Question

If the area of each plate is A and then successive separations are `d, 2d` and `3d`, then find the equivalent capacitance across A and B.
.
A. `(epsilon_0A)/(6d)`
B. `(epsilon_0A)/(4d)`
C. `(3epsilon_0A)/(4d)`
D. `(epsilon_0A)/(3d)`

Answer 1

Correct Answer - B

Plates can be rearranged as shown in fig. plates 1 and 2 and plates 3 and 4 form two capacitors which are in series between A and B. plates 2 and 3 do not form any capacitor as they are at same potential
so, `C_(eq)=(C_(1)C_(2))/(C_(1)+C_(2))=(((E_(o)A)/(d))xx((epsilon_(0)A)/(3d)))/((epsilon_(0)A)/(d)+(epsilon_(0)A)/(3d))`
`=(epsion_(0)A)/(4d)`