Finding the time constant in a RC circuit given no time?

Discussion in 'Homework Help' started by ABCJ6, Dec 4, 2014.

  1. ABCJ6

    Thread Starter New Member

    Dec 4, 2014
    2
    0
    I'm a little unsure of how to go about with this question for part b since i wasn't given a time for it.

    An 18 μF capacitor has been charged to 100V. A15 kΩ resistor

    and a 5 kΩ resistor, are connected in series with the capacitor.

    (a) What is the time constant of this circuit? (found this to be 0.36s)
    (b) Approximately how long (in terms of τ) will it take for the
    charge stored on the resistor to drop to 0.1% of its original
    charge?
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,163
    1,796
    An RC circuit is described by a first order differential equation. You solve that differential equation. Form the solution, you plug in the time constant and the final value and solve for t, the time it takes to reach the final value. Can you do that?
     
  3. ABCJ6

    Thread Starter New Member

    Dec 4, 2014
    2
    0
    okay, thank you!!
     
  4. WBahn

    Moderator

    Mar 31, 2012
    17,777
    4,805
    Since there isn't any charge stored on the resistor, it won't take any time for it to drop to 0.1% of that.

    Now, if you were asked how many time constants does it take for a quantity to exponentially decay to 0.1% of it's initial value, that will have the same answer regardless of what the time constant is or whether we are talking about charge on a capacitor, current in an inductor, amount of radioactive material, whatever.
     
  5. MrAl

    Well-Known Member

    Jun 17, 2014
    2,440
    492

    Hi,

    Are you sure you wrote part (b) the way it was supposed to be written? There is no charge 'stored' on the resistor, the charge is stored in the capacitor.

    Also, i dont think you should have to resort to differential equations for this simple circuit unless you have never done this before. The well known solutions are:

    Vc=Vs*(1-e^(-t/RC))
    and
    Vc=Vc(0)*e^(-t/RC)

    Vs is source voltage, Vc(0) is initial cap voltage.
    You'll have to figure out which one to use for a given problem.
     
  6. Papabravo

    Expert

    Feb 24, 2006
    10,163
    1,796
    Charge on a resistor. I missed that minor detail. Good catch.
     
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