Finding the function of the cap.

[johndoe]

This is one of the questions I got in my finals, and I couldn't do it back then. I want to find Vc(t) , given the cap is initially charged up to 10V, the switch is then opened. My approach is to find the thevein eq of the circuit, which I would came up with a resistor in parallel with the cap, and then find the function using the expression Vc(t) = final + (initial - final) e^(t/RC).
sounds good?

 

[berkeman]

This is one of the questions I got in my finals, and I couldn't do it back then. I want to find Vc(t) , given the cap is initially charged up to 10V, the switch is then opened. My approach is to find the thevein eq of the circuit, which I would came up with a resistor in parallel with the cap, and then find the function using the expression Vc(t) = final + (initial - final) e^(t/RC).
sounds good?

After the switch is opened, the cap disappears from the circuit, no?

 

[johndoe]

After the switch is opened, the cap disappears from the circuit, no?

ops the switch should be opened initially and then closed(drawing error)

 

[berkeman]

What is the source on the right? It can't be a current source of value 5ix, since there is only one ix flowing through the resistor before the switch is closed...

I think you need to re-draw the circuit correctly, and then show us your work on the solution. Then we may be able to offer some help.

 

[johndoe]

Question:
Finding the function of the 0.1uF cap Vc(t) when the switch is closed at t=0 given that the cap is initial charged up to 10V.

ok my attempt at this I find the thevenin eq of the right hand side circuit and come up with :

Vc(infinite) = 0, Vc(0)=10 , time constant = RC = 1.67x10^-7

Vc(t) = 0 + ( 10-0) e^(t/(1.67x10^-7 ))

Appreciate if u could have a look at it.

 

[Defennder]

How did you get 1.67 ohms for your thevenin equivalent circuit? I got an indeterminate answer for the thevenin equivalent circuit. You could do it without that. Furthermore, your final answer doesn't make much physical sense; Vc(t) would increase exponentially without limit as time passes.

 

[johndoe]

How did you get 1.67 ohms for your thevenin equivalent circuit? I got an indeterminate answer for the thevenin equivalent circuit. You could do it without that. Furthermore, your final answer doesn't make much physical sense; Vc(t) would increase exponentially without limit as time passes.

This is what I did :

I hook up a 1V source and solve for I1 and thus the Rth.

And I left out a - sign in my final answer
Vc(t) = 10e^-t/RC