The outer sphere of a spherical air capacitor is earthed. For increasing its capacitance

A parallel plate capacitor has plate area $100\, m ^{2}$ and plate separation of $10\, m$. The space between the plates is filled up to a thickness $5\, m$ with a material of dielectric constant of $10 .$ The resultant capacitance of the system is $'x'$ $pF$. The value of $\varepsilon_{0}=8.85 \times 10^{-12} F \cdot m ^{-1}$ The value of $'x'$ to the nearest integer is............

In a parallel plate capacitor with air between the plates, each plate has an area of $6 \times 10^{-3}\; m ^{2}$ and the distance between the plates is $3 \;mm$ the capacitance of the capacitor is $17.71 \;pF$. If this capacitor is connected to a $100\; V$ supply, $3\; mm$ thick mica sheet (of dielectric constant $=6$ ) were inserted between the plates,

$(a)$ while the voltage supply remained connected.

$(b)$ after the supply was disconnected.

There are two identical capacitors, the first one is uncharged and filled with a dielectric of constant $K$ while the other one is charged to potential $V$ having air between its plates. If two capacitors are joined end to end, the common potential will be

Write the capacitance of parallel plate capacitor with medium of dielectric of dielectric constant $\mathrm{K}$.

Two identical charged spheres are suspended by string of equal lengths. The string make an angle of $37^{\circ}$ with each other. When suspended in a liquid of density $0.7 \mathrm{~g} / \mathrm{cm}^3$, the angle remains same. If density of material of the sphere is $1.4 \mathrm{~g} / \mathrm{cm}^3$, the dielectric constant of the liquid is_____$\left(\tan 37^{\circ}=\frac{3}{4}\right)$.