A parallel plate capacitor has an area of 0.5 m ^2 and a plate separation of 8.85 mm . A constant displacement current of 2 mA flows through the capacitor. If the rate of change of potential difference across the plates is x 10^6 V/s , the value of x is _______. (Given: Permittivity of free space ₀ = 8.85 10⁻¹² C ^2 N ⁻¹ m ⁻² )

Step-by-step solution

Capacitance of the parallel plate capacitor is given by C = ₀ A d Substituting the given values: C = 8.85 10⁻¹² 0.5 8.85 10⁻³ = 0.5 10⁻⁹ F The displacement current is given by i_d = C dV dt Rearranging for the rate of change of potential difference: dV dt = i_d C = 2 10⁻³ 0.5 10⁻⁹ = 4 10^6 V/s Comparing with x 10^6 V/s , we get x = 4 . Answer: 4