Two capacitors of capacitances 3 F and 6 F are connected in series across an 18 V battery. After they are fully charged, the battery is removed and the capacitors are disconnected from each other. The space between the plates of the 3 F capacitor is then completely filled with a dielectric material of dielectric constant 4 . Finally, the two capacitors are connected in parallel such that their positive plates are joi

Step-by-step solution

In the initial series combination, the equivalent capacitance is C_ eq = C₁ C₂ C₁ + C₂ = 3 6 3 + 6 = 2 F . The charge on each capacitor in series is Q = C_ eq V = 2 F 18 V = 36 C . When disconnected, each capacitor holds a charge of 36 C . A dielectric of K=4 is inserted into the 3 F capacitor, making its new capacitance C₁' = 4 3 F = 12 F . The 6 F capacitor remains unchanged ( C₂' = 6 F ). When connected in parallel with like plates together, the total charge is the sum of their individual charges: Q_ total = Q₁