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Question about analogies

  1. Mar 13, 2009 #1
    1. The problem statement, all variables and given/known data

    The discharge of a capacitor through a resistor is analogous to radioactive decay.

    Write down the equation for capacitor discharge which is analogous to [itex] A = \lambda N[/itex].

    Explain the analogy between A and the subject of your equation.


    2. Relevant equations



    3. The attempt at a solution

    The only equation I can think of is [itex] Q = Q_0 e^{-\frac{t}{RC}}[/itex] and the similar ones for voltage and current but this can't be the one which is analogous to that equation because it is analogous to [itex] N = N_0 e^{-\lambda t}[/itex].
     
  2. jcsd
  3. Mar 13, 2009 #2
    You thought of the right equation, you just need to get it in a different form. How do we get the equation [itex]N = N_{0}e^{-\lambda{t}}[/itex]?
     
  4. Mar 13, 2009 #3
    Is the A in [itex] A = \lambda N[/itex] equal to [itex] \frac{dN}{dt}[/itex]?
     
  5. Mar 13, 2009 #4
    That does seem to be what the question is driving at, yeah.
     
  6. Mar 14, 2009 #5
    Is the answer [itex] I = \frac{Q}{RC}[/itex].

    I neglected the negative like they did in the question. Why do they get rid of the negative when we talk about activity? Is it because we need it when using differential equations because it is decaying but we leave it when not using the differential equation because we know it is decaying?

    What does the negative in [itex] I = - \frac{Q}{RC}[/itex] mean physically? Of course it tells us that charge is decreasing but does it tell us about the direction of current flow?
     
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