LRC equation using Poynting theorem and conservation laws

[emeriska]

Homework Statement

We have an ordinary LRC circuit with inductance L, capacitance C and resistance R with an oscillating voltage with low frequency (U^e). Using the energy conservation law and Poynting's theorem, find the differential equation:

$$L \frac{\partial ^2}{\partial t^2}I + R \frac{\partial }{\partial t}I + L \frac{1}{C}I = \frac{\partial }{\partial t}U^e$$

Homework Equations

I'll need to take advantage from the fact that I is defined as
$$I = \frac{\partial}{\partial t}q$$.

Knowing q is the charge.

The Attempt at a Solution

Well, I've been looking around on the web to find something but I really can't find how to connect the Poynting theorem to that kind of circuit.

If any of you have some insights of a head start to give me that'd be great!

 

[Oxvillian]

Hi emeriska!

Your equation looks a lot like what I would get if I wrote down Kirchoff's 2nd law for the circuit and differentiated with respect to time. Except I think you have an extra factor of $L$ in the 3rd term?

Poynting's theorem would give you a nice 3d snapshot of the energy flow going on in and around the circuit.