Dear friends,
In the circuit below, I would like to find its time constant by trying to convert that circuit into an equivalent one that contains a voltage source, one resistor and one capacitor. Could you please give me some clues as to how to proceed? thank you!
Hi,
I believe this is an aberration of some more simple question that was to be asked within a known framework of assumptions that were meant to be taken for granted as being part of the total problem.
To make a long story short, you cant really answer this question because it is ill posed. There's no time constant for a voltage source in parallel with either one capacitor or any number of capacitors connected in series regardless of any resistors in parallel with them. That's because the time to charge one or two in series with a voltage source is zero, and also to charge one or two in zero time takes an infinite current, which is not practical. So theoretically you'd have to place some series resistance in series with something like the voltage source for example.
So the circuit is not theoretically sound to begin with for a DC source, and for an AC source it would have to start up at exactly zero volts and with an AC source that starts at 0v the time constant would be meaningless anyway. The phase shift would then be of interest.
Circuit simulators will either give incorrect results varied by how they handle voltages with capacitors and min series resistances, and some will actually reject this circuit outright and post an error about connecting voltage source and capacitors directly together without even attempting to provide any calculation points.
So the first thing we would need here is clarification of what exactly they are looking for here. It is probably that they intended to solve the circuit for a voltage source that acts as the input voltage to the network and that voltage source has some internal impedance but knowing where this problem came from (seeing other problems just before it for example) might help clear this up.
On the practical side, this kind of circuit can be used as a bias network where the resistor ratio sets the reference bias voltage, while the two capacitors add filtering but at the same time force the output voltage to reach the target value in a very short time. With only one capacitor as filter it would take much longer to reach the DC operating point. But the time to charge is then dependent on the power supply impedance plus the network, not the network alone. The short time charge voltage is then dependent mostly on the capacitor values, which would be set to oppositely match the two resistor values.