An uncharged parallel plate capacitor having a dielectric of constant K is connected to a similar air-cored parallel capacitor charged to a potential V. The two capacitors share charges and the common potential is V'. The dielectric constant K is:

1. $\frac{\mathrm{V}\text{'}-\mathrm{V}}{\mathrm{V}\text{'}+\mathrm{V}}$

2. $\frac{\mathrm{V}\text{'}-\mathrm{V}}{\mathrm{V}\text{'}}$

3. $\frac{\mathrm{V}\text{'}-\mathrm{V}}{\mathrm{V}}$

4. $\frac{\mathrm{V}-\mathrm{V}\text{'}}{\mathrm{V}\text{'}}$

A battery does 200 J of work in charging a capacitor. The energy stored in the capacitor is:
1. 200 J
2. 100 J
3. 50 J
4. 400 J

Two identical capacitors are connected in parallel across a potential difference V. After they are fully charged, the positive plate of the first capacitor is connected to the negative plate of the second and the negative plate of the first is connected to the positive plate of the other. The loss of energy will be:

1. $\frac{1}{2}{\mathrm{CV}}^2$

2. ${\mathrm{CV}}^2$

3. $\frac{1}{4}{\mathrm{CV}}^2$

4. Zero

The figure shows equipotential surfaces for a two charges system. At which of the labeled points will an electron have the highest potential energy?

1. Point \(A\)
2. Point \(B\)
3. Point \(C\)
4. Point \(D\)

A thin, metallic spherical shell contains a charge Q on it. A point charge q is placed at the centre of the shell and another charge q₁ is placed outside it as shown in the figure. All the three charges are positive. The force on the central charge due to the shell is:

1. towards left

2. towards right

3. upward

4. zero

In the electric field of a point charge q, a certain charge is carried from point A to B, C, D, and E, the work done:

1. is least along the path AB

2. is least along the path AD

3. is zero along any one of the paths AB, AC and AE

4. is least along AE.

In a certain region of space, the electric field is zero. From this we can conclude that the electric potential in this region is:

1. constant

2. zero

3. positive

4. negative

An uncharged aluminium block has a cavity within it. The block is placed in a region permeated by a uniform electric field which is directed upwards. Which of the following is a correct statement describing conditions in the interior of the block's cavity?

1. The electric field in the cavity is directed upwards

2. The electric field in the cavity is directed downwards

3. There is no electric field in the cavity

4. The electric field in the cavity is of varying magnitude and is zero at the exact center.

A capacitor is filled with an insulator and a certain potential difference is applied to its plates. The energy stored in the capacitor is U. Now the capacitor is disconnected from the source and the insulator is pulled out of the capacitor. The work performed against the forces of the electric field in pulling out the insulator is 4U. Then dielectric constant of the insulator is:

1. 4

2. 8

3. 5

4. 3

An insulator plate is passed between the plates of a capacitor. Then current(outside the capacitor):

1. Always flows from A to B

2. Always flows from B to A

3. First flows from A to B and then from B to A

4. First flows from B to A and then from A to B