# When does an RC Transient period end?

I have struggled with this question and read many articles and watched youtube videos but to no avail. For this circuit the time constant or "Tau" is 80 micro Farads (or$$80*10^-6$$)

My issue lies with questions b and c, as I thought the transient period is infinite, I cannot figure out when it ends . I am using the universal time constant formula $$(Final - Start) * (1-(1/e(^T/t))$$

lower case t being 80 x10 ^ -6. however what is meant to be my value for T ? I imagine this would allow me to solve b and c.

Very sorry to post a question like this however I have been trying to solve it for hours.

• I bet your textbook mentions a handful tau when the circuit can be considered stable. No need to consider infinity for that. Also I would expect to see tau in your universal time constant formula. – jippie Jan 9 '16 at 10:27
• I read somewhere that 4 time constants is considered fully charged, would this be correct? in that case the denominator for the power of e would be 80x10-6, and its numerator would be 320x10-6 ? this is for an important exam so i need to know a definite value for when the transient period ends – Aztec warrior Jan 9 '16 at 10:38
• Resistance times capacitance is time, i.e. 80us, not 80uF. – Ignacio Vazquez-Abrams Jan 9 '16 at 10:40
• Order magnitude is correct, but I haven't seen 4 being mentioned in my textbooks. Is this really the first exercise you see on this subject before your exam? I would file a complaint with the institute. – jippie Jan 9 '16 at 10:41
• I thought it was 5$\tau$ that it breached 99%. – Ignacio Vazquez-Abrams Jan 9 '16 at 10:42

When does an RC Transient period end?

Never. Its effects do diminish over time, so at some point the effect of the transient isn't relevant anymore. For example, if the circuit settled to within 95% of its new value is good enough to consider the transient as "ended", then it takes 3 time constants. If it needs to settle to 99% of its final level, then you have to wait 4.6 time constants. For 99.9%, it's 6.9 time constants.

For this circuit the time constant or "Tau" is 80 micro Farads

No! The time constant has units of time. Note that you multiplied Farads and Ohms to get it. Since Ohms are not dimensionless, it should be obvious that the resulting product can't be in units of Farads.

or 80∗10−6

Again, No, the time constant is not dimensionless either. Also, it seems you meant to say 10-6 in place of "10-6".

Welcome to StackExchange, @Calculon, and it's a good first post as you have shown all the details and your work. The exam question is poorly worded.

Usual 'rule of thumb' values for RC time constants is that at $\tau$ voltage will have changed to 63% of difference between initial and final value (0 to 10 V in your question), at $3\tau$ it will be 95% and at $5\tau$ it will be 99%.

If faced with the exam problem I would explain it like that, point out that I don't understand the question but am going to assume that the question means, for example, $3\tau$ and work from there.

One answer is that the transient never ends, an exponential response goes on until infinity.

That's fine in mathematical theory, but in engineering practice, you can argue for definite end points. The response goes on until there are no significant changes, where 'significant' is defined by the user of the system.

In a capacitor charging question, the end point may be arbitrarily set at 99%, or 95%.

In a signal measurement question, settled to within the inherent noise of the circuit would be a pretty bomb-proof assumption.

Five RC (<1% error) is a very common figure that comes up, when nobody can be bothered to think carefully about how relevant the end point error is.

• +1 For mentioning that in real circuits the "theoretical" end of the transient is when the signal is indistinguishable from the noise in the circuit. – Lorenzo Donati -- Codidact.org Jan 9 '16 at 17:03