A parallel-plate capacitor filled with air is to be constructed to store 12 C of charge when operated at 1200 V . Determine the minimum possible plate area for this capacitor. The dielectric strength of air is given as 3 10^6 V m ⁻¹ .

Step-by-step solution

Given Q = 12 10⁻⁶ C , V = 1200 V , and E_ max = 3 10^6 V m ⁻¹ . The capacitance of the capacitor is given by C = Q V . For a parallel-plate capacitor, C = ₀ A d . The electric field between the plates is E = V d , which gives d = V E . Substituting d in the capacitance formula: C = ₀ A E V Equating the two expressions for C : Q V = ₀ A E V A = Q ₀ E For the minimum possible plate area, the electric field must be at its maximum permissible value (dielectric strength), i.e., E = E_ max . A_ min = Q ₀ E_ max A_ min =