A capacitor with a capacitance of 100 F is charged to a potential difference of 50 V . After the charging battery is disconnected, a dielectric of dielectric constant 2.5 is inserted, which changes the potential difference. What charge would have produced this new potential difference in the absence of the dielectric slab?

Step-by-step solution

Initial charge on the capacitor is given by Q₀ = C₀ V₀ Substituting the given values: Q₀ = 100 F 50 V = 5000 C = 5 mC Since the battery is disconnected, the charge remains constant. When a dielectric of constant K = 2.5 is inserted, the new capacitance becomes C = K C₀ The new potential difference is V = Q₀ C = Q₀ K C₀ = V₀ K V = 50 2.5 = 20 V The charge Q' required to produce this new potential difference in the absence of the dielectric slab (i.e., with capacitance C₀ ) is: Q' = C₀ V Q' = 100 F 20 V = 2000 C = 2