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I need to derive an expression (with respect to time) of the current flowing through the short circuit. The capacitors are charged to some voltage value.

I know the solution but I am trying to understand how the time-constant of each capacitor in the circuit is determined only by the resistor in its branch. How come the other resistors have no effect?

I other words, how come the time-constant of C1 is 20uX100 and R2 and R3 have no effect on C1 time-constant?

schematic

simulate this circuit – Schematic created using CircuitLab

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  • \$\begingroup\$ I think the answer to that is because of the short circuit, each cap sees only its resistor in his branch. But I'm not 100% sure. \$\endgroup\$ – SHR Nov 10 '19 at 17:34
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Because of the short circuit, none of the current through C1 and R1 can flow through R2/C2 or R3 (because KCL). So, whatever happens with R1/C1 has no effect on R2/C2 or on R3. The two RC networks can be considered separately and combined by superposition.

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