Answer
The potential difference across the capacitor with the dielectric decreases.
Work Step by Step
When a dielectric is inserted in a capacitor, the dielectric increases the capacitance of the capacitor.
The capacitance increases.
Because the capacitance of the capacitor with the dielectric increases, the equivalent capacitance of the two capacitors also increases.
Since the total potential difference across both capacitors remains the same, the charge must increase, since in general $~~q = CV$
The charge on the capacitor with the dielectric increases.
Then the charge on the other capacitor must also increase, which in turn produces a greater potential difference across the other capacitor.
Since the total potential difference across both capacitors is equal to the battery voltage which does not change, the potential difference across the capacitor with the dielectric must decrease.
