RC Circuit, Need help forming equation.

[EEhokie13]

Homework Statement

The switch has been in position 1 for a long time before moving to position 2 at t=0. Find i(0) for t>0.

Image of circuit:
http://img215.imageshack.us/img215/9200/circuit3.png

Homework Equations

KVL
First Order Diff Eq

The Attempt at a Solution

So to start the problem what I did was look at the circuit at t<0. I got a current for i(0) to be 0 because the circuit is open at t<0. When I switched it to position two I did KVL to form a first order linear equation. For my answer I got i(0)=Ce^(-1000t)
My teacher gave us the answer to work too and I cannot get it. He said the answer should be .3125e^(-500t)mA. Can anyone help me?

 

[Quinzio]

That diamond shaped thing is a voltage generator ?
It's voltage is $$20.000 i_0$$ ?

 

[EEhokie13]

That diamond shaped thing is a voltage generator ?
It's voltage is $$20.000 i_0$$ ?

the voltage is a dependent source. and yes it is 20,000i_0

 

[Quinzio]

For my answer I got i(0)=Ce^(-1000t)

I checked your teacher answer an it is correct (no wonder).
That circuit is very simple for who (like me) works in the electornic field.

What steps did you do to get your answer ?

 

[EEhokie13]

I checked your teacher answer an it is correct (no wonder).
That circuit is very simple for who (like me) works in the electornic field.

What steps did you do to get your answer ?

I looked at the circuit at t< 0 and said that the capacitor makes an open circuit. So the dependent voltage source goes away and you are left with an open circuit and the voltage source and resistor. Since its an open circuit I said there is no current for t < 0.

For t > 0 you have only part of the circuit do to the switch so you are left with: The 60k ohm resistor, the dependent source, and the capacitor. I did KVL and ot 60ki(0) - (2*10^4)i(0) - 1/c(integral from 0 to t)idt + 25V = 0

From that I got an differtial of 1000i(0) a di/dt = 0 and got i(0)=Ce^-1000t

 

[Quinzio]

60ki(0) - (2*10^4)i(0) - 1/c(integral from 0 to t)idt + 25V = 0

There are/is mistakes with signs.
Run the looop in the direction of i(0), and pay attention to signs.

 

[EEhokie13]

60ki(0) - (2*10^4)i(0) - 1/c(integral from 0 to t)idt + 25V = 0

There are/is mistakes with signs.
Run the looop in the direction of i(0), and pay attention to signs.

I am not sure then, I thought I was using one of the sign conventions. My professor has told us that you can do it two ways and you will get the same answer. I change it to what I believe will be the proper sign convention. Otherwise I am stuck. If you are able to please explain more it will be really helpful.

60ki(0) + (2*10^4)i(0) - 1/c(integral from 0 to t)idt + 25V = 0