The effective capacity of the network between terminals \(\mathrm{A}\) and \(\mathrm{B}\) is:

1. \(6~\mu\text{F}~\)
2. \(20~\mu\text{F} ~\)
3. \(3~\mu\text{F}~\)
4. \(10~\mu\text{F}\)

Eight equally charged tiny drops are combined to form a big drop. If the potential on each drop is 10 V, then the potential of the big drop will be:

The energy and capacity of a charged parallel plate capacitor are \(E\) and \(C\) respectively. If a dielectric slab of ${}_{}$\(E_r=6\) is inserted in it, then the energy and capacity become:
(Assuming the charge on plates remains constant)

A capacitor is charged with a battery and energy stored is U. After disconnecting the battery another capacitor of the same capacity is connected in parallel with it. The energy stored in each capacitor is:

1. U/2

2. U/4

3. 4 U

4. 2 U

Energy per unit volume for a capacitor having area \(A\) and separation \(d\) kept at a potential difference \(V\) is given by:
1.  $\frac{1}{2}{\epsilon }_0\frac{V^2}{d^2}$

2. $\frac{1}{2{\epsilon }_0}\frac{V^2}{d^2}$

3.  $\frac{1}{2}C{V}^2$

4. $\frac{Q^2}{2C}$

Some charge is being given to a conductor. Then it's potential:

A capacitor of capacity C₁ is charged up to V volt and then connected to an uncharged capacitor C₂. Then final P.D. across each will be:

1. $\frac{{\mathrm{C}}_2\mathrm{V}}{{\mathrm{C}}_1+{\mathrm{C}}_2}$

2. $\frac{{\mathrm{C}}_1\mathrm{V}}{{\mathrm{C}}_1+{\mathrm{C}}_2}$

3. $\left(1+\frac{{\mathrm{C}}_2}{{\mathrm{C}}_1}\right)$

4. $(1-\frac{{\mathrm{C}}_2}{{\mathrm{C}}_1})\mathrm{V}$

If identical charges (–q) are placed at each corner of a cube of side 'b' then the electrical potential energy of charge (+q) which is placed at centre of the cube will be:

1. $\frac{-4\sqrt{2}{\mathrm{q}}^2}{{\mathrm{\pi \epsilon }}_0\mathrm{b}}$

2. $\frac{-8\sqrt{2}{\mathrm{q}}^2}{{\mathrm{\pi \epsilon }}_0\mathrm{b}}$

3. $\frac{-4{\mathrm{q}}^2}{\sqrt{3}{\mathrm{\pi \epsilon }}_0\mathrm{b}}$

4. $\frac{8\sqrt{2}{\mathrm{q}}^2}{4{\mathrm{\pi \epsilon }}_0\mathrm{b}}$

Three capacitors each of capacity \(4\) µF are to be connected in such a way that the effective capacitance is \(6\) µF. This can be done by:

A bullet of mass 2 g is having a charge of 2 µC. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of 10 m/s?
1. 50 kV
2. 5 V
3. 50 V
4. 5 kV