# Equivalent Resistance Across Capacitor in RC Circuits

I need to find the equivalent resistance of the circuit here in order to find time constant. I know that I should replace current source with open circuit, then we have this:

That 1k Ohm confuses me. Is it serial or parallel to others? What about 2k and 3k ones? I assume that we should ignore the 1k and then 2k and 3k ones will be serial to each other. But I'm not sure. Can you tell me about how to determine the equivalent resistance of circuits with capacitors in general?

Note: I do not know Thevenin or superposition or such. I know the Nodal analysis method. Please do not include thevenin in your answers.

• One can approach this by using the complex (imaginary) impedance of the capacitor, but that's doing it the hard way, and might be a technique a bit out of reach given the simplicity of the set-up. Don't concern yourself with the resistance of the capacitor. I'm not sure what you mean by "nodal analysis", but that approach might also be impeding progress. Oct 21 '20 at 13:15
• @garyp i'm not concerned with capacitors resistance. I need to find the equivalent resistance of the circuit. Oct 21 '20 at 13:27
• Well, then you should reword your question because you did ask about the resistance of the capacitor. Why do you want the equivalent resistance of the circuit? I think you don't. That path won't lead to a time constant. Oct 21 '20 at 13:32
• @garyp why won't it lead me to a time constant? the formula is RC. I obviously need R. Oct 21 '20 at 13:43
• @garyp If one open circuits the current source, won't that give you the equivalent resistance across the capacitor and thus the $R$ for the $RC$ time constant? I don't know what you can do with it in this circuit since there is no switching device involved to charge/discharge the capacitor. I think the first order of business is to determine the voltage across the capacitor due to the current source. Oct 21 '20 at 14:38

## 1 Answer

That 1k Ohm confuses me. Is it serial or parallel to others?

Ask yourself, how much current flows through this resistor?

With that in mind, how does it affect the rest of the circuit?

Can you tell me about how to determine the equivalent resistance of circuits with capacitors in general?

In general, you apply a test current into or test voltage across the terminals you want to know the equivalent resistance between. Then you can use mesh or node analysis to find the unknown voltage or current. Divide voltage by current and you have the equivalent resistance.

In more complicated circuits you can't reduce everything as serial and parallel combinations, so you have to use this more general method.