A parallel plate condenser has a capacitance \(50~\mu\text{F}\) in air and \(110~\mu\text{F}\) when immersed in an oil. The dielectric constant \(k\) of the oil is: 
1. \(0.45\)
2. \(0.55\)
3. \(1.10\)
4. \(2.20\)

Two parallel metal plates having charges +Q and –Q, face each other at a certain distance between them. If the plates are now dipped in the kerosene oil tank, the electric field between the plates will:

The capacitance of a parallel plate capacitor is C. If a dielectric slab of thickness equal to one-fourth of the plate separation and dielectric constant K is inserted between the plates, then the new capacitance will be: 

Two thin dielectric slabs of dielectric constants K₁&K₂ ($K_1<K_2$) are inserted between plates of a parallel capacitor, as shown in the figure. The variation of electric field E between the plates with distance d as measured from plate P is correctly shown by:  
  

1.		2.
3.		4.

A parallel plate capacitor with cross-sectional area \(A\) and separation \(d\) has air between the plates. An insulating slab of the same area but the thickness of \(\frac{d}{2}\) is inserted between the plates as shown in the figure having a dielectric constant, \(K=4\). The ratio of new capacitance to its original capacitance will be:

A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness d