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

B, C

Explanation

(between two successive plates).
The effective capacity has to be found between `V_1` and `V_2`

`C_(n et)=C+((2C)(C))/(2C+C)=5/3C=5/3(epsilon_0A)/d`
`q_3=+[C(V_1-V_2)+C(V_1-V_3)]`
`=(epsilon_0A)/d[V_0+V_0/3]=(4epsilon_0AV_0)/(3d)`
`q_5=C(V_3-V_2)=((epsilon_0A)/d)((2V_0)/3)`
`(2epsilonK_0AV_0)/(3d)`