Capacitance

Two metallic plates form a parallel plate capacitor. The distance between the plates is '$d$'. A metal sheet of thickness $\dfrac d2$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?

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 :

Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R).

Assertion (A) : Non-polar materials do not have any permanent dipole moment.

Reason (R) : When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it's individual atom or molecule coincides with the centre of the negative charge distribution.

In the light of above statements, choose the most appropriate answer from the options given below.

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

A parallel plate capacitor with plate area A and plate separation d = 2 m has a capacitance of $4\ \mu$F. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant K = 3 (as shown in figure) will be :

A force of 10 N acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be.

A capacitor of capacitance 50 pF is charged by 100 V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is ______ nJ.

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.

A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15. Then the energy of capacitor will :

A capacitor is discharging through a resistor R. Consider in time $t_1$, the energy stored in the capacitor reduces to half of its initial value and in time $t_2$, the charge stored reduces to one eighth of its initial value. The ratio $t_1/t_2$ will be

$C_o$ 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 :

A condenser of 2 $\mu$F capacitance is charged steadily from 0 to 5 C. Which of the following graph represents correctly the variation of potential difference (V) across it's plates with respect to the charge (Q) on the condenser ?

Capacitance of an isolated conducting sphere of radius $R_1$ becomes n times when it is enclosed by a concentric conducting sphere of radius $R_2$ connected to earth. The ratio of their radii $\left(\dfrac{R_2}{R_1}\right)$ is :

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.

A source of potential difference V is connected to the combination of two identical capacitors as shown in the figure. When key 'K' is closed, the total energy stored across the combination is $E_1$. Now key 'K' is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored across the combination is now $E_2$. The ratio $E_1/E_2$ will be :

As show in the figure, in steady state, the charge stored in the capacitor is ______ $\times10^{-6}$ C.

A parallel plate capacitor with width 4 cm, length 8 cm and separation between the plates of 4 mm is connected to a battery of 20 V. A dielectric slab of dielectric constant 5 having length 1 cm, width 4 cm and thickness 4 mm is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be ______ $\varepsilon_0$ J.

(Where $\varepsilon_0$ is the permittivity of free space)