Hello everyone,
I need some help finding the Vc(t). there are a few methods i have read, but am still a little confused. One method i have read involves the natural response, and stead state response, but the examples i have seen involves a decaying voltage, which is not what i have.

Here is what i know, since the switch is at (a) at t<0 the resistors consume any power in the capicitor. Therefore:

Vc(0-)= 0 Volts
and since the voltage cannot change instantenously accross a capicitor,
Vc(0+) = 0

Now i need to find Vc when t> 0, this is where im stuck i need some hints on how to do so.

Thank you for your replies.

 

1. Write Kirchoff's voltage law around the loop.
2. Solve the resulting 1st order differential equation.

Because \(R_T\) is used for both charging and discharging the solution is the same but with different initial conditions

 

I used KVL, but didnt solve the diff Eqn, i will try that next. I used the method in my text book, shown here:

and came up with:

is this also acceptable? it seems correct to me, because the voltage at t=0 is 0 and increases as t increases. this is also what the graph shows.

 

can someone help with this problem?

 

Your solution is correct.

 

Thank you sir.