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https://www.allaboutcircuits.com/textbook/direct-current/chpt-16/voltage-current-calculations/

 

I'm not sure what you are asking about.

That formula gives you the voltage across the capacitor in a first order circuit as a function of time. So 't' is the value of time that you are interested in.

In your schematic, what do you mean by "the voltage of this capacitor"? The value is changing, so you either need to specify the time at which you want the value, or the answer needs to reflect the changing nature of the voltage.

How the simulator does it is to calculate the voltages and currents at each moment in time, using the voltages and currents from the prior time step to update the changes to the next time step.

You could actually do a very similar thing with a spreadsheet.

 

I dont have T , the problem only says its in

steady state

what does that mean?

So, "in steady state" means that after the circuit reaches a point such that things are no longer changing.

So look at that formula and consider what happens as 't' gets larger and larger and larger. What you should observe is that, while strictly speaking the voltage continues to change forever, it quickly reaches a point where it is arbitrarily close to a particular voltage.

If it still isn't obvious to you, see what you get for t = 0.05·tau, 0.5·tau, tau, 5·tau, 50·tau, and I think you'll get the idea.

Another approach is to use a spreadsheet (or whatever) and plot the capacitor voltage as a function of time and then ask what value it has when it stops changing.

If not, we can talk more.

 

Oh. Is this homework of any kind? If so, I can move it to Homework Help where the kind of assistance you will get is more in tune with helping you learn the concepts.

 

MOD NOTE: Moved to Homework Help.