Electric potential and capacitance practice · Mixed difficulty

Three point charges $1 \mathrm{~C}, 2 \mathrm{~C}$ and $3 \mathrm{~C}$ are placed at the corners of an equilateral triangle of side $1 \mathrm{~m}.$ The work done in bringing these charges to the vertices of a smaller similar triangle of side $0.5 \mathrm{~m}$ is:

Assertion: If an electric dipole of dipole moment $30 \times 10^{-5} \mathrm{Cm}$ is enclosed by a closed surface, the net flux coming out of the surface will be zero.

Reason: An electric dipole consists of two equal and opposite charges.

A dielectric of thickness $5 \mathrm{~cm}$ and dielectric constant 10, is introduced in between the plates of a parallel plate capacitor having plate area $500 \mathrm{~cm}^2$ and separation between plates $10 \mathrm{~cm}.$ The capacitance of the capacitor is $\text{(If }\varepsilon_0=\mathrm{8 . 8} \times 10^{-12} \text{ SI units}):$

The capacity of a parallel plate condenser consisting of two plates each 20 cm square and are separated by a distance of 8 mm is (Take air as the medium between the plates).

Capacitance of a parallel plate capacitor becomes $4/3$ times its original value if a dielectric slab of thickness $t = d/2$ is inserted between the plates ($d$ is the separation between the plates). The dielectric constant of the slab is

Force of attraction between the plates of a parallel plate capacitor 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.

A capacitor with stored energy 4.0 J is connected with an identical capacitor with no electric field in between. Find the total energy stored in the two capacitors

The potential difference between two points $x = 10\,m$ and 20 m in the field $E = \frac{{100}}{{{x^2}}}$ will be in volt

A conductor carries a certain charge. When it is connected to another uncharged conductor of finite capacity, then the energy of the combined system is:

If a slab of insulating material $4 \times {10^{ - 3}}m$ thick is introduced between the plates of a parallel plate capacitor, the separation between plates has to be increased by $3.5 \times {10^{ - 3}}m$ to restore the capacity to original value. The dielectric constant of the material will be

A cylindrical capacitor is constructed using two coaxial cylinders of the same length $10 \mathrm{~cm}$ and of radii $2 \mathrm{~mm}$ and $4 \mathrm{~mm}$. Calculate the capacitance.

Assertion: Electrons move away from a low potential to high potential region.

Reason: Because electrons has negative charge

Assertion:- On filling the space between the plates of a parallel plate air capacitor with dielectric, capacity of the capacitor is increased.
Reason:- The same amount of charge can be stored at a reduced potential.

Twenty-Seven drops of same size are charged at 220 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

Consider a capacitor - charging circuit. Let $Q_1$ be the charge given to the capacitor in time interval of $20 \mathrm{~ms}$ and $Q_2$ be the charge given in the next time interval of $20 \mathrm{~ms}$. Let $10 \mu \mathrm{Ccharge}$ be deposited in a time interval $t_1$ and the next $10 \mu \mathrm{C~charge}$ is deposited in the next time interval $t_2$. Then,

A point charge $q_1=q$ is placed at point $P$. Another point charge $q_2=-q$ is placed at point $Q$. At some point $R(R \neq P, R \neq Q)$, electric potential due to $q_1$ is $V_1$ and electric potential due to $q_2$ is $V_2$. Which of the following is correct?

A dielectric introduced between the plates of a parallel plate condenser

A dipole of electric dipole moment p is placed in a uniform electric field of strength E. If $\mathrm{\theta }$ is the angle between positive directions of p and E, then the potential energy of the electric dipole is largest when $\mathrm{\theta }$ is

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

$n$ small drops of same size are charged to potential $V$ volt each. If they coalesce to form a single large drop, then its potential will be

A conductor with a positive charge:

Ten electrons are equally spaced and fixed around a circle of radius $R.$ Relative to $V = 0$ at infinity, the electrostatic potential $V$ and the electric field $E$ at the centre $C$ are

Equal charges are given to two spheres of different radii. The potential will

A uniform electric field pointing in positive x-direction exists in a region let $A$ be the origin $B$ be the point on x-axis at $x = + 1\,cm$ and $C$ be the point on y-axis at $y = + 1\,cm$. Then the potentials at points A,B, and C satisfy.

Three identical charges are placed at corners of an equilateral triangle of side $l$. If force between any two charges is $F$, the work required to double the dimensions of triangle is

One volt is equivalent to:

The work done in bringing a unit positive charge from infinite distance to a point at distance $x$ from a positive charge $Q$ is $W.$ Then the potential $\phi$ at that point is

Assertion: When a proton with certain energy moves from low potential to high potential then its ${KE}$ decreases.

Reason: The direction of electric field is opposite to the potential gradient and work done against it is negative.

Assertion:- If three capacitors of capacitances $\mathrm{C}_1 < \mathrm{C}_2 < \mathrm{C}_3$ are connected in series and parallel, then $\mathrm{C}_{\text {parallel }} > \mathrm{C}_{\text {series }}$.
Reason:- $\mathrm{C}_{\text {series }}=\mathrm{C}_1+\mathrm{C}_2+\mathrm{C}_3$ and $\frac{1}{\mathrm{C}_{\text {parallel }}}=\frac{1}{\mathrm{C}_1}+\frac{1}{\mathrm{C}_2}+\frac{1}{\mathrm{C}_3}$