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Homework Help: Capacitor and Variable resistor

  1. Apr 19, 2005 #1
    A controller on an electronic arcade game consists of a variable resistor connected across the plates of a [tex]0.220\mu F[/tex] capacitor. The capacitor is charged to [tex]5.00V[/tex], then discharged through the resistor. The time for the potential difference across the plates to decrease to [tex]0.800V[/tex] is measured by a clock inside the game. If the range of discharge times that can be handled effectivly is from [tex]10.0\mu s[/tex] to [tex]6.00ms[/tex], what should be the resistance range of the resistor?

    I have solved the problem and I get a maximum resistance of [tex]27272.7\Omega[/tex] and a minimum resistance of [tex]45.45\Omega[/tex].
    But these values seem a bit too large.

    The way I did it:
    [tex]I = q/t[/tex]
    [tex]q = CV[/tex]
    so [tex] I = CV/t[/tex]
    and [tex]R = V/I[/tex]

    and solved it for all 4 cases:
    (max voltage, largest discharge time)
    (max voltage, smallest discharge time)
    (min voltage, largest discharge time)
    (min voltage, smallest discharge time)

    An found there are two different values for the resistor:
    [tex]27272.7\Omega[/tex] and [tex]45.45\Omega[/tex].

    Does anyone know if there is anything I have done wrong?
    Many thanks
     
  2. jcsd
  3. Apr 19, 2005 #2
    I think you can use the formula:
    [tex]V=V_{0}e^{-\frac{t}{RC}}[/tex]
     
  4. Apr 19, 2005 #3
    I tried it using your formula and I get 24.8 ohms and 14882 ohms.
    This is roughly half of what I got before.
    Any ideas?
     
  5. Apr 19, 2005 #4
    the way it is worded, cartoon kid is correct.

    jw, but what was your reasoning behind this?

     
    Last edited: Apr 19, 2005
  6. Apr 19, 2005 #5
    In a RC circuit, when a capacitor is discharging, the charges, current and voltage across the capacitor are decreasing exponentially. It's a continuous process. The bigger the R, the slower the discharing process.
     
  7. Apr 19, 2005 #6
    well I wasnt sure what the relationships were all about so I just decided to try all possible cases and see what I came up with.
     
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