Series parallel capactitive circuit

[gneill]

So the question says that it has reached its final value, does it mean that it is at 5 time constant?

The number of time constants does not matter if enough time is allowed to pass. Assume that 10¹⁰⁰time constants have passed...

 

[freshbox]

Do you mean that it can happen at any time? Why does it not matter? Is it because this circuit has 2 type of device?

Thanks.

 

[gneill]

Do you mean that it can happen at any time? Why does it not matter? Is it because this circuit has 2 type of device?

The problem statement says to assume that the currents and voltages have reached their final values. There are no constraints placed on how long you are allowed to wait to ensure that this happens. So just assume that enough time has passed regardless of how long it might be (and you do not care about the specific amount of time!); once a circuit reaches steady state it will no longer change no matter how much more time passes.

Any DC circuit that contains resistance will eventually reach steady state because the energy driving any transients must eventually by dissipated by Ohmic losses. This is true even for RLC circuits containing both L and C components, even if the time constants involved may be tricky to work out. No matter how long it might take for 'ringing' or 'oscillations' to damp out, they must eventually damp out as resistance bleeds away their power, so one just assumes that a sufficiently long time has been allowed for this to occur.

You don't need to know precisely how long this process takes; just assume it has been long enough and the circuit is at steady state.