Series and parallel combinations

The difference in the capacitance (in F) between the metal plates at $t=0$ and that at $t=500$ s is $(8-n)\epsilon_0$, where $\epsilon_0$ is the permittivity of free space. The value of $n$ is:

A parallel plate air capacitor has a capacitance $C$. When it is half filled as show in figure with a dielectric constant $K=5$, the percentage increase in the capacitance is ________.

From the circuit given below, the capacitance between terminals $A$ and $B$ shown in the circuit is ________ μF.
(take $C_1=C_2=C_3=1$ μF and $C_4=2$ μF.)

Four identical thin, square metal sheets, $S_1$, $S_2$, $S_3$ and $S_4$, each of side $a$ are kept parallel to each other with equal distance $d\ (\ll a)$ between them, as shown in the figure. Let $C_0 = \varepsilon_0 a^2/d$, where $\varepsilon_0$ is the permittivity of free space.

Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

A container has a base of $50\ \text{cm}\times5\ \text{cm}$ and height 50 cm, as shown in the figure. It has two parallel electrically conducting walls each of area $50\ \text{cm}\times50\ \text{cm}$. The remaining walls of the container are thin and non-conducting. The container is being filled with a liquid of dielectric constant 3 at a uniform rate of $250\ \mathrm{cm^3\,s^{-1}}$. What is the value of the capacitance of the container after 10 seconds?

[Given: Permittivity of free space $\epsilon_0 = 9\times10^{-12}\ \mathrm{C^2N^{-1}m^{-2}}$, the effects of the non-conducting walls on the capacitance are negligible]

In the following circuit $C_1 = 12\ \mu F$, $C_2 = C_3 = 4\ \mu F$ and $C_4 = C_5 = 2\ \mu F$. The charge stored in $C_3$ is _____ $\mu C$.

The equivalent capacitance between points A and B in below shown figure will be ______ $\mu$F.

Two capacitors having capacitance $C_1$ and $C_2$ respectively are connected as shown in figure. Initially, capacitor $C_1$ is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor $C_1$ is now connected to uncharged capacitor $C_2$ by closing the switch S. The amount of charge on the capacitor $C_2$, after equilibrium, is :

The charge on capacitor of capacitance $15\ \mu F$ in the figure given below is :

A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is $\dfrac x{15}\dfrac{\varepsilon_0A}b$. The value of $x$ is ______.

A capacitor $C_1$ of capacitance 5 $\mu$F is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor $C_2$ of capacitance 10 $\mu$F as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor $C_2$ is ______ $\mu$C.

$C_o$ is the capacitance of a parallel plate capacitor with air as a medium between the plates (as shown in Fig. 1). If half space between the plates is filled with a dielectric of relative permittivity $\varepsilon_r$ (as shown in Fig. 2), the new capacitance of the capacitor will be :

Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9. The final potential difference across the combination of capacitors will be ______ V.

The total charge on the system of capacitors $C_1=1$ $\mu$F, $C_2=2$ $\mu$F, $C_3=4$ $\mu$F and $C_4=3$ $\mu$F connected in parallel is :

(Assume a battery of 20 V is connected to the combination)

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness ($t_1$ and $t_2$) as shown in figure. The two different dielectric materials are separated by a conducting foil F. The voltage of the conducting foil is ______ V.

Two capacitors, each having capacitance 40 μF are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant K such that the equivalence capacitance of the system became 24 μF. The value of K will be :

Combination of four parallel plate air capacitors is shown in figure. Separation between the plate P$_1$ & P$_2$ is $\dfrac d3$ and separation between the plates P$_2$ and P$_3$ is d. The equivalent capacitance of the configuration is _______ μF.

(Given $\dfrac{\epsilon_0A}d=4$ μF. Where A = Area of plates)

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be :

Two capacitors with capacitance values $C_1 = 2000 \pm 10$ pF and $C_2 = 3000 \pm 15$ pF are connected in series. The voltage applied across this combination is $V = 5.00 \pm 0.02$ V. The percentage error in the calculation of the energy stored in this combination of capacitors is ______.

In the circuit shown, initially there is no charge on capacitors and keys $S_1$ and $S_2$ are open. The values of the capacitors are $C_1 = 10\ \mu$F, $C_2 = 30\ \mu$F and $C_3 = C_4 = 80\ \mu$F.

Which of the statement(s) is/are correct?