$A$ parallel plate capacitor is formed by connecting $n$ plates placed at equal distances alternately. If the capacitance between any two adjacent plates is $C$,find the resultant capacitance.

Two charged capacitors have their outer plates fixed and inner plates connected by a spring of force constant $k$. The charge on each capacitor is $q$. Find the extension in the spring at equilibrium.

The capacitance of a parallel plate capacitor is $12 \ \mu F$. If the distance between the plates is doubled and the area of the plates is halved,then the new capacitance will be ... $\mu F$.

$A$ parallel plate capacitor has $1\,\mu F$ capacitance. One of its two plates is given $+2\,\mu C$ charge and the other plate,$+4\,\mu C$ charge. The potential difference developed across the capacitor is......$V$

$A$ capacitor is made of a flat plate of area $A$ and a second plate having a stair-like structure as shown in the figure. If the area of each stair is $\frac{A}{3}$ and the height of each step is $d$,the capacitance of the arrangement is:

The capacity of a parallel plate capacitor increases with the