A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25 % more charge from the battery. The dielectric constant of mica is _ _ _ _ .

Step-by-step solution

Initial capacitor has plate separation 5 mm with capacitance C₁ = ₀ A / 5 . After inserting 2 mm mica sheet, the gap remaining is 3 mm of air. The effective separation becomes: d_ eff = 3 + 2/k where k is the dielectric constant of mica. New capacitance: C₂ = ₀ A 3 + 2/k Since battery remains connected, voltage is constant. The charge is: Q = CV Ratio of charges: Q₂ Q₁ = C₂ C₁ = ₀ A/(3 + 2/k) ₀ A/5 = 5 3 + 2/k Given that charge increases by 25%: Q₂ = 1.25 Q₁ 5 3 + 2/k = 1.25 5 = 1.25(3 + 2/k) 5 = 3.75 + 2.5/k 1.25