Need help with a derivation

  • Thread starter frankkk
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I am trying to solve a homework problem. I need some help to get going in the right direction if possible. My equation I am starting with is:

Vc(t) = 5(1-e^(-t/T))

and I have to end up with these two equations:
If T > 1/10f then for a 5 V square wave with a 50% duty cycle, the capacitor voltage is given by

Vc(t) = 5 - (5 / 1+e^(-1/2*f * T)) * e^(-t/T)


Vc(t) = (5 / 1+e^(-1/2*f * T)) * e^(-t/T)

Last edited:


Welcome to PF, Frank. Homework problems are supposed to be posted in the PF Homework forum area, and you need to show your initial work in order for us to help you. We're happy to help, we just need to be sure that you do the bulk of the work, and learn from the exercise.

This thread may get moved by the moderators, or you could start a new thread in one of the homework forums, or you could see if it is allowed to stay here and we just follow the homework forum guidelines here.

So to get you started, I don't quite understand the problem statement. How can Vc(t) be equal to three different things? Is maybe Vc(t) a forcing function, and you are asked to find some kind of circuit response from the forcing function through some source impedance?

Try cleaning up the equations some or describing what is going on, and then show us what your first few steps are in trying to solve the problem. We can offer hints at that point.

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