Three dielectrics of relative permittivities `epsilon_(r_(1))=1,epsilon_(r_(2))=2`, and `epsilon_(r_(3))=3`
are introduced in a parallel plate capacitor of plate A and B. Find equivalent capacitance between A and B
.

Explanation

The given system can be made equivalent to two capcitors `C_(1)` and `C_(2)` in parallel.
For upper part
,
`C_(1)=(epsilon_(0)epsilon_(r_(1))(A/2))/(d)=(epsi_(0)A)/(2d)`
For lower part
`C_(2)=(epsilon_(0)(A/2))/((d//2)/(epsi_(r_(2)))+(d//2)/epsi_(r_(2)))=(epsi_(0)A//2)/(d/2(1/2+1/3))=(6epsi_(0)A)/(5d)`
Then `C_(AB)=C_(1)+C_(2)`("because" `C_(1)` and `C_(2)` are in parallel)
`=(epsilon_(0)A)/(2d)+(6epsilon_(0)A)/(5d)=(17epsilon_(0)A)/(10d)`.