Electric potential and capacitance practice · Mixed difficulty

Which of the following quantities don’t depend on the choice of zero potential?

Two positive point charges of $12$ and $5{\;\mathrm{ }}micro\;coulombs,$ are placed $10cm$ apart in air. The work needed to bring them $4cm$ closer is

Two charges of $4\;\mu C$ each are placed at the corners $A$ and $B$ of an equilateral triangle of side length $0.2\;m$ in air. The electric potential at $C$ is $\left[ {\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {{10}^9}\frac{{N - {m^2}}}{{{C^2}}}} \right]$

A capacitor of capacitance $2\,\mu F$ is charged to $40\,\,\mathrm{V}$ and another capacitor of capacitance $4\,\mu F$ is changed to $20\,\,\mathrm{V}.$ If the capacitors are connected together in same polarity, then the energy lost in reorganisation of charge will be

A parallel plate capacitor having capacitance $C$ Farad is connected with a battery of emf V volts. Keeping the capacitor connected with the battery, a dielectric slab of dielectric constant $\mathrm{K}$ is inserted between the plates. The dimensions of the slab are such that it fills the space between the capacitor plates, consider the following statements
(i) Potential difference between the capacitor plates remains the same
(ii) The capacitance increases by a factor $K$

(iii) The energy stored increases by a factor $\mathrm{K}$ Then the correct statements are -

A parallel-plate capacitor having plate area $100 \mathrm{~cm}^2$ and separation $1.0 \mathrm{~mm}$ holds a charge of $0.12 \mu \mathrm{C}$ when connected to a $120 \mathrm{~V}$ battery. Find the dielectric constant of the material filling the gap.

Which among the following is an example of polar molecule?

Two similar parallel-plate capacitors each of capacity $C_0$ are connected in series. The combination is connected with a voltage source of $V_0$. Now, separation between the plates of one capacitor is increased by a distance $d$ and the separation between the plates of another capacitor is decreased by the distance $d / 2$. The distance between the plates of each capacitor was $d$ before the change in separation. Then, select the correct choice.

A dielectric slab is inserted between the plates of an isolated charged capacitor. Which of the following quantities remain unchanged?

If $\text{n}$ drops of potential $\text{V}$ merge, find new potential on the big drop.

When air in a capacitor is replaced by a medium of dielectric constant $K,$ the capacity

A parallel plate air capacitor is charged and then isolated. When a dielectric material is inserted between the plates of the capacitor, then which of the following does not change

Three condensers of capacities $\text{C}_1, \text{C}_2, \text{C}_3$ are connected in series with a source of e.m.f. $\text{V}.$ The potentials across the three condensers are in the ratio of

A capacitor having capacitance $C$ is charged to a voltage $V.$ It is then removed and connected in parallel with another identical capacitor which is uncharged. The new charge on each capacitor is now

In a certain region of space the electric field is zero. If follows that in this region

For measurement of potential difference, potentiometer is preferred in comparison to voltmeter because:-

A closed solid conductor of irregular shape is given some charge. Which of the following statement is correct?

A parallel capacitor of capacitance $C$ A parallel capacitor of capacitance $E$. If a dielectric slab of dielectric constant 4 is inserted between the plates of the capacitor then energy and capacitance will become.

Three capacitors each of capacitance C and of break down voltage V and joined in series. The capacitance and breakdown voltage of the combination will be

On decreasing the distance between the plates of a parallel plate capacitor, its capacitance:

If a charged spherical conductor of radius $10cm$ has potential $V$ at a point distant $5\;cm$ from its centre, then the potential at a point distant $15\;cm$ from the centre will be

Work done in moving a unit positive charge through a distance of R metre on an equipotential surface is

On the axis and on the equator of an electric dipole for all points

Three capacitors of $3\mu F,\,2\mu F$ and $6\mu F$ are connected in series. When a battery of $10V$ is connected to this combination then charge on $2\mu F$ capacitor will be

The amount of work done in increasing the voltage across the plates of capacitor from $5 \mathrm{~V}$ to $10 \mathrm{~V}$ is '$\text{W}$'. The work done in increasing it from $10 \mathrm{~V}$ to $15 \mathrm{~V}$ will be

Equipotential surface for a spherical charge distribution is

A given charge is situated at a certain distance from an electric dipole in the end-on position experiences a force $F.$ If the distance of the charge is doubled, the force acting on the charge will be

An ebonite plate $(\kappa=3), 6 \mathrm{~mm}$ thick, is introduced between the parallel plates of a capacitor of plate area $2 \times 10^{-2} \mathrm{~m}^2$ and plate separation $0.01 \mathrm{~m}$ Find the capacitance.

The condensers of capacity ${C_1}\mathrm{ and }\,\,{C_2}\,$ are connected in parallel, then the equivalent capacitance is:

Assertion (A) : Two capacitors are connected in series with a battery. Energy stored across them is in inverse ratio of their capacity.

Reason (R): $U=\frac{1}{2} q V$ or $U \propto q V$.