Capacitance Problem: Find Potential Difference Change

[Gamerex]

The Problem: An empty capacitor is connected to a 12.0 V battery and charged up. The capacitor is then disconnected from the battery, and a slab of dielectric material (k=2.8) is inserted between the plates. Find the amount by which the potential difference changes, and state whether this change is an increase or a decrease.

My attempt at a solution:

Using the equations Q=CV and C=(k*A*ε)/d

And considering that A, ε, d, and Q stay constant,
And k is 1 to begin with since the space is empty, and 2.8 after the material is inserted,

I get
1*12(volts)=2.8V
Thus, V=4.3 Volts.

However, the book gives the answer as 7.7 V. Help?

 

[TSny]

Everything's ok except you didn't quite answer the question as stated. You want to find how much V changes.

 

[Gamerex]

Oh, I see!

ΔV=V_f-V_i=4.3V-12V=-7.7 V

Thus, the voltage decreases by 7.7 V.

Thanks for your help!