A capacitor of $30 \mu \mathrm{F}$ charged up to $500$ volt is connected in parallel with another capacitor of $15$ $\mu \mathrm{F}$ which is charged up to $300 \mathrm{V}$. The common potential is

Three capacitors $\mathrm{C}_{1}, \mathrm{C}_{2}$ and $\mathrm{C}_{3}$ are connected to a battery of e.m.f. $120 \mathrm{V}$ as shown in the figure. The potential difference across $C_{1}$ is

A $8 \mu \mathrm{F}$ capacitor is fully charged across a $12 \mathrm{V}$ battery. It is then disconnected from the battery and connected to an uncharged capacitor. If the voltage across the capacitor becomes $3 \mathrm{V}$, then the capacitance of the uncharged capacitor will be

In polar dielectrics, tiny electric dipoles are randomly oriented

The capacitance of a parallel plate capacitor with air as dielectric is $C$. If a slab of dielectric constant $K$ and of the same thickness as the separation between the plates is introduced so as to fill ${\frac{1}{4}}^{\mathrm{th}}$ of the capacitor (shown in figure), then the new capacitance is,

A parallel plate capacitor is filled with dielectric as shown in the figure. Its capacitance has a ratio with that without dielectric as

A parallel plate capacitor is charged to a certain potential difference. A slab of thickness $3 \mathrm{mm}$ is inserted between the plates and it becomes necessary to increase the distance between the plates by $2.4 \mathrm{mm}$ to maintain the same potential difference. The dielectric constant of the slab is