step response of RLC circuit example, IE7.11

Discussion in 'Math' started by PG1995, Nov 30, 2011.

  1. PG1995

    Thread Starter Active Member

    Apr 15, 2011
    753
    5
    Hi

    Please have a look on the attachment. What would be the voltage across the capacitor before the switch is placed in position 2? I'm confused about it. Please help me with it. Thank you.

    Regards
    PG
     
  2. steveb

    Senior Member

    Jul 3, 2008
    2,433
    469
    That is the right question to ask when you first look at this problem. The other good question to ask is "what is the current in the coil when the switch is placed in position 2?".

    Both capacitor voltage and coil current are two values that will not change instantaneously when the switch is thrown. Hence, these values become the initial conditions for the problem.

    The problem is very vague about the initial conditions. It does not say that the switch was first left in position 1 for a long time, hence you can't determine what the initial current is.
    Nor, does it say anything about whether the switch was previously in position 2 for a long time before being switched to position 1, hence you can't determine what the initial voltage is.

    Personally, I would write the solution in a general way in terms of the initial conditions. I prefer not to deliberately make assumptions that are not explicitly stated.

    If you don't do this, then you have two other options as follows. First, you have to assume that the switch was in position 1 for a long time giving an initial current of 0.5 A. Then, you can either assume capacitor voltage is zero, or assume it is fully charged (to 8 V) as a result of being in position 2 for a long time before being put in position 1 for a long time.

    The safest way to not get the problem wrong is to solve it first with general initial conditions and then solve and discuss these two interesting cases with specific initial conditions.
     
    PG1995 likes this.
  3. PG1995

    Thread Starter Active Member

    Apr 15, 2011
    753
    5
    Before I slept four hours ago I used Vc(0)=0V (capacitor's voltage initially) and assumed before the switch is moved the circuit is steady DC state, and I was able to solve the problem. Thank you for your explanation. You are right saying there is a bit of vagueness. Generally, I don't think that is a good book.

    My best wishes
    PG
     
  4. PG1995

    Thread Starter Active Member

    Apr 15, 2011
    753
    5
    Hi :)

    Could you please help me with the query enclosed in the attachment? Thank you.

    Regards
    PG
     
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