A parallel plate capacitor has plate area 100 m 2 and plate separation of 10 m . The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10 . The resultant capacitance of the system is x pF . The value of ε 0 = 8 . 85 × 10 - 12 F m - 1 . The value of x to the nearest integer is ______.

Step-by-step solution

Here, Plate area A = 100   m 2 Using, Capacity of parallel plate capacitor is, C = k ε 0   A   d ; where d is separation between the plates and k is dielectric constant. The capacitance with dielectric will be, C 1 = 10 ϵ 0 ( 100 ) 5 = 200 ϵ 0 The capacitance without dielectric or air will be, C 2 = ϵ 0 ( 100 ) 5 = 20 ϵ 0 C 1   &   C 2 are in series so, C eqv.  = C 1 C 2 C 1 + C 2 = 4000 ϵ 0 220 = 160 . 9 × 10 - 12 ≃ 161 pF