stuck on exam question

me2gud4u

please, could anyone help me with this question.

what is the significance of the time constant of an RC circuit.


how would you answer this?
thanks.

Michael Collins

It gives a figure for how long transient behavoir will be present (about 4 time constants and the circuit will have effectively reached "steady state" - i.e. no more changing voltages or currents). You can also calculate from the time contant what corner frequency of an RC filter is.

fishdog

about 4 time constants and the circuit will have effectively reached "steady state" - i.e. no more changing voltages or currents).

It takes 5 time constants to reach its steady state value (well 98%).

The first time constant it will reach 63.2% of its final value. If you were to plot the voltage across the capacitor against time as it charges the plot would be an exponential growth curve. When discharging it would be an exponential decay curve. If you were to multiply the resistance by the capacitance the answer would give you time constant in seconds.

You can also calculate from the time contant what corner frequency of an RC filter is.

I think you mean the "cut off frequency"

The cut off frequency = 1/ (2 x Pi x time constant) Hz

Michael Collins

fishdog wrote: »

It takes 5 time constants to reach its steady state value (well 98%).

After a period of 4 time constants the voltage on the capacitor in a series RC circuit will have reached



times its final value. Which comes out to 3 significant digits as 0.982 times the final voltage. Granted 5 time constants will be closer to the final value, but not much really at 0.993.

It all depends on your application how accurate you need it to be. I mean, in theory, it will never reach it's steady state value - but in practise with noise and everything else you can take it to be after 4 or 5 time constants.

I think you mean the "cut off frequency"

The cut off frequency = 1/ (2 x Pi x time constant) Hz

Nope, corner frequency is what I meant . It is another term for cut-off frequency so it means the same thing, however since the actual output power isn't really "cut-off" only reduced by 3 dB at that frequency, I prefer corner frequency i.e. where the response can be considered to start rolling off.

fishdog

After a period of 4 time constants the voltage on the capacitor in a series RC circuit will have reached

1- e^-4

times its final value. Which comes out to 3 significant digits as 0.982 times the final voltage.

I checked this and I have to admit you are correct!!:o I did not expect 4 time constants to get as close as that (98%)to the staedy state value. I should know this stuff because I am studying this stuff at the moment :eek: So I did a bit more reasearch (I have an exam on this stuff very soon!). Here is what I found:

5 time constants will get you to within 99.32% of steady state value (as I am sure you know). I realise that even at 100 time constants it will never reach 100%.

Admittedly 5 time constants is only slightly more (1.15%), but this is generally accepted as the steady state value. Source: Electrical Circuit Theory and Technology - John Bird

Nope, corner frequency is what I meant . It is another term for cut-off frequency so it means the same thing, however since the actual output power isn't really "cut-off" only reduced by 3 dB at that frequency, I prefer corner frequency i.e. where the response can be considered to start rolling off.

I never heard of the term, but I am sure you are correct. It may help me now that I know it so thanks!!:)