Potential and Potential Difference

Q. Two capacitors of capacities $2C$ and $C$ are joined in parallel and charged up to potential $V$. The battery is removed and the capacitor of capacity $C$ is filled completely with a medium of dielectric constant $K$. The potential difference across the capacitors will now be :

1. $\frac{3V}{K}$
2. $\frac{V}{K}$
3. $\frac{3V}{K+2}$
4. $\frac{V}{K+2}$

Q. A capacitor $0.2\mu \text{F}$ is charged to $600\text{V}.$ After removing the battery, it is connected to $1\mu \text{F}$ capacitor in parallel. The voltage across $1\mu \text{F}$ will become

1. $300\text{V}$
2. $600\text{V}$
3. $100\text{V}$
4. $120\text{V}$

Q. A parallel plates capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved farther apart by means of insulating handles, then

1. the charge on the capacitor increases
2. the voltage across the plates increases
3. the capacitance increases
4. the electrostatic energy stored in the capacitor increases.

Q. Five capacitors are connected as shown in the figure. Initially, all capacitors are uncharged and $S$ is open. When $S$ is closed, then the potential difference between points $\text{M}$ and $\text{N}$ is :
[assume steady state to be achieved after $S$ closes]

1. $14\text{V}$
2. $12\text{V}$
3. $10\text{V}$
4. $15\text{V}$

Q. A parallel plate capacitor has $1\mu \text{F}$ capacitance. One of its two plates is given $+2\mu \text{C}$ charge and the other plate, $+4\mu \text{C}$ charge. The potential difference developed across the capacitor is,

1. $5\text{V}$
2. $1\text{V}$
3. $2\text{V}$
4. $3\text{V}$

Q. An uncharged parallel-plate capacitor having a dielectric of dielectric constant $K$ is connected to a similar air cored parallel-plate capacitor charged to a potential $V_0$. The two share the charge and the common potential becomes $V$. The dielectric constant $K$ is

1. $\frac{V_0}{V}-1$
2. $\frac{V_0}{V}+1$
3. $\frac{V}{V_0}-1$
4. $\frac{V}{V_0}+1$

Q. A parallel-plate capacitor has plates of area $A$ and separation $d$ and is charged to a potential difference $V$. The charging battery is then disconnected and the plates are pulled apart until their separation is $2d$. What is the work required to separate the plates?

1. $\frac{2{\in }_{0}A{V}^2}{d}$
2. $\frac{{\in }_{0}A{V}^2}{d}$
3. $\frac{3{\in }_{0}A{V}^2}{2d}$
4. $\frac{{\in }_{0}A{V}^2}{2d}$

Q. Three uncharged capacitors of capacitance $C_1=1\mu \text{F},C_2=2\mu \text{F}$ and $C_3=3\mu \text{F}$ are connected as shown in figure. If potential at shown points are $V_A=10\text{V};V_B=25\text{V}$ and $V_D=20\text{V}$. The potential at point $O$ will be

1. $20\text{V}$
2. $10\text{V}$
3. $30\text{V}$
4. $40\text{V}$

Q. Four charges $+q,-q,+q$ and $-q$ are placed in order on the four consecutive corners of a square of side $a$. The work done in interchanging the positions of any two neighbouring charges of the opposite sign is

1. $\frac{q^2}{4\pi {\epsilon }_{0}a}(-4+\sqrt{2})$
2. $\frac{q^2}{4\pi {\epsilon }_{0}a}(4+2\sqrt{2})$
3. $\frac{q^2}{4\pi {\epsilon }_{0}a}(4-2\sqrt{2})$
4. $\frac{q^2}{4\pi {\epsilon }_{0}a}(4+\sqrt{2})$

Q. A parallel plate capacitor of capacitance $90\text{pF}$ is connected to a battery of emf $20\text{V}$. If a dielectric material of dielectric constant $K=\frac{5}{3}$ is inserted between the plates, the magnitude of induced charge will be:

