I'm currently taking a course in electromagnetism, and I got stuck with this problem:
The Problem:
All of the resistors and capacitors have the same values, R and C respectively. The circuit is analyzed after a very long time. What is the voltage on the capacitors?
My Reasoning:
After a long time, the capacitors charge up and every loop that contains a capacitor has no current flowing.
C1 was charging through current I, I then was split and the rest of the capacitors where charging with current I1.
So the moment the current stopped flowing in the circuit, C1 built up Q1 charge and the other capacitors built up the same amount of charge Q2 (Same current flow through them for the same amount of time)
For some reason I get weird results, I would really appreciate it if someone could point to my mistake
Best Answer
It's correct.
I would say to simplify that after long time the green current I is 0, so it is the voltage drop on the vertical resistor.
Knowing that in the second loop on the right also the current is 0 because we have at least 1 capacitor is series, the also the voltage drop across the horizontal resistor is 0.
The sum of voltages along the right loop is equal to 0 (Kirchhoff Voltage Law), so the only terms remaining are the voltage drops across the capacitors C2 ad C34, that must be 0. An objection might be that I cannot infer it, because they might be any value, one positive and the other negative, and they would compensate each other ad give a 0 anyway. But the flow of current was unidirectional, so they must have the same sign, and thus the only solution is VC2=0 ad VC34=0.