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Parellel RC with DC voltage source?

Discussion in 'Electronic Basics' started by E. Thomson, Dec 1, 2004.

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  1. E. Thomson

    E. Thomson Guest

    This should be a simple analysis. I am analyzing a parallel RC
    circuit, with a DC voltage source. I have not yet studied AC analysis.
    The circuit looks like this:

    | | |
    V R C
    | | |

    V is really V*u(t), so the voltage is turned on at t=0.

    I want to calculate Vc and Vr. On one hand, Vc and Vr should be the
    same, as they are in parallel. On the other hand, Vc cannot jump
    to voltage V instantaneously. I have not been able to set up the
    differential equation to get a solution with any time-varying
    behavior at the capacitor.

    Thanks for any help, especially with setting up the equation to get
    this right.
  2. CFoley1064

    CFoley1064 Guest

    Subject: Parellel RC with DC voltage source?
    If the R and C are in parallel, the voltage rise across the R and C will be the
    same. Also, the rise in voltage across the R and C will be entirely dependent
    on the internal resistance of the DC voltage source and the residual resistance
    of the wire.

    I believe you're thinking about R and C in series. This is covered here:

    Actually, if you can find the internal resistance of your voltage source, you
    can use this information to calculate the voltage across the R and C for any
    given time with this information, too.

    Good luck
  3. The circuit has only two nodes, so it can have only a single voltage
    difference between those two points. You have arbitrarily defined the
    voltage between those two nodes, and it will appear across all paths
    between those nodes. However, an instantaneous step change in the
    voltage across the capacitor will require an impulse of current
    (infinite magnitude, zero duration).
  4. John Larkin

    John Larkin Guest

    In theory, the charging current is infinite, which differential
    equations don't like. EE's use the concept of an impulse of current, a
    pulse of current of zero width but finite charge (the "delta"
    function, Laplace transform = 1) This is sort of like dividing by
    zero, and is mathematically iffy.

    In real life, there's always some resistance and inductance in the
    charging path; if you include either or both of these, the circuit
    becomes mathematically tractable.

  5. E. Thomson

    E. Thomson Guest

    (CFoley1064) wrote
    entirely >dependent on the internal resistance of the DC voltage
    source and the residual >resistance of the wire.

    OK, so in other words using an ideal source it is correct that there
    should be no time varying dynamics in the voltage, other than at t=0.

    No, that problem is relatively easy to solve, and inspired me to
    explore other possibilities for theoretical interest. In reality if I
    build it with a breadboard there is small R in series with V, so the
    circuit as I've drawn it is mpossible to build. So, basically, I'd get
    a delta function for current through the capacitor, which would charge
    up instantaneously, and never discharge.

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