# Energy Stored in an Inductor

1. Nov 27, 2013

### AlphaMaleMatt

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

Not really relevant here.

2. Relevant equations

U = LI^2 -- maybe?

3. 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.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 27, 2013

### Staff: Mentor

The inductor is in a circuit.

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

3. Nov 27, 2013

### 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"

4. Nov 28, 2013

### rude man

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.

5. Nov 28, 2013

### AlphaMaleMatt

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

6. Nov 28, 2013

### rude man

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.

7. Nov 28, 2013

### Staff: Mentor

Because the L-C elements represent a resonant circuit (having no resistive losses). Just as a child's swing oscillates when you release it from some height, so does the energy in the analogous L-C circuit.