characteristic equation

losafojjog

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

3. 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.

klondike

combine L1 and L2 in parallel into L_total (assuming you don't care mutal inductance), now you have one less component.

Defennder

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?

CEL

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.