Transient Analysis

Discussion in 'Homework Help' started by jeffkal, Mar 30, 2007.

  1. jeffkal

    Thread Starter New Member

    Nov 30, 2006
    I'm new here but I wanted to get some help in the area of RC analysis to Vc(t) I have a200uf cap and the switch opens at t=0 ok here's my question
    I know when the switch was closed I had 15v at the cap and when the switch open i had 8v at the cap what i am having a problem with is this equation K1+k2e^t/(RC)and the thevins resistane that the cap see is 7k how do i find Vc(t)
    thanks Jeff
  2. Dave_


    Mar 22, 2007
    So the capacitor is discharging from 15V, and after T seconds you measured the voltage and it was 8V?

    So are you trying to calculate the time it took for that?

    If that is the case, check out the formulas here:

    I'm guessing
    K1 = Voltage over capacitor at any instant
    K2 = Voltage applied to the circuit
  3. antseezee

    Active Member

    Sep 16, 2006
    We just spent a whole month on transient analysis. Here ya go:

    Vc(0-) = 15V
    Vc(0+) = 15V (since capacitor voltage cannot change instantaneously)
    Vc (infinite) = 8V

    Vc(0+) = K1 + K2 = 15
    Vc (infinite) = K1 = 8

    Therefore, 8 + K2 = 15 , K2 = 7

    Tau = Rth*C
    Tau = (7k)*(200u)
    Tau = 1.4s

    Your answer will then be:

    Vc(t)= 8 + 7*e^-(t/1.4)

    I'm assuming this problem is just a word problem and involves no circuit. Remember that your voltage conditions on the capacitor at time 0- & 0+ are equivalent since there cannot be instantaneous change of voltage on a cap. Remember that your current conditions on an inductor at time 0- & 0+ are equivalent since there cannot be an instant change.

    This is using the step-by-step method in case you google it. It will get much harder when you have capacitors and inductors in the same circuit, since there is no shortcut method. You will have use derivates & integrals to calculate second-order cases.
  4. farmosh203


    Nov 26, 2006
    I'm a little confused what you are asking, but I think just putting everything in frequency domain, use a simple loop method to solve the circuit, and convert it back to time domain and you'll have your answer.
  5. antseezee

    Active Member

    Sep 16, 2006
    He's talking about First Order Transient Circuits (capacitor or inductor only in a circuit). We used the same variables in our book (K1 & K2), which represent initial conditions before a switch opens/closes, and the conditions AFTER the switch has stayed in the position for time infinite.