Question about oscillating currents. (the sign of the phase constant)

[LogicX]

Homework Statement

This is more of a conceptual problem I'm having with in a problem. I'm trying to find the phase constant of the equation for a capacitor that is charging at time zero. I'm having trouble with figuring out what sign the phase constant should have.

Homework Equations

q=Qcos($$\omega$$t+ $$\vartheta$$)

dq/dt=-$$\omega$$Q sin($$\vartheta$$)

The Attempt at a Solution

Ok, I know the max charge on the capacitor, and I know q at time zero, so I solved for the angle. I just don't know how to determine it's sign (the answer is positive).

So here is one way of thinking about it:

dq/dt should be positive because the capacitor is charging. Therefore -$$\omega$$Q sin($$\vartheta$$) must be positive which only happens when I choose the negative angle. Voila, the angle is negative if it is charging.

BUT, I thought that if the capacitor was charging, the current should be decreasing? So how can dq/dt (which is the current) be positive if the capacitor is charging? Based on the two equations for energy U=q^2/2C and U=Li^2/2, if the charge increases the current must decrease to conserve energy.

I seem to be contradicting myself.

EDIT: Nevermind, I got it. The current is decreasing, but it is still positive for the capacitor to be charging.

 

[lippyka]

The current is just the rate of change of charge, so if charge is increasing, then the current must be positive.