Say we have two capacitors C1 and C2, initially isolated from each other and each having an initial voltage Vc1 and Vc2 respectively, where Vc1>Vc2. When suddenly connected to each other in parallel, obviously C1 will discharge to C2 until their voltages meet at a steady state value. Assuming zero resistance between the two capacitors, what is the expression for this steady state voltage Vc in terms of Vc1 and Vc2? Is it just the average of Vc1 and Vc2?
Just got a likely answer to my own question by asking a friend, who pointed out that charge is always conserved.
The total charge in our circuit (two capacitors in parallel) is Q = Vc1*C1 + Vc2*C2. We can then equate this to the total charge when voltage has settled, Vc*(C1+C2), giving a final expression of
Vc = (Vc1*C1 + Vc2*C2)/(C1+C2)
Sure the circuit in question doesn't have real life relevance, but I think this equation is very handy when you're just concerned with the steady state values.