A parallel plate capacitor has plates of area A separated by distance ' $d$ $$ ' between them. It is filled with a dielectric which has a dielectric constant that varies as $k\left(n\right)=k(1+$ $\alpha n)$ $$ $$ where ' $$ $x$ ' is he distance measured from one of the plates.

If $\left(\alpha \mathrm{d}\right)<<1$ $$ , the total capacitance of the system is best given by the expression:

Six capacitors each of capacitance of  $2\mu F$  are connected as shown in the figure. The effective capacitance between A and B is

In the circuit shown, charge on the $5\mu \mathrm{F}$ $$ capacitor is:

A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as

ε(x) = ε? + kx, for 0 < x ≤ d/2
ε(x) = ε? + k(d-x), for d/2 ≤ x ≤ d
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Four metallic plates, each with a surface area A, are placed at a distance d from each other as shown in the figure. If points A and B is connected with a battery of emf V, then the charge on the plate a will be   

A cube of side a has charge q at two diagonally opposite vertices as shown in the figure. The net electric potential at the centre of the cube will be