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.
A characteristic equation is a mathematical equation that relates the coefficients and roots of a polynomial equation. It is used to find the roots or solutions of a polynomial equation.
A polynomial equation is a general form of an equation, while a characteristic equation is specifically used to find the roots or solutions of a polynomial equation.
The characteristic equation is significant because it allows us to find the roots or solutions of a polynomial equation, which are important in various mathematical applications such as optimization, physics, and engineering.
To solve a characteristic equation, you first need to write the polynomial equation in standard form. Then, you can use various methods such as factoring, the quadratic formula, or the rational root theorem to find the roots of the polynomial. These roots will be the solutions to the characteristic equation.
Yes, a characteristic equation can have complex roots. Complex roots can occur when the polynomial equation has coefficients that are complex numbers, or when the polynomial has repeated roots. In these cases, the characteristic equation will also have complex roots.