A circuit is connected as shown in the figure with the switch $S$ open. When the switch is closed, the total amount of charge that flows from $Y$ to $X$ is

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 $\frac{d}{3}$ initially. Suppose the liquid level decreases at a constant speed $V$, the time constant as a function of time $t$ is figure

A $2 \mathrm{\mu F}$ capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch $S$ is turned to the position $2$ is

In the given circuit, a charge of $+80 \mathrm{\mu C}$ is given to the upper plate of the $4 \mathrm{\mu F}$ capacitor. Then in the steady state, the charge on the upper plate of the $3 \mathrm{\mu F}$ capacitor is

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance $C$. The switch $S_1$ is pressed first to fully charge the capacitor $C_1$ and then released. The switch $S_2$ is then pressed to charge the capacitor $C_2$. After some time, $S_2$ is released and then $S_3$ is pressed. After some time.

A parallel plate capacitor has a dielectric slab of a 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 $Q_2$. Choose the correct option/options, ignoring edge effects.

A parallel plate capacitor having plates of area $S$ and plate separation $d$, has the capacitance $C_1$ in air. When two dielectrics of different relative permittivity $\left({\epsilon }_1=2 \text{and} {\epsilon }_2=4\right)$ are introduced between the two plates as shown in the figure, the capacitance becomes $C_2$. The ratio $\frac{C_2}{C_1}$ is, 

Three identical capacitors $C_1$, $C_2$ and $C_3$ have a capacitance of $1.0 \mathrm{\mu F}$ 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 $\left(\mathrm{emf}\right) V_0=8V$. 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 $5 \mathrm{\mu C}$. The value of ${\epsilon }_r$