RC Circuit Discharge Conceptual Question

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DaleSwanson
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http://i.imgur.com/ZCcaZpq.png
Circuit schematic labelled Figure P7.8: 6 V source, 12 kΩ resistor, node A, 200 μF capacitor, node B, 6 kΩ resistors, a switch marked t = 0 to node C, a 12 kΩ resistor with current i₀(t) to ground.


I have the solution manual, so this is more just a question of why, rather than what.

I understand that with the switch open:
vA = 3v
vB = vC = 0v
i0 = 0.25 mA

When the switch closes it creates a short that makes the two 6kΩ resistors irrelevant. What I don't understand is why anything should change then. The solution manual tells me that a current would flow from the capacitor from B to C, but why? It seems like nodes B and C should be at 0v both before and after the switch is closed.
 
Yes, node B is at zero both before and after the switch is closed, but after the switch is closed, what is the voltage across the capacitor? Is it any different than before the switch is closed?
 
As far as I can tell the voltage across the capacitor should always be 3v.