Five identical conducting plates, `1, 2,3,4` and `5` are fixed parallel pltes equidistant from each other (see figure). A conductor connects plates 2 and 5 while another conductor joins 1 and 3. The junction of 1 and 3 and the plate 4 are connected to a source of constant emf `V_0`. Find

(a) the effective capacity of the system between the terminals of source.
(b) the charges on the plates 3 and 5. Given, `d =` distance between any two successive plates and `A = ` area of either face of each plate.

Answer

(i) `(5)/(3) ((in_(0)A)/(d))`;
(ii) `Q_(3) = (4)/(3) ((in_(0)AV_(a))/(d)), Q_(5) = (2)/(3)((in_(0)AV_(a))/(d))`

Explanation

Let potential on plates `2 & 5` in `x`. Since plate `3 &5` is isolated so `Sigmaq = 0`
`(x-V_(0)) C +(x-V_(0))C +xC = 0`
`x = (2V_(0))/(3)`

`q_(3) = (V_(0)-(2V_(0))/(3)) C+V_(0)C`
`q_(3) = (CV_(0))/(3)+CV_(0) = (4CV_(0))/(3) = (4)/(3)(inAV_(0))/(d)`,
`q_(5) = (2CV_(0))/(3) = (2)/(3) (in_(0)AV_(0))/(d)`
`C_(eq) = (Q)/(V_(0)) = (5CV_(0))/(3V_(0)) = (5C)/(3) = (5in_(0)A)/(d)`