# Voltage across a capacitor as a function of time.

Discussion in 'Homework Help' started by testing12, Mar 12, 2011.

1. ### testing12 Thread Starter Member

Jan 30, 2011
80
2
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.

2. ### Papabravo Expert

Feb 24, 2006
10,016
1,754
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

3. ### testing12 Thread Starter Member

Jan 30, 2011
80
2
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.

Last edited: Mar 12, 2011
4. ### testing12 Thread Starter Member

Jan 30, 2011
80
2
can someone help with this problem?

Mar 6, 2009
5,448
782

6. ### testing12 Thread Starter Member

Jan 30, 2011
80
2
Thank you sir.