ch31-p023 - V across the capacitor: V = L ( di/dt ), and we...

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23. The loop rule, for just two devices in the loop, reduces to the statement that the magnitude of the voltage across one of them must equal the magnitude of the voltage across the other. Consider that the capacitor has charge q and a voltage (which we’ll consider positive in this discussion) V = q/C . Consider at this moment that the current in the inductor at this moment is directed in such a way that the capacitor charge is increasing (so i = + dq/dt ). Eq. 30-35 then produces a positive result equal to the
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Unformatted text preview: V across the capacitor: V = L ( di/dt ), and we interpret the fact that di/dt > 0 in this discussion to mean that d ( dq/dt)/dt = d 2 q/dt 2 < 0 represents a deceleration of the charge-buildup process on the capacitor (since it is approaching its maximum value of charge). In this way we can check the signs in Eq. 31-11 (which states q/C = L d 2 q/dt 2 ) to make sure we have implemented the loop rule correctly....
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