Capacitor Voltage changed instantaneously?

Say you have a capacitor in series with a resistor and a battery. After a while the capacitor has a voltage equal to the battery. After you flip a switch a new capacitor gets placed in series with the other capacitor. Using the conservation of charge, the voltage across the equivalent capacitance is (C1 + C2)*V/C2. Where C1 is the original capacitor, C2 is the new capacitor in series, and V is the voltage of the battery. Why is the voltage across the equivalent capacitance higher than the battery dissatisfying KVL and why does the voltage change instantaneously? My professor said this is right but did not explain why.