Electric potential and capacitance practice · Mixed difficulty

Assertion (A): When two unlike charges are brought nearer, their electrostatic potential energy decreases.

Reason (R) : All conservative forces act in the direction of decreasing potential energy.

Assertion: If the distance between parallel plate of a capacitor is halved and dielectric constant is three times, then the capacitance become 6 times.

Reason: Capacity of the capacitor does not depend upon the nature of the material.

Assertion (A): In a region of constant potential, the electric field is zero and there can be no charge inside the region.

Reason (R): According to Gauss law, charge inside the region should be zero if electric field is zero.

A parallel plate capacitor is charged by a battery after charging the capacitor, the battery is disconnected and if a dielectric plate is inserted between the plates, then which one of the following statements is not correct

You have a parallel plate capacitor, a spherical capacitor and cylindrical capacitor. Each capacitor is charged by and then removed from the same battery. Consider the following situations
(i) separation between the plates of parallel plate capacitor is reduced
(ii) radius of the outer spherical shell of the spherical capacitor is increased
(iii) radius of the outer cylinder of cylindrical capacitor is increased
Which of the following is correct ?

An electric dipole is kept on the axis of a uniformly charged ring at distance $\frac{R}{\sqrt{2}}$ from the centre of the ring. The direction of the dipole moment is along the axis. The dipole moment is ${P}$, the charge of the ring is ${Q}$ and the radius of the ring is ${R}$. The force on the dipole is nearly

Three capacitor each of $6\mu F$ are available. The minimum and maximum capacitances which may be obtained are

The electrostatic potential due to an electric dipole at a distance $r$ varies as:

Assertion (A): Conductors having equal positive charge and volume, must also have same potential.
Reason (R): Potential depends only on charge and volume of conductor.

The potential due to the electric dipole at a distance $r$ from the dipole on the axial line is

Statement-1: The heat produced by a resistor in any time $t$ during the charging of a capacitor in a series circuit is half the energy stored in the capacitor by that time.
Statement-2: Current in the circuit is equal to the rate of increase in charge on the capacitor.

The minimum value of effective capacitance that can be obtained by combining 3 capacitors of capacitances $1\,\,pF,\,\,2\,\,pF$ and $4\,\,pF$ is

A $10\mu F$ capacitor is charged to a potential difference of $1000V.$ The terminals of the charged capacitor are disconnected from the power supply and connected to the terminals of an uncharged $6\mu F$ capacitor. What is the final potential difference across each capacitor

The energy of a charged capacitor is given by the expression ($q =$ charge on the conductor and $C =$ its capacity)

A point charge q is placed at a distance ‘r’ from the centre of an uncharged conducting sphere of radius R. The potential at any point on the sphere is

A parallel plate capacitor is connected to a 5V battery and charged. The battery is then disconnected and a glass slab is introduced between the plates. Then, the quantities that decrease are

If the plates of a charged capacitor are brought closer, then the $p$.($d$) between the plates will

A parallel plate capacitor is charged and then charging battery is disconnected. If the plates are now pulled apart with insulated handless

An electric dipole consisting of two opposite charge of $2 \times {10^{ - 6}}C$ each separated by a distance of 3cm is placed in an electric field of $2 \times {10^5}N/C$. The maximum torque on the dipole will be

The capacity of a spherical conductor in $\mathrm{MKS}$ system is

A spherical condenser has inner and outer spheres of radii $a$ and $b$ respectively. The space between the two is filled with air. The difference between the capacities of two condensers formed when outer sphere is earthed and when inner sphere is earthed will be

$A$ and $B$ are two points in an electric field. If the work done in carrying 4 coulomb of electric charge from $A$ to $B$ is 16 Joule. Then the potential difference between $A$ and $B$ will be.

Statement-1: If the potential difference across a plane parallel plate capacitor is doubled then the potential energy of the capacitor becomes four times under all conditions.
Statement-2: The potential energy $U$ stored in the capacitor is $U=\frac{1}{2} C V^2$, where $C$ and $V$ have usual meaning.

Stored electrostatic energy in a capacitor of capacity $C,$ which is charged upto $Q$ charge, is:

If a dielectric substance is introduced between the plates of a charged air-gap capacitor. The energy of the capacitor will

A parallel plate condenser with dielectric of constant ${K}$ between the plates has a
capacity ${C}$ and is charged to a potential ${V}$ volt. The dielectric slab is slowly removed from between the plates of the capacitor and is again reinserted The net work done by the system in this process is

Two charges +q and –$q$ are kept apart. Then at any point on the right bisector of line joining the two charges

The equivalent capacitance of three capacitors of capacitance ${C_1},{C_2}$ and ${C_3}$ are connected in parallel is 12 units and product ${C_1}.{C_2}.{C_3} = 48$ unit. When the capacitors ${C_1}$ and ${C_2}$ are connected in parallel, the equivalent capacitance is 6 units. Then the capacitances are

The capacity of a parallel plate capacitor is $8.85 \times {10^{ - 12}}\,\,F$ and area of each plate is $4\,\,c{m^2}$ then the distance between two plates is

What is the ratio of the electrostatic potentials at one corner and in the centre point of a uniformly charged cube of conductor? (The potential is considered 0 at infinity) -