How do you determine the effective value of exponential quantities?
How can you calculate the RMS value of an exponential quantity? For example, acoustic or electrical signals such as capacitor discharges, crackling sounds, damped sine waves, etc.? Are there simple formulas for this? I read a description somewhere about calculating the RMS value of an e-function. However, there's practically nothing about this on the internet.
Perhaps the presentation from my old teaching concept will help you a little further.
My full-time teaching concept electrodynamics (for LK physics) can be found under https://www.dropbox.com/sh/x56zbd1s9h9s199/AACTraaBO6hPukv2PMkjFB-_a?dl=0
I don’t know if that’s enough for you.
I already know. That’s easy.
Somehow you have to do something with the area under the curve, but how? It is necessary to say, in a simple way, to pour the bent area into a straight shape, parallel to time.
It is about a work on the risk of electrical impact due to electrostatic discharges. I have understood this in such a way that one does not, as I would have done, calculate the discharge until one has reached a harmless current (I < 20 mA DC), but that in principle one calculates only with three Tau, or up to 500 mA. The whole thing I find is a bit worn out and doesn't cover with my experience. Because I have already experienced strong shocks (starting muscle cramping) with less than 10 mJ, but on the other hand I already get several hundred millijoules without being noticeable as muscle irritation. I guess that depends on the fact that the body reacts very differently at different frequencies. Very short pulses with relatively high currents therefore probably act less dramatic than longer pulses with smaller currents, as long as no thermal damage occurs.
However, there is no frequency or flow time at which no muscle or nerve irritation can occur at all. A weak irritation is always present. Considering that the already stop at 500 mA or 3 T, the m.E. is going to pass very much on the reality, because the actual muscle irritation may only get really started when you arrive in the later area of the exponential current curve.
I have always worked with the new models so far that the pulse duration is from Î to I < 20 mA and not up to 5 % of Î, because this can be a few more amperes left there.
In addition, you get smaller effective values with x arbitrary exchange, which then deviate too much from reality.
The damage caused by a current impact is also very dependent on the path the current could take. In the case of current passages through the brain I do not know any reports (apart from execution cells). During the passage of current through the center of the body (heart), the duration seems to be essential. In particular, alternating voltages are considered particularly dangerous in this respect because they can trigger cardiac chamber flimmers. The current intensity seems to be rather minor in this respect. Mostly, the skin resistance should be so large that only a very small part of the total current strength passes through the body center. A large part of the current is likely to take the path over the slightly moist skin. In the case of large currents, this can lead to burns. This corresponds to the experiences of people who have been hit by the flash and have survived this.
Here is the diagram: https://ibb.co/RTTfC1n
Well. Most of the current flows more at the edge of the body that’s right. Finally, it also spreads and then flows preferably over peripheral nerves. Both time and power are important. All in all, however, this applies especially to AC from 10 ms. What’s happening below, i.e. in pulse discharges, is less researched.