I learnt about the basics of RC circuits, taking a simple case of only a resistor and a capacitor connect in series to a battery.
But following this I faced several questions which involved a more complicated arrangements of resistors around a single capacitor.
My teacher and all the online articles I read told me to find the steady state charge separately and the time constant seperately.
The charge part was fairly easy to find and understand.
However coming to the time constant part, everyone only mentioned that I had to replace the battery with a conducting path and find net resistance across the capacitor.
Though I managed to avoid this process by directly using differential equations to solve it, however the process was greatly simplified with the first method.
But I could not form any intuition for why we replace the battery by a wire and find resistance over the capacitor.
Moving on I found several more complicated questions involving several capacitors and resistors like this:
For finding the time constant of a particular capacitor I was again told to connect the battery by a wire and also replace the other capacitors with wires.
All these methods seem very un-intuitive to me to be able to use properly, whereas proceeding in the general way is very time inefficient.
Can someone please help me understand why we do whatever we do here?