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Time Constant 2

Discussion in 'General Electronics Chat' started by herbymcduff, Dec 6, 2002.

  1. herbymcduff

    herbymcduff New Member

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    It doesn't matter what circuit, a RC, or a 555 astable, I just want to know how the .693 in the time constant formula came from. :roll:
     
  2. kinjalgp

    kinjalgp Active Member

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    Dear herbymcduff,
    It is not necessary to post every new reply of yours as a new topic. This forum has a facility to append your questions/anserwer within the same topic using the Big Blue/Orange colored button with "Post Reply" caption on it. Please use this facility next time you post the reply related to same topic and do not create a new topic as a reply to other post. Hope you got my point. :wink:

    Your point:
    The charging equation of capacitor is given by:
    q = qf{1 - e-t/RC}

    Here,
    q=charge at given instant in capacitor
    qf=final charge in capacitor
    t=time
    R=resistor
    C=cap. value

    Now the half-life (qf/2) of the circuit is calculated as
    qf/2 = qf{1 - e-t/RC}
    1/2 = 1 - e-t/RC
    0.5 - 1 = - e-t/RC
    -0.5 = - e-t/RC
    0.5 = e-t/RC
    Taking Natural Log in both sides,
    ln(0.5)=ln(e-t/RC)
    ln(0.5)=-t/RC
    t=-ln(0.5)RC
    t=0.693RC

    Hope now your point is clear.
     
  3. herbymcduff

    herbymcduff New Member

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    thanks
     

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