How Does Energy in an Inductor Change When Disconnected?

[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.

 

[mfb]

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"

 

[rude man]

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 U_L.

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 U_L.

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?

 

[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∫₀^t 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.

 

[NascentOxygen]

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

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.