Characteristic Equation for Parallel Circuit with Current Source and 3 Elements

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Discussion Overview

The discussion revolves around finding the characteristic equation for a parallel circuit consisting of a current source, a resistor, and two inductors (L1 and L2). Participants explore the theoretical aspects of circuit analysis, particularly focusing on the relationships between voltage, current, and the components involved.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant proposes that the current can be expressed as i(t) = v(t)/R + iL1(t) + iL2(t), but questions whether their approach to finding the characteristic equation is correct.
  • Another participant suggests combining L1 and L2 into a total inductance (L_total) under the assumption that mutual inductance is not a concern, simplifying the circuit analysis.
  • A different participant questions whether the current source is constant or time-dependent, and raises concerns about treating the currents through the inductors as identical without knowing if their inductances are the same.
  • One participant reiterates the initial problem statement and equations, emphasizing that if the current source is constant, the inductors would behave as short circuits, leading to no voltage across the resistor and no dynamic equation. They clarify that the characteristic equation arises from applying the Laplace transformation to the differential equation.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the current source and its implications for the circuit's behavior. There is no consensus on the correct approach to finding the characteristic equation, and multiple perspectives on the treatment of the inductors and current source remain unresolved.

Contextual Notes

Participants highlight the importance of the current source's characteristics (constant vs. time-dependent) and the assumptions regarding the inductors, which may affect the analysis. The discussion does not resolve these assumptions or their implications for the characteristic equation.

losafojjog
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Homework Statement



im trying to find the characteristic equation of a circuit with a current source and 3 elements all in parallel: a resistor and 2 inductors L1 and L2.

Homework Equations



i believe the current can be calculated as:
i(t) = v(t)/R + iL1(t) + iL2(t)

The Attempt at a Solution



is this anywhere close?
(1/R)dv/dt + 1/L1(v) + 1/L2(v) = 0
i guess i don't understand what is equated in a characteristic equation.
 
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combine L1 and L2 in parallel into L_total (assuming you don't care mutal inductance), now you have one less component.
 
Is the current source a constant source or one of a function of time? And how could you write iL1 and iL2 as though the two i's for both are the same? Is it given that the inductance of both are the same?
 
losafojjog said:

Homework Statement



im trying to find the characteristic equation of a circuit with a current source and 3 elements all in parallel: a resistor and 2 inductors L1 and L2.

Homework Equations



i believe the current can be calculated as:
i(t) = v(t)/R + iL1(t) + iL2(t)

The Attempt at a Solution



is this anywhere close?
(1/R)dv/dt + 1/L1(v) + 1/L2(v) = 0
i guess i don't understand what is equated in a characteristic equation.

Unless your current source is a constant, its derivative is not zero. If the source is constant, both inductors will act as short circuits, so there is no voltage across the resistor and no dynamic equation.
The characteristic equation is the algebraic equation you obtain when you apply the Laplace transformation to your differential equation.
 

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