# Energy Stored in an Inductor

AlphaMaleMatt

## Homework Statement

Not really relevant here.

## Homework Equations

U = LI^2 -- maybe?

## The Attempt at a Solution

http://i.imgur.com/Pq4dOex.png

The picture is there, as well as the answer. Why is that the answer? How do inductors work when completely disconnected, and not in a circuit? Thanks.

## Answers and Replies

Mentor
The inductor is in a circuit.

1/2 LI^2 (note the prefactor) is indeed the energy stored in an inductor.

AlphaMaleMatt
I'm an idiot. The question asks what happens when the switch is switched over to position B, after being in position A for "a very long time"

Homework Helper
Gold Member
I'm an idiot. The question asks what happens when the switch is switched over to position B, after being in position A for "a very long time"

That sine curve in the illustration tells you what happens to UL.

Hint: the instantaneous sum of stored energies in C and L is a constant.

AlphaMaleMatt
That sine curve in the illustration tells you what happens to UL.

Hint: the instantaneous sum of stored energies in C and L is a constant.

I guess I'm just confused as to why the energy in the inductor decreases, but then increases again?

Homework Helper
Gold Member
I can't give you a good verbal explanation. A publication like the ARRL Handbook can.

Mathematically, the integro-differential equation 1/C∫0t i(t') dt' = -L di/dt is solved with initial condition i(0+) = E/R

where i is the current flowing out of the inductor and into the capacitor. Each term is the voltage at the capacitor and inductor.

Staff Emeritus