1. $0.9\text{nC}$
2. $1.2\text{nC}$
3. $0.3\text{nC}$
4. $2.4\text{nC}$

Q. A parallel plate capacitor having capacitance $12\text{pF}$ is charged by a battery to a potential difference of $10\text{V}$ between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant $6.5$ is placed between the plates. The work done by the capacitor on the slab is:

1. $560\text{pJ}$
2. $508\text{pJ}$
3. $692\text{pJ}$
4. $600\text{pJ}$

Q. A parallel-plate capacitor has plates of area $200c{m}^2$ and separation between the plates $1mm$. The potential difference developed if a charge of $1nC(i.e.1\times {10}^{-9}C)$ is given to the capacitor is something, then if the plate separation is now increased to $2mm$, what will be the new potential difference?

Q. A parallel plate capacitor is charged by a battery and after charging the battery is removed. Now the distance between the plates is reduced. Choose the correct statement

1. Electric field is not constant
2. Potential difference is increased
3. Capacitance is decreased
4. Electrostatic potential energy is decreased

Q. A parallel plate air capacitor is connected to a battery. If plates of the capacitor are pulled further apart, then which of the following statements are correct?

1. Strength of electric field inside the capacitor remain unchanged, if battery is disconnected before pulling the plate.
2. During the process, work is done by an external force applied to pull the plates whether battery is disconnected or it remain connected.
3. Potential energy in the capacitor decreases if the battery remains connected during pulling plates apart.
4. Potential energy in the capacitor decreases if the battery is disconnected before pulling plates apart.

Q. A parallel plate capacitor of capacitance $200\mu \text{F}$ is connected to a battery of $200\text{V}$. A dielectric slab of dielectric constant $2$ is now inserted into the space between plates of capacitor while the battery remains connected. The change in the electrostatic energy in the capacitor will be
$\text{J}$

Q. A dielectric slab is inserted between the plates of an isolated charged capacitor. Which of the following will remain the same?

1. The electric field in the capacitor
2. The charge on the capacitor
3. The potential difference between the plates
4. The stored energy in the capacitor

Q. The capacity of a condenser is $4\mu F$ and its potential is $100\text{volts}$. The energy released while discharging of capacitor will be

1. $0.02\text{Joule}$
2. $0.05\text{Joule}$
3. $0.025\text{Joule}$
4. $0.04\text{Joule}$

Q. Rows of capacitors containing $1,2,4,8,....\infty$ capacitors, each of capacitance $2\mu \text{F}$, are connected in parallel as shown in figure. The potential difference across $\text{AB}=10\text{volts}$, then:

1. Equivalent capacitance across $\text{AB}$ is $2\mu \text{F}$.
2. Charge on the capacitor in the first row is less than on any other capacitor
3. Charge on the capacitor in the first row is more than on any other capacitor
4. Energy of all the capacitors is $50\text{J}$

Q. A capacitor stores $50\mu \text{C}$ charge when connected across battery. When the gap between the plates is filled with a dielectric, a charge of $100\mu \text{C}$ flows through the battery. Find the dielectric constant of the material inserted.

1. $3$
2. $5$
3. $6$
4. $7$

Q. A parallel plate capacitor with a dielectric of dielectric constant $K$ between the plates has a capacitance $C$ and it is charged to $V\text{Volts}$. The dielectric slab is slowly removed from the capacitor and then re-inserted between its plates. The net work done by the system in this process is:

1. $\frac{1}{2}(K-1)C{V}^2$
2. $C{V}^2(K-1)K$
3. $(K-1)C{V}^2$
4. zero

Q. Two capacitors $\text{A}$ and $\text{B}$ with capacitances $3\mu \text{F}$ and $2\mu \text{F}$ are charged to a potential difference of $100\text{V}$ and $180\text{V}$ respectively. They are connected to an uncharged $2\mu \text{F}$ capacitor $C$ through a switch $S$ as shown. When the switch is pressed, the charge flown in the circuit is

1. $180\mu \text{C}$
2. $190\mu \text{C}$
3. $200\mu \text{C}$
4. $210\mu \text{C}$

Q. A $10\mu \text{F}$ capacitor is fully charged across a $12\text{V}$ battery. The capacitor is then disconnected from the battery and connected across an initially uncharged capacitor $C$. The voltage across each capacitor is now $3\text{V}$. What is the unknown capacitance $C$ (in $\mu \text{F}$)?

Q. A parallel plate capacitor consists of two plates, each with area $A$ and separated by a distance $d$. What will be the work done against electrostatic force in increasing the separation between the plates from $l_1$ to $l_2$, while the potential difference $V$ across the capacitor is kept constant ?

1. $\frac{{ϵ}_{0}A{V}^2}{2}\left(\frac{l_1}{l_1+l_2}\right)$
2. $\frac{{ϵ}_{0}A{V}^2}{2}\left(\frac{l_1}{l_1-l_2}\right)$
3. $\frac{{ϵ}_{0}A{V}^2}{2}\left(\frac{l_1+l_2}{l_1{l}_2}\right)$
4. $\frac{{ϵ}_{0}A{V}^2}{2}\left(\frac{l_2-l_1}{l_1{l}_2}\right)$

Q. A parallel plate capacitor is charged with a battery of emf $V$ volts. After charging, the battery is disconnected and the distance between the plates is increased to $1.5$ times the initial value. The new potential across the plates of the capacitor will become

$[$0.77 Mark$]$

1. $V$
2. $2V$
3. $1.5V$
4. $2.8V$

Q. In the given circuit, the charge on $2\mu \text{F}$ capacitor $($connected to $-ve$ terminal of $25\text{V}$ battery $)$ will be
(Initially, all capacitors are uncharged)

1. $58\mu \text{C}$
2. $60\mu \text{C}$
3. $48\mu \text{C}$
4. $16\mu \text{C}$

Q. Plates of capacitor carries unequal charges as shown in figure, then which statement is wrong

1. $V_A>V_B$
2. $E_A=E_B$
3. $E_C=0$
4. $|E_A|>|E_C|$

Q. Four condensers are joined as shown in the adjoining figure. The capacity of each is $8\mu \text{F}$. The equivalent capacity between the points $A$ and $B$ will be :-

1. $32\mu \text{F}$
2. $2\mu \text{F}$
3. $8\mu \text{F}$
4. $16\mu \text{F}$

Q. The work done in increasing the potential of a capacitor from $V$ volt to $2V$ volt is $W$. Then, the work done in increasing the potential of the same capacitor from $2V$ volt to $4V$ volt will be

1. $W$
2. $8W$
3. $4W$
4. $2W$

Q. $\text{Statement}1:$ A parallel plate capacitor is charged by a battery of voltage $V$. The battery is then disconnected. If the space between the plates is filled with a dielectric, the energy stored in the capacitor will decrease.

$\text{Statement}2:$ The capacitance of a capacitor increases due to the introduction of a dielectric between the plates.

1. Both the statements are correct.
2. Statement 1 is correct, statement 2 is incorrect.
3. Statement 1 is incorrect, statement 2 is correct.
4. Both the statements are incorrect.

Q. A parallel plate capacitors of capacitance $C_0$ is charged to voltage $V$ and then battery is disconnected. A dielectric covering one third area of each plate is now inserted. Charges on plates get redistributed such that portion covered by dielectric and vaccum shares equal amount of charge, then which of the statements are true?

1. Dielectric constant is 2.
2. Charges due to polarization on surface of dielectric is 0.25 $C_{0}V$.
3. Electric field inside dielectric is same as in vaccum.
4. Electric field inside dielectric is $\frac{2}{3}$ of that in vaccum.