Capacitance — JEE Advanced PYQs

A container of height 2 m, length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates (${\mathrm{M}}_1$ and ${\mathrm{M}}_2$) which extend far beyond the vertical walls in all directions. The container is partitioned into two eq …

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 $C_0={\epsilon }_0{\mathrm{a}}^2/\mathrm{d}$, where …

A container has a base of 50 cm × 5 cm and height 50 cm, as shown in the figure. It has two parallel electrically conducting walls each of area 50 cm × 50 cm. The remaining walls of the container are thin and non-conducting. The container is being filled with a liquid of dielectr …

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 ____ $\mu C$.

A medium having dielectric constant $K>1$ fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is $d$. The capacitor is connected to a battery of voltage $V$, as shown in Figure (a). Now, both the plates …

In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes ${\mathrm{q}}_1\mu$C. Then S is switched to position Q. After a long time, the charge on the capacitor is ${\mathrm{q}}_2\mu$C.

The magnitude of …

In the circuit shown, initially there is no charge on capacitors and keys ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ are open. The values of the capacitors are ${\mathrm{C}}_1=10\mu \mathrm{F},{\mathrm{C}}_2=30\mu \mathrm{F}$ and ${\mathrm{C}}_3={\mathrm{C}}_4=80\mu \mathrm{F}$ …

A parallel plate capacitor of capacitance C has spacing d between two plates having area A. The region between the plates is filled with N dielectric layers, parallel to its plates, each with thickness $\delta =\frac{\mathrm{d}}{\mathrm{N}}$. The dielectric constant of the …

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 …

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 (${\epsilon }_1=2$ and ${\epsilon }_2=4$) are introduced between the two plates as shown in the figure, the capacitan …

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 $C_1$. W …

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 so …

Two large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage source of potential difference $X$. A proton is released at rest midway between the two plates. It is found to move at $45^{\circ }$ to the vertical JUST after release. Then …

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

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

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