Electrostatic Potential And Capacitance Practice Questions

A parallel plate capacitor with width $4 {\text{cm}}$, length $8 {\text{cm}}$ and separation between the plates of $4 {\text{mm}}$ is connected to a battery of $20 {\text{V}}$. A dielectric slab of dielectric constant 5 having length $1 {\text{cm}}$, width $4 {\text{cm}}$ and thickness $4 {\text{mm}}$ is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be _______ $E_0 {\text{J}}$. (Where $E_0$ is the permittivity of free space) [27-Jul-2022-Shift-2]

The equivalent capacitance between points $A$ and $B$ in below shown figure will be _______$\mu {\text{F}}$ [25-Jun-2022-Shift-1]

A capacitor ${\text{C}}_1$ of capacitance $5 \mu {\text{F}}$ is charged to a potential of $30 {\text{V}}$ using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor ${\text{C}}_2$ of capacitance $10 \mu {\text{F}}$ as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor ${\text{C}}_2$ is ____$\mu {\text{C}}$ [28-Jun-2022-Shift-2]

The charge on capacitor of capacitance $15 \mu {\text{F}}$ in the figure given below is : [26-Jun-2022-Shift-2]

A parallel plate capacitor is made up of stair like structure with a plate area ${\text{A}}$ of each stair and that is connected with a wire of length ${\text{b}}$, as shown in the figure. The capacitance of the arrangement is $\;\frac{x}{15} \;\frac{E_0 A}{b}$. The value of ${\text{x}}$ is_____ [27-Jun-2022-Shift-2]

Two capacitors having capacitance ${\text{C}}_1$ and ${\text{C}}_2$ respectively are connected as shown in figure. Initially, capacitor ${\text{C}}_1$ is charged to a potential difference ${\text{V}}$ volt by a battery. The battery is then removed and the charged capacitor ${\text{C}}_1$ is now connected to uncharged capacitor ${\text{C}}_2$ by closing the switch ${\text{S}}$. The amount of charge on the capacitor ${\text{C}}_2$, after equilibrium, is : [26-Jun-2022-Shift-1]

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 ${\text{F}}$. The voltage of the conducting foil is V. [26-Jul-2022-Shift-1]

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 thecharge $(Q)$ on the condenser? [25-Jul-2022-Shift-1]

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 : [26-Jul-2022-Shift-2]

Two identical thin metal plates has charge $q_1$ and $q_2$ respectively such that $q_1 > q_2$. The plates were brought close to each other to form a parallel plate capacitor of capacitance ${\text{C}}$. The potential difference between them is: [29-Jul-2022-Shift-2]

A capacitor of capacitance $50 {\text{pF}}$ is charged by $100 {\text{V}}$ source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is____ nJ. [27-Jun-2022-Shift-1]

$C_0$ 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 $\epsilon _r$ (as shown in Fig. 2), the new capacitance of the capacitor will be : [30-Jun-2022-Shift-1]

A slab of dielectric constant ${\text{K}}$ has the same cross-sectional area as the plates of a parallel plate capacitor and thickness $\;\frac{3}{4} {\text{d}}$, where $d$ is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be :(Given ${\text{C}}_0=$ capacitance of capacitor with air as medium between plates.) [28-Jul-2022-Shift-2]

A parallel plate capacitor with plate area ${\text{A}}$ and plate separation ${\text{d}}=2 {\text{m}}$ has a capacitance of $4 \mu {\text{F}}$. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant ${\text{K}}=3$ (as shown in figure) will be [26-Jun-2022-Shift-2]

If the charge on a capacitor is increased by $2 {\text{C}}$, the energy stored in it increases by $44 \%$. The original charge on the capacitor is (in C) [24-Jun-2022-Shift-2]

A force of $10 {\text{N}}$ 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. [27-Jun-2022-Shift-1]

Two capacitors, each having capacitance $40 \mu {\text{F}}$ are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant ${\text{K}}$ such that the equivalence capacitance of the system became $24 \mu {\text{F}}$. The value of ${\text{K}}$ will be : [28-Jul-2022-Shift-1]

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 $(\;\frac{R_{2}}{R_{1}})$ is : [25-Jul-2022-Shift-2]