Talk:Time constant

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Untitled[edit]

Moved initial content to RC time constant because it was too specific. Added temporary redirect but eventually the time constant of a first-order linear system should be discussed here.

Time constant in a two-phase asynchronous motor model[edit]

J = moment of inertia
f = rotational friction coefficient

Two stator coils with each nst sinusoidal distributed windings
Two rotor coils with each nrot sinusoidal distributed windings
The angle between the coils is 90 degrees.
Two voltage sources applied on the stator, the angle between the voltages is 90 degrees.
Ust = effective value of each stator voltage
fst = stator frequency
ωst = 2πfst = angular stator frequency

Two external rotor resistances, each Rrot

Time constant = J/(f+2(Ust/ωst)^2/Rrot')
with Rrot'= Rrot(nst/nrot)^2
Starting from zero the motor speed remains constant after a time 5*(time constant).

Martin Segers (talk) 08:20, 5 January 2008 (UTC)[reply]

Thermal transfer section[edit]

Please, include the corresponding units.
Please, correct references as to allow all users to acces them.
Please, include the permafrost reference.

The time constant for heat applied at the surface of an insulating body with thermal diffusivity κ to penetrate a distance L can be expressed thus:

\tau \ =\ L^{2}/\kappa

This equation can be used to determine, for example, the thickness of the active permafrost layer (where κ ~ 10^-6), or how long it takes to boil an egg.^[1]^[2]

Time constant in electrophysiology[edit]

I believe that the statement that the exponential functions describe the rise and fall of the action potential is false. I was under the impression that those particular expressions describe only the response of an ideal specially uniform cell without any voltage gated ion channels to a current injection. For a reference take a look at Purves et al. Chapter three Box C --Dylan2106 (talk) 23:45, 18 March 2008 (UTC)[reply]

The passive membrane properties of a cell are modeled by a simple RC circuit, hence why tau = RC--Dylan2106 (talk) 23:47, 18 March 2008 (UTC)[reply]

Ha, that reference is available online --Dylan2106 (talk) 23:49, 18 March 2008 (UTC)[reply]

You're correct. Almost every statement in that section of the page is incorrect. Action potentials have nothing to do with the time constant. Also tau = R_i C_m only applies to passive cells, as you correctly stated. Short of rewriting the section, it would almost be better to outright delete it given the inaccuracy. 155.41.24.252 (talk) 17:10, 7 December 2010 (UTC)[reply]

Differential equation[edit]

Hello, I'm doubting whether the statement of the differential equation as written in the article

${\frac {dV}{dt}}+{\frac {1}{\tau }}V=f(t)$

is correct. Should this not be

$\tau {\frac {dV}{dt}}+V=f(t)$

or in other words

${\frac {dV}{dt}}={\frac {1}{\tau }}(f(t)-V)$

I'm not sure that the differential equation as written in the article (the first one listed above) integrates to the correct solution. — Preceding unsigned comment added by 2620:0:1000:7200:4419:426B:1992:A8BF (talk) 00:31, 10 December 2014 (UTC)[reply]

No it does not. The solution is wrong. Indeed the steady state solution reported in the article itself is wrong. To check it just take the equation

$V_{\infty }(t)=A{\frac {e^{j\omega t}}{j\omega +1/\tau }}.$

and evaluate it with $A=1,\omega =0$ . The response to a constant unitary input must be equal to 1. Instead, this equation returns $\tau$ . This is off by exactly $1/\tau$ . QED

^ See Equation 18, Roura, P. (2000). "How long does it take to boil an egg? A simple approach to the energy transfer equation" (PDF). Eur. J. Phys. 21: 95–100. Retrieved 2007-05-26. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
^ Buay, D. (2006). "How long does it take to boil an egg? Revisited" (PDF). EUROPEAN JOURNAL OF PHYSICS. 27 (1): 119. Retrieved 2007-05-26. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

[Roura2000-1] See Equation 18, Roura, P. (2000). "How long does it take to boil an egg? A simple approach to the energy transfer equation" (PDF). Eur. J. Phys. 21: 95–100. Retrieved 2007-05-26. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

[Buay2006-2] Buay, D. (2006). "How long does it take to boil an egg? Revisited" (PDF). EUROPEAN JOURNAL OF PHYSICS. 27 (1): 119. Retrieved 2007-05-26. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

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