# RC Circuit Oscillation

1. Nov 7, 2009

### Oijl

1. The problem statement, all variables and given/known data
An oscillating LC circuit has a current amplitude of 7.20 mA, a potential amplitude of 250 mV, and a capacitance of 240 nF.

(a) What is the period of oscillation?

(e) What is the maximum rate at which the inductor gains energy?

2. Relevant equations
Possibly: Energy stored in an inductor = 1/2 * L * I^2
i = -wQsin(wt+ø)

3. The attempt at a solution
Energy per unit of time is Watts.

If I find the equation for energy stored in an inductor, I can differenceate that with respect to time and find its maximum value.

I thought that this would be:
dE/dt = P = -L(w^3)(Q^2)sin(wt)cos(wt)

And isn't the maximum value for this just

(1/2)L(w^3)(Q^2) ?

And isn't that just

0.9 mW ?

I've done this problem wrong several times so far, so is this one right?

Last edited: Nov 7, 2009
2. Nov 7, 2009

### willem2

U = ((Q^2)/2C) cos(^2)(wt+ø) is the equation for the energy contained in the capacitor,
not for the potential across it.

3. Nov 7, 2009

### Andrew Mason

How are you determining Q? I get Q = VC = .25 *2.4e(-7) = 6e(-8) C.

$$Q = VC = \int_0^{\pi/2} dQ = \int_0^{\pi/2} idt = \int_0^{\pi/2} i_{max}\sin{\omega t}dt$$

so:

$$Q = VC = i_{max}/\omega$$

AM

4. Nov 7, 2009

### Oijl

Oh, I see. I misunderstood the equation for U I had written, and therefore got a bad Q. Thanks to both.

5. Nov 7, 2009

### Oijl

But now I have another question for this problem, and I've edited the first post for it.