Electric potential and capacitance practice · Mixed difficulty

Two capacitors connected in parallel having the capacities ${C_1}$ and ${C_2}$ are given $'q'$ charge, which is distributed among them. The ratio of the charge on ${C_1}$  and ${C_2}$ will be

The outer sphere of a spherical air capacitor is earthed. For increasing its capacitance

An air capacitor is connected to a battery. The effect of filling the space between the plates with a dielectric is to increase

A parallel plate capacitor with dielectric is charged completely and then the battery is disconnected. Now the dielectric is pulled out. Due to such pulling the

A powerful machine used for producing high positive potentials is

Two identical capacitors have same capacitance $C$. One of them is charged to the potential $V$ and other to the potential $2 V$. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is:

If $E_1$ be the electric field strength of a short dipole at a point on its axial line and $E_2$ that on the equatorial line at the same distance, then

The difference in the effective capacitance of two equal capacitors when joined in parallel and series is $3\,\,\mu F.$ The value of each capacitor is

Three capacitors of capacitance $3\;\mu \;F$ are connected in a circuit. Then their maximum and minimum capacitance will be

Two spherical conductors A and B of radii $1\;mm$ and 2 $mm$ are separated by a distance of $5\;cm$ and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres A and B is

An electric dipole is made up of two equal and opposite charges of $2 \times 10^{-6} {C}$ at a distance of $3 {~cm}$. If this is kept in an electric field of $2 \times 10^5$ ${N} / {C}$, then the maximum torque acting on the dipole is

Statement I : The circuits containing capacitor be handed cautiously, even when there is no current.

Statement II : A dielectric differs from an insulator.

‘Debye’ is the unit of

Assertion (A) : When an uncharged capacitor is charged by a battery, only $50 \%$ of the energy supplied by a battery is stored in the capacitor.

Reason (R): Rest $50 \%$ is lost.

Statement-1: Two concentric conducting spherical shells are charged. The charge on the outer shell is varied keeping the charge on inner shell constant, as a result the electric potential difference between the two shells does not change.
Statement-2: If charge is changed on an isolated thin conducting spherical shell, the potential at all points inside the shell changes by same amount.

A spherical equipotential surface is not possible

Assertion (A) : In series combination, charges on two capacitors are always equal.

Reason (R) : If charges are same, the total potential difference applied across two capacitors will be distributed in inverse ratio of capacities.

If 3 charges are placed at the vertices of equilateral triangle of charge $'q'$ each. What is the net potential energy, if the side of equilateral $\Delta$ is $l\;cm$

An electric charge $10^{-6} \mu \mathrm{C}$ is placed at origin $(0,0)$ m of X-Y co-ordinate system. Two points $P$ and $Q$ are situated at $(\sqrt{3}, \sqrt{3}) \mathrm{m}$ and $(\sqrt{6}, 0) \mathrm{m}$ respectively. The potential difference between the points $P$ and $Q$ will be:

The electric potential of the earth is taken to be

A point $A$ is at potential $+500 \mathrm{~Volt}$ and $B$ is a point of potential $-500 \mathrm{~Volt}.$ The work done by an external agent to take a unit positive charge from $A$ to $B$ is

An electric dipole of moment p placed in a uniform electric field E has minimum potential energy when the angle between p and E is

A charge $Q$ is uniformly distributed through out the volume of a dielectric sphere of radius $R$. If potential at its surface is 24 volts. Then potential at $r=\frac{R}{2}$ and $r=\frac{3 R}{2}$ respectively are. (where $r$ distance from the centre of sphere) :-

Capacity of parallel plate capacitor in air and on immersing it into oil is $50 \,{mF}$ and $110 \,{mF}$ respectively. The dielectric constant of oil is

Assertion (A): At a point electric potential is decreasing along $x$-axis at a rate of $10 \mathrm{~V} / \mathrm{m}$. Therefore, $x$-component of electric field at this point should be $10 \mathrm{~V} / \mathrm{m}$ along $x$-axis.

Reason (R) : Magnitude of $E_x=\frac{\partial V}{\partial x}$

Can a metal be used as a medium for dielectric

An electric dipole is placed making at an angle $60\,^\circ C$ with an electric field of strength $4 \times {10^5}\,\,N/C$. It experiences a torque equal to $8\sqrt 3 \,\,N - m$. Calculate the charge on the dipole, if it is of length 4 cm.

A parallel plate capacitor with plate area $A$ and distance of separation $d$ is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as
$\varepsilon \,(X) = {\varepsilon _0} + \,\,kx,$ for $\left( {0 < x \le \frac{d}{2}} \right)$
$\varepsilon \,(X)\,\, = \,\,{\varepsilon _0} + k\,(d - x)$ for $\left( {\frac{d}{2} \le x \le d} \right)$

A molecule with a dipole moment $p$ is placed in an electric field of strength E. Initially the dipole is aligned parallel to the field. If the dipole is to be related to be anti-parallel to the field the work required to be done by an external agency is

Two capacitances $C_1$ and $C_2$ are connected in series; assume that $C_1 < C_2$. The equivalent capacitance of this arrangement is $C$, where: