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.

    Thank you for your replies.


    [​IMG]
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,163
    1,797
    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:

    [​IMG]

    and came up with:

    [​IMG]

    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?
     
  5. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    Your solution is correct.
     
  6. testing12

    Thread Starter Member

    Jan 30, 2011
    80
    2
    Thank you sir.
     
Loading...