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

The distance between the plates of a parallel plate capacitor is $4 \ mm$ and the potential difference is $60 \ V$. If the distance between the plates is increased to $12 \ mm$,then:

$A$ parallel plate capacitor is made up of a stair-like structure with a plate area $A$ for each stair,and the plates are separated by distances $b$,$2b$,and $3b$ as shown in the figure. The capacitance of the arrangement is $\frac{ x }{15} \frac{\varepsilon_{0} A }{ b }$. The value of $x$ is ............

One plate of a parallel plate capacitor is connected to a spring as shown in the figure. The area of each plate of the capacitor is $A$ and the distance between the plates is $d$,when the battery is not connected and the spring is unstretched. After connecting the battery,in the steady state the distance between the plates is $0.75 d$,then the force constant of the spring is

Six metallic plates,each with a surface area $A$ on one side,are placed at a distance $d$ from each other. The alternate plates are connected to points $P$ and $Q$ as shown in the figure. The capacitance of the system is:

The electric field between the plates of a parallel plate capacitor is $E$. If the charge on the plates is $Q$, then the force on each plate is: