Dielectrics

Three identical capacitors $C_1$, $C_2$ and $C_3$ have a capacitance of $1.0\ \mu$F each and they are uncharged initially. They are connected in a circuit as shown in the figure and $C_1$ is then filled completely with a dielectric material of relative permittivity $\epsilon_r$. The cell electromotive force (emf) $V_0 = 8$ V. First the switch $S_1$ is closed while the switch $S_2$ is kept open. When the capacitor $C_3$ is fully charged, $S_1$ is opened and $S_2$ is closed simultaneously. When all the capacitors reach equilibrium, the charge on $C_3$ is found to be $5\ \mu$C. The value of $\epsilon_r$ = ______.

A combination of parallel plate capacitors is maintained at a certain potential difference.

When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2.4 mm. Find the dielectric constant of the slab.

A parallel plate capacitor having plates of area $S$ and plate separation $d$, has capacitance $C_1$ in air. When two dielectrics of different relative permittivities ($\varepsilon_1=2$ and $\varepsilon_2=4$) are introduced between the two plates as shown in the figure, the capacitance becomes $C_2$. The ratio $\dfrac{C_2}{C_1}$ is

A parallel plate capacitor has a dielectric slab of dielectric constant $K$ between its plates that covers 1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is $C$ while that of the portion with dielectric in between is $C_1$. When the capacitor is charged, the plate area covered by the dielectric gets charge $Q_1$ and the rest of the area gets charge $Q_2$. The electric field in the dielectric is $E_1$ and that in the other portion is $E_2$. Choose the correct option/options, ignoring edge effects.

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is $3\times10^4$ V/m, the charge density of the positive plate will be close to :

A parallel plate capacitor is made of two plates of length $l$, width $w$ and separated by distance $d$. A dielectric slab (dielectric constant K) that fits exactly between the plates is held near the edge of the plates. It is pulled into the capacitor by a force $F=-\dfrac{\partial U}{\partial x}$ where U is the energy of the capacitor when dielectric is inside the capacitor up to distance $x$ (See figure). If the charge on the capacitor is Q then the force on the dielectric when it is near the edge is :

The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation :
$$K(x)=K_o+\lambda x\quad(\lambda=\text{ a constant})$$
The capacitance C, of this capacitor, would be related to its 'vacuum' capacitance $C_o$ as per the relation :

The gap between the plates of a parallel plate capacitor of area A and distance between plates d, is filled with a dielectric whose permittivity varies linearly from $\epsilon_1$ at one plate to $\epsilon_2$ at the other. The capacitance of capacitor is :

A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current $I_R$ through the resistor and voltage $V_C$ across the capacitor are compared in the two cases. Which of the following is/are true?

A parallel plate capacitor C with plates of unit area and separation $d$ is filled with a liquid of dielectric constant $K=2$. The level of liquid is $\frac d3$ initially. Suppose the liquid level decreases at a constant speed $V$, the time constant as a function of time $t$ is