A parallel plate capacitor without any dielectric has capacitance C 0 . A dielectric slab is made up of two dielectric slabs of dielectric constants K and 2K and is of same dimensions as that of cap

Question

A parallel plate capacitor without any dielectric has capacitance $C_{0}$ . A dielectric slab is made up of two dielectric slabs of dielectric constants K and 2K and is of same dimensions as that of capacitor plates and both the parts are of equal dimensions arranged serially as shown. If this dielectric slab is introduced (dielectric K enters first) in between the plates at constant speed, then variation of capacitance with time will be best represented by

TestHub · Accepted Answer

C = C 1 ​ + C 2 ​ C = d ε 0 ​ a ( L − x ) ​ + d K ε 0 ​ a x ​ C = d ε 0 ​ a ​ [ L − x + K x ] C = d ε 0 ​ a ​ [ L + x ( K − 1 )] C = d ε 0 ​ a ​ [ L + v t ( K − 1 )] t 0 ​ = v L ​ x = v ( t − t 0 ​ )

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