# Homework Help: My try

1. Feb 11, 2004

### ismael18

as far as i know about inductors i think it'll make an harmonic type of move...
but it seems to make no sense
can anyone help?

2. Feb 12, 2004

### Tom Mattson

Staff Emeritus
Since you weren't very explicit as to what kind of circuit you are talking about, let's keep it simple: An LC circuit with a fully charged capacitor at t=0.

Now let the capacitor discharge through the inductor. What happens?

The voltage drop across the capacitor is EC=-q/C, and that across the inductor is EL=-L(di/dt)=-L(d2i/dt2). I will let q" (q-double-prime) denote the second time derivative of q from now on.

Kirchhoff's voltage law says that the sum of the voltages around a closed loop in a circuit must be zero. This is just the conservation of energy in disguse. So, we have:

EI+EC=0

or

q"+(1/LC)q=0

The solution to this equation, with q(0)=Q and i(0)=q'(0)=0, is

q(t)=Q*cos(&omega;t),

where &omega;=(1/LC)1/2.

As you can see, the oscillatory behavior of q(t) is due to the combined influences of the element laws and the conservation of energy.