Question about oscillating currents. (the sign of the phase constant)by LogicX Tags: constant, currents, oscillating, phase, sign 

#1
Apr2411, 05:24 PM

P: 181

1. The problem statement, all variables and given/known data
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. 2. Relevant equations q=Qcos([tex]\omega[/tex]t+ [tex]\vartheta[/tex]) dq/dt=[tex]\omega[/tex]Q sin([tex]\vartheta[/tex]) 3. 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 [tex]\omega[/tex]Q sin([tex]\vartheta[/tex]) 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. 


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