If two conducting spheres are separately charged and then brought in contact -

1. The total energy of the two spheres is conserved

2. The total charge on the two spheres is conserved

3. Both the total energy and charge are conserved

4. The final potential is always the mean of the original potentials of the two spheres

Eight drops of mercury of equal radii possessing equal charges combine to form a big drop. Then the capacitance of bigger drop compared to each individual small drop is 

1. 8 times

2. 4 times

3. 2 times

4. 32 times

A parallel plate condenser has a capacitance 50 μF in air and 110 μF when immersed in an oil. The dielectric constant ‘k’ of the oil is 

1. 0.45

2. 0.55

3. 1.10

4. 2.20

Separation between the plates of a parallel plate capacitor is d and the area of each plate is A. When a slab of material of dielectric constant k and thickness t(t < d) is introduced between the plates, its capacitance becomes -

1. $\frac{{\epsilon }_{0}A}{d+t\left(1-\frac{1}{k}\right)}$

2. $\frac{{\epsilon }_{0}A}{d+t\left(1+\frac{1}{k}\right)}$

3. $\frac{{\epsilon }_{0}A}{d-t\left(1-\frac{1}{k}\right)}$

4. $\frac{{\epsilon }_{0}A}{d-t\left(1+\frac{1}{k}\right)}$

The capacity of parallel plate condenser depends on 

1. The type of metal used

2. The thickness of plates

3. The potential applied across the plates

4. The separation between the plates

The capacity of a parallel plate condenser is C. It's capacity when the separation between the plates is halved will be?

1. 4 C

2. 2 C

3. $\frac{C}{2}$

4. $\frac{C}{4}$

Eight small drops, each of radius r and having same charge q are combined to form a big drop. The ratio between the potentials of the bigger drop and the smaller drop is 

1. 8 : 1

2. 4 : 1

3. 2 : 1

4. 1 : 8

1000 small water drops each of radius r and charge q coalesce together to form one spherical drop. The potential of the big drop is larger than that of the smaller drop by a factor of 

1. 1000

2. 100

3. 10

4. 1

A parallel plate condenser is immersed in an oil of dielectric constant 2. The field between the plates is 

1. Increased proportional to 2

2. Decreased proportional to $\frac{1}{2}$

3. Increased proportional to $\sqrt{2}$

4. Decreased proportional to $\frac{1}{\sqrt{2}}$ 

If the dielectric constant and dielectric strength be denoted by \(k\) and \(x\) respectively, then a material suitable for use as a dielectric in a capacitor must have:
1. high \(k\) and high \(x\).
2. high \(k\) and low \(x\).
3. low \(k\) and low \(x\).
4. low \(k\) and high \(x\).