Two identical air-filled parallel-plate capacitors C1 and C2 are connected in series to a battery that has voltage V. The charge on each capacitor is Q0. While the two capacitors remain connected to the battery, a dielectric with dielectric constant K>1 is inserted between the plates of capacitor C1, completely filling the space between them.

What is the total positive charge stored on the two capacitors?
Express your answer with the appropriate units.

Explanation:

In the first case,

Q₀ = C₁ V, where C₁ is equivalent capacitance of two capacitor having capacitance C  each.

C₁ = C / 2

Q₀ = CV / 2

CV = 2Q₀

Total charge = 2Q₀ = CV

In the second case ,

capacitance will be kC and C .

equivalent capacitance

C₂ = kC x C / ( kC + C)

= kC / ( 1+k)

Charge on each capacitor = V x C₂

= kCV / ( 1+k)

=  2kQ₀ / ( 1+k)

This will be the charge on each capacitor. So

total charge = 4kQ₀ / ( 1+k)

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