The capacitance of a parallel plate capacitor is 2.5 F . When it is half filled with a dielectric as shown in figure, its capacitance becomes 5 F . The dielectric constant of the dielectric is

Step-by-step solution

Given C = ₀ ~A ~d =2.5 F When half filled with air, C ₁= ₀( ~A / 2) d = ₀ ~A 2 ~d ( _ r =1 ) When half filled with a dielectric, C ₂= _ r ₀( ~A / 2) d = _ r ₀ ~A 2 ~d , From the figure, it can be seen that C ₁ and C ₂ are in parallel configuration. array ll & C _ eq = C ₁+ C ₂ & Given, C _ eq =5 F & 5 F = ₀ ~A 2 ~d + _ r ₀ ~A 2 ~d & 5= 2.5 2 + _ r 2.5 2 & 3.75 1.25 = _ r & _ r =3 array