KVL and KCL of circuit

Discussion in 'General Electronics Chat' started by letoppina, Jan 8, 2018.

  1. letoppina

    Thread Starter New Member

    Dec 11, 2017
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    Hi,

    I am solving the equations of the circuit of an inductor and resistor in series with a parallel capacitor (see attached imaged). I am not sure about the signs of each term of the equation. What I am getting is the following:

    KVL: L(di/dt)^2 + R(di/dt) + (1/C)i = 0
    KCL: (dv/dt)^2 + (1/RC)(dv/dt) + (1/LC)v = 0

    Do you think it's correct?
     
  2. WBahn

    Moderator

    Mar 31, 2012
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    It would help if you defined what your voltages are and what your current is, including their polarities.
     
  3. MrAl

    AAC Fanatic!

    Jun 17, 2014
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    Hi,

    No sources or initial energy in the circuit?
     
  4. letoppina

    Thread Starter New Member

    Dec 11, 2017
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    The current is flowing clockwise. The initial conditions are:

    q(0) = q0 = CV0 (considering that V0 is sinusoidal)
    i(0) = i0
     
  5. Dodgydave

    AAC Fanatic!

    Jun 22, 2012
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    How can you work out anything without a power supply?
     
  6. letoppina

    Thread Starter New Member

    Dec 11, 2017
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    The capacitance is simulating the piezoelectric material (so it's already charged). The i(0) is not zero because the inductor is, in reality, an electromagnetic generator. A switch between the capacitance and the inductor is supposed to be closed at time t=0+.
     
  7. WBahn

    Moderator

    Mar 31, 2012
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    What is v? There are three components, so v could refer to the voltage across any one of them. In addition, it could be defined with either polarity. So there are six possible interpretations of v. Which one is the one you are using?

    What do you mean V0 is sinusoidal? q(0) is the charge on the capacitor at a particular moment in time. So V0 is a fixed value. Do you mean it is the amplitude of some sinusoidal waveform?
     
  8. WBahn

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    Mar 31, 2012
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    If the switch is changed from open to closed at t=0, then i(t=0-) is zero because there is an open circuit. However, the current in an inductor must be continuous, so i(t=0-) = i(t=0+). Thus you have a physically inconsistent problem statement unless i(o) IS zero. The switch would need to move from short circuiting the inductor (or inductor/resistor) to connecting the capacitor.
     
  9. letoppina

    Thread Starter New Member

    Dec 11, 2017
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    yes, you are right. Instead, considering the circuit always short circuited (without the switch) with the same initial conditions, how would the problem be solved?
     
  10. WBahn

    Moderator

    Mar 31, 2012
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    You still haven't defined which of the six possibilities your choice of 'v' refers to.
     
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