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Maximal voltages across cap. and res. in serial RC circuit with pulse voltage source

  1. Jan 31, 2013 #1
    1. The problem statement, all variables and given/known data
    For the circuit in the picture below, with [itex]V_{c}(t=0) = 0[/itex] and a voltage source with period T described by
    [tex]V_s(t) = \sum_{-\infty}^\infty (-1)^{n}g(t-nT)[/tex]
    where
    [tex]g(t) = 7[u(t)-u(t-T)]\quad [Volt][/tex]
    and [itex]u(t)[/itex] is a step function described by
    [tex]
    u(t) =
    \begin{cases}
    1 & \text{if } t \geq 0 \\
    0 & \text{if } t < 0
    \end{cases}
    [/tex]
    What is the maximal voltages across the capacitor?
    What is the maximal voltages across the resistor?


    2. Relevant equations



    3. The attempt at a solution
    The voltage source is a pulse train with amplitude [itex]\pm 14 \quad [Volts][/itex] and since at time [itex]t = 0[/itex] we may consider the cap. as a short-circuit, we have [itex]V_{R}(t=0) = 14 \quad [Volts]. [/itex]
    I'm having trouble figuring out what the maximal voltage across the cap. is.
    Should I apply transient analysis?

    Thanx.
     

    Attached Files:

  2. jcsd
  3. Jan 31, 2013 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Re: Maximal voltages across cap. and res. in serial RC circuit with pulse voltage sou

    First, never mind the voltage anywhere at t=0. You don't know what t=0 is. This voltage wavetrain has been running since t = -∞.

    Now my gut reaction was Fourier series. But that's the hard way. Instead:

    1. realize that v(t), the voltage across C, will vary symmetrically about zero volts since that is the average value of your input, from Vmin to Vmax = |Vmin|.

    2.Then realize that the most negative C voltage is just before the input goes from -E to +E (why?). Then realize by symmetry that the max C voltage will occur just before the input transitions from +E to -E (again, be able to justify this statement).

    3. Write the KVL: current thru R = current into C starting with t=0 at the -E to +E input transition. This will be a differential equation, easy to solve, in capacitor voltage v(t). Solve with the initial condition v(0+) = Vmin, then solve for v(T) = Vmax. The rest should "follow immediately" as the textbooks say.
     
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