# LC Circuit

1. Apr 6, 2010

### reising1

1. The problem statement, all variables and given/known data

In an oscillating LC circuit, L = 2.93 mH and C = 3.21 μF. At t = 0 the charge on the capacitor is zero and the current is 2.14 A. What is the maximum charge (in C) that will appear on the capacitor?

2. Relevant equations

I know that for an LC Circuit, the charge q at a given time t is:
q = Q cos(wt + phi)

3. The attempt at a solution

At t = 0, q = 0;
Thus,
0 = Q cos(phi),
which implies Q = 0.

So the maximum charge is 0.

However this is not right.

2. Apr 6, 2010

### vela

Staff Emeritus
The other possibility (the correct one) is that cos(phi)=0.

Try differentiating q(t) and use the other information given in the problem.

3. Apr 6, 2010

### reising1

Okay, so

i = dq/dt = -wq sin(wt + phi)

Plugging in,
since w = 1 / sqrt(LC)
2.14 A = Q (-1 / sqrt(2.93 mH * 3.21 microF)) sin(phi)

However I'm not sure what phi is. In fact, I'm not quite sure specifically what phi is. I know it is the phase difference. But in this case, the phase difference between what?

Thanks so much.

4. Apr 6, 2010

### vela

Staff Emeritus
The phase phi simply tells you where in the cycle you're starting.

With the information you're given, you can solve for phi. First, you know cos(phi)=0, so phi=pi/2 or -pi/2. From your equation for the current, you can figure out which of the two possibilities is the correct one.

5. Apr 6, 2010

### reising1

Okay. I understand that one. Now here's the next part;

(b) At what earliest time t > 0 is the rate at which energy is stored in the capacitor greatest?

So, I know that U = q^2 / 2C
So U = (Q^2)(sin^2(wt)) / (2C)

deriving this (to find the "rate at which energy is stored"), we get

dU/dt = (Q^2)(w)(sin(wt))(cos(wt)) / C

The maximum occurs when sin(wt)cos(wt) is at a max, which is when wt = pi/4

So, wt = pi/4 implies that the time when the rate at which energy is stored in the capacitor is greatest is
t = (pi/4)(1/w)
plugging in values, I get
t = 7.61686 E-5 seconds

However, this is incorrect.
See my flaw anywhere?
Thanks!

6. Apr 6, 2010

### vela

Staff Emeritus
Other than perhaps the number of significant figures, it looks right to me.

7. Apr 6, 2010

### reising1

Going back to before, why is it that we know cos(phi) = 0?