Question

Six plates of equal area A and plate separation as shown in figure as shown are arranged. The equivalent capacitance between A and B is

A. `(epsilon_0A)/(d)`
B. `(2epsilon_0A)/d`
C. `(3epsilon_0A)/d`
D. `(epsilon_0A)/d`

Answer 1

Correct Answer - A

Given paltes can be rearranged as shown
`C_(1)=(epsilon_(0)A)/(d),C_(2)=(epsilon_(0)A)/(2d)`
`C_(3)=(epsilon_(0)A)/(3d),C_(4)=(epsilon_(0)A)/(2d),C_(5)=(epsilon_(0)A)/(d)`
`C_(1)` and `C_(2)` are in series and its effective capacity is
`((epsilon_(0)A)/(d)xx(epsilon_(0)A)/(2d))/((epsilon_(0)A)/(d)+(epsilon_(0)A)/(2d))=(epsilon_(0)A)/(3d)`
effective capacitance of `C_(4)`
and `C_(3)=(epsilon_(0)A)/(3d)`
`C_(AB)=(epsilon_(0)A)/(3d)+(epsilon_(0)A)/(3d)+(epsilon_(0)A)/(3d)=(epsilon_(0)A)/(d)`