Final answer:
The total positive charge stored on two series-connected parallel-plate capacitors remains 2Q0 even after inserting a dielectric into one of them. Capacitors in series have the same charge despite changes in voltage distribution after the insertion of the dielectric.
Step-by-step explanation:
When two identical air-filled parallel-plate capacitors, C₁ and C₂, are connected in series to a battery with voltage V and each has an initial charge of Q0, inserting a dielectric with dielectric constant K into one of them (C₁) while keeping the battery connected does not change the total charge in the system. The total charge remains the same because the battery ensures that the voltage across the entire series combination stays constant, and therefore, the series combination must hold the same total charge Q0. However, what does change is the voltage distribution across the two capacitors and the individual stored charge. The capacitor with the dielectric (C₁) will end up with a reduced voltage across it compared to the capacitor without the dielectric (C₂).
The total positive charge stored on the two capacitors is 2Q0, considering both the positive sides of C₁ and C₂. The initial charge on each capacitor is Q0, and since the capacitors are in series, the charge on each one remains the same even after the dielectric is inserted into C₁.