A capacitor is charged by connecting a battery across its plates. It stores energy U. Now the battery is disconnected and another identical capacitor is connected across it, then the energy stored by both capacitors of the system will be:

1. U

2. $\frac{U}{2}$

3. 2U

4. $\frac{3}{2}U$

A bullet of mass 2g is having a charge of $2\mathrm{\mu C}$. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of $10<mspace\; width="1em"></mspace>{\mathrm{ms}}^{-1}$ ?

1. 20 kV

2. 5 V

3. 50 kV

4. 5 kV

An electric dipole of moment $\overrightarrow{\mathrm{p}}$ is lying along a uniform electric field $\overrightarrow{\mathrm{E}}$. The work done in rotating the dipole by $90°$ is

1. $\sqrt{2}pE$

2. $\frac{\mathrm{pE}}{2}$

3. 2pE

4. pE

A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates

1. decreases

2. does not change

3. becomes zero

4. increases.

Charges +q and -q are placed at points  A and B respectively which are distance 2L apart, C is the midpoint between A and B. The work done in moving a charge +Q along the semicircle CRD is

1. $\frac{qQ}{2\pi {\epsilon }_{0}L}$

2. $\frac{qQ}{\mathit{6}\pi {\epsilon }_{0}L}$

3. $-\frac{qQ}{\mathit{6}\pi {\epsilon }_{0}L}$

4. $\frac{qQ}{\mathit{4}\pi {\epsilon }_{0}L}$

Two condensers one of capacity C and other of capacity C/2 are connected to a V-volt battery, as shown. The work done in charging fully both the condensers is

1. $\frac{1}{4}C{V}^2$

2. $\frac{3}{2}C{V}^2$

3. $\frac{1}{2}C{V}^2$

4. $2{\mathrm{CV}}^2$

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

1. $3\mathrm{C},<mspace\; width="1em"></mspace>\frac{\mathrm{V}}{3}$

2. $\frac{\mathrm{C}}{3}$, 3V

3. 3C, 3V

4. $\frac{C}{3},<mspace\; width="1em"></mspace>\frac{V}{3}$

A parallel plate condenser has a uniform electric field E ($\mathrm{V}<mspace\; width="1em"></mspace>{\mathrm{m}}^{-1}$) in the space between the plates. If the distance between the plates is d (m) and area of each plate is A $\left({\mathrm{m}}^2\right)$, the energy (joules) stored in the condenser is

1. $\frac{1}{2}{\epsilon }_0{E}^{2}Ad$

2. $E^{2}Ad/{\epsilon }_0$

3. $\frac{1}{2}{\epsilon }_0{E}^2$

4. ${\mathrm{\epsilon }}_0\mathrm{EAd}$

Three charges each +q are placed at the corners of an isosceles triangle ABC of sides BC and AC equal to 2a. D and E are the midpoints of BC and CA. The work done in taking a charge Q from D to E is

1. $\frac{3qQ}{4\pi {\epsilon }_{0}a}$

2. $\frac{3qQ}{8\pi {\epsilon }_{0}a}$

3. $\frac{qQ}{4\pi {\epsilon }_{0}a}$

4. zero

A, B and C are three points in a uniform electric field. The electric potential is

1. maximum at A

2. maximum at B

3. maximum at C

4. same at all the three points A, B and C