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Question: Answered & Verified by Expert
A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants K1, K2, K3, K4 arranged as shown in the figure. The effective dielectric constant K will be:

PhysicsCapacitanceJEE MainJEE Main 2019 (09 Jan Shift 2)
Options:
  • A K=K1K2K1+K2+K3.K4K3+K4
  • B K=K1+K2K3+K42K1+K2+K3+K4
  • C K=(K1+K4)(K2+K3) 2K1+K2+K3+K4 
  • D K=K1+K2(K3+K4)K1+K2+K3+K4
Solution:
2851 Upvotes Verified Answer
The correct answer is: K=K1K2K1+K2+K3.K4K3+K4



C1 and C2 are in series.

The equivalent capacitance of C1 and C2 is

C12=0A2d2K1+d2K2=0AdK1K2K1+K2

C3 and C4 are in series

C34=0A2d2K3+d2K4=0AdK3K4K3+K4

Ceq=C12+C34=0AdK1K2K1+K2+K3K4K3+K4

Keq=K1K2K1+K2+K3.K4K3+K4

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