How Do You Calculate the Oscillation Period and Energy Gain in an LC Circuit?

[Oijl]

Homework Statement

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?

Homework Equations

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

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?

 

[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.

 

[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

 

[Oijl]

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

 

[Oijl]

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