First Order RC Circuits

Discussion in 'Homework Help' started by LightAce, Sep 19, 2010.

  1. LightAce

    Thread Starter New Member

    Sep 19, 2010
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    Question:If a 100μF capacitor is initially charged to 100 V and it is desired that 90% of that voltage remain stored after the source of that charge has been removed for one minute, what is the maximum value for the leakage resistance that can be tolerated?

    So I'm assuming your trying to find what resistor would allow the capacitor to have 90 V by the end of one minute. I'm really not sure what to do here or what formulas to use, so if anyone can explain in detail on how to get started with this, it would be much appreciated.
     
  2. Georacer

    Moderator

    Nov 25, 2009
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    Here we have, as you already said, a first order RC circuit. It involves a capacitor and a resistance connected in a loop. The time constant of this circuit is T=RC, where R the resistance and C the capacitance.

    The voltage of the capacitor as a function of time is described by the equation V_c(t)=V_0 (1-e^{-\frac{t}{RC}})

    In order to solve your problem, substitute time for 60 seconds, the capacitance, V_c with the desired final voltage and V_0 with the initial voltage, and solve for R.

    Any questions?

    Refer to "RC circuits" in Wikipedia for more reading.
     
  3. LightAce

    Thread Starter New Member

    Sep 19, 2010
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    Thank you so much, that was more than clear enough for me to understand.
     
  4. Ron H

    AAC Fanatic!

    Apr 14, 2005
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  5. Georacer

    Moderator

    Nov 25, 2009
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    Yes, it seems I did. The correct one is V_c(t)=V_0 e^{-\frac{t}{RC}}

    I never learned them by heart. Thanks for the correction!
     
  6. Ghar

    Active Member

    Mar 8, 2010
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    Yeah I never get them right on the first try either... you need to plug in t = 0 and see what it gives you, nice fast and simple check.
     
  7. Ron H

    AAC Fanatic!

    Apr 14, 2005
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    Same here. That's how I discovered the error.
    Here is the equation that always works:

    V(t)=V_f+(V_i-V_f)*e^{\frac{-t}{R*C}}
    Where

     V(t)is the instantaneous voltage across the capacitor,

     V_i is the initial voltage across the capacitor,

    and  V_f is the final (target) voltage.

    I memorized it in college, about 50 years ago, when capacitors were Leyden jars and resistors were all wirewound.:D
     
  8. LightAce

    Thread Starter New Member

    Sep 19, 2010
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    Glad this assignment isn't due till Thursday. Thanks for noticing the error but is it possible that the resistance could be as high as 5692K ohms, because that is what I had gotten for the resistance
     
    Last edited: Sep 21, 2010
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