • What is that supposed to be if there was a physical unit in the exponent?

e high Bratkartoffeln = 0.4 times e high Pommes?

Auxiliary question: The exponent counter has a time in seconds. What unit does the name of the exponent have?

Do not let physical equations take you off the path of mathematics you know.

Good luck!

Lutz28213
1 year ago

The exponent must be dimensionless.

This means that there must also be a time in the denominator – here: 5 seconds. In general, the e-function is e^(t/T) ,

Because there is in the counter 2t. is equivalent to e^(t/0.5*5).
The time constant is therefore T=2.5 seconds

isohypse
1 year ago
Reply to  Lutz28213

I don’t see it like this: it’s exp(-2t/s). This notation is quite common (I do not like it) when you calculate with numbers that also have one unit. Here is the time constant τ=0.5s. This would first write as

exp(-t/τ)=exp(-t/0.5)=exp(-2t).

Only that is not true when you look at the unit t has unit seconds (s). That’s why you have to divide t through s, or what is here you could write as well

exp(-t/τ)=exp(-t/0.5s)=exp(-2t/s)

As I said, this is quite common. The fact that the time constant cannot be 2.5s can be seen in the picture at the time: there is τ=0.5s:

https://www.wolframalpha.com/input?i=plot+y+%3D+0.5*+exp%28-2t+%29+%2C+t%3D0..2.5%2C+y%3D0.0.5

Lutz28213
1 year ago
Reply to  isohypse

OK – I didn’t pay attention to the picture; I guess that’s half a second.
ABER: The spelling for the given function is VERY unusual, so a misunderstanding – especially because the “s” in the picture can really be a “5” – can certainly happen. In particular, the mixed way of specifying the dimension in the function: at the voltage in brackets and at the time suddenly as a denominator.

Spikeman197
1 year ago
Reply to  isohypse

That’s it!

Spikeman197
1 year ago
Reply to  Lutz28213

This throws a sparkling light on the University of Bremen 🤪

SevenOfNein
1 year ago

Actually, I only know this as tau = R*C. The so-called time constant.