All the plates shown in the figure are parallel to each other, the area of each plate is A, and the separation between each pair of facing plates is d. The equivalent capacitance between points A and B is

Options

A. `(2epsilon_(0)A)/(3d)`
B. `(2epsilon_(0)A)/(3d)`
C. `(2epsilon_(0)A)/(5d)`
D. `(3epsilon_(0)A)/(5d)`

Answer

D

Explanation

We can number all the plate surfaces, except the ones on the outside, starting from the top. Then, we can draw a circuit diagram, such that each pair of facing surfaces becomes a capacitor and a zero-resistance wire can be shown between the two faces of the same plate. This will result in the following diagram:
There are four capacitors, and the capacitance of each one of them,
`C=(epsi_(0)A)/(d)`, So, the capacitance between M and N, `C_(MN)=(3)/(5) C=(3epsi_(0)A)/(5d)`