RLC Series Circuit: Understanding Inductor Behavior

[jcoona]

Homework Statement

I am not sure how an Inductor behaves in an RLC Series Circuit

Homework Equations

The Attempt at a Solution

I know that after a long time, that the circuit above, the voltage in the capacitor is max. Generally, I also know that the current through an inductor after a long time is max... but after a long time, the current through the capacitor is 0. Since the two are in series, I don't know if to go with inductor current being max or 0... [/B]

 

[axmls]

As [itex]t \to \infty[/itex], what does each of the elements look like?

 

[jcoona]

Well, the inductor would act as a short circuit, and the capacitor would act as an open circuit

So i think the entire circuit would just open and as t→∞ the current is 0...

 

[axmls]

Correct. The inductor accepts the maximum current for the given branch of the circuit as t goes to infinity. In this case, that max is 0, because the capacitor acts as a short circuit, so there can be no current in that branch.

This is of course, assuming a DC input voltage.

 

[jcoona]

Yup, it's a DC voltage source

Ok that makes sense! I was thinking that would work, but i was not sure... thank you so much!

 

[LvW]

Yup, it's a DC voltage source

Ok that makes sense! I was thinking that would work, but i was not sure... thank you so much!

Was this really your question (what happens at t approaching infinity) ? Are you not required to find the timely behaviour of the current after applying the voltage?

 

[psparky]

Yes, usually they are interested in the transient analysis of that type of circuit...generally a 2nd order differiantial equation.
Or you could use S domain depending where you are in your studies.

Steady state just seems to easy in this case.

 

[axmls]

From their posts, OP is in an introductory circuits course. Some programs don't do transient analysis in the first semester course. Given that either no element values are given (or OP has withheld them), it seems this is more of a conceptual question.

 

[psparky]

From their posts, OP is in an introductory circuits course. Some programs don't do transient analysis in the first semester course. Given that either no element values are given (or OP has withheld them), it seems this is more of a conceptual question.

Either way, OP now knows that transient analysis is a much bigger fish to fry.

In the real world, the biggest transient current is the use of electric motors. Massive in rush currents especially on high HP motors.
Steady state is no problem, but start up is much more complicated. Breaker settings down the line of the substations must be carefully selected in industry.
That being said, VFD drives (Variable frequency drives) now are the remedy for taming the large inrush current. Although VFD's have their own set of complications...expensive, make lots of heat and I hear of them breaking in 10 years or less.

 

[LvW]

Was this really your question (what happens at t approaching infinity) ? Are you not required to find the timely behaviour of the current after applying the voltage?

I did ask this question because the original task description (post#1) contains the current i=i(t) .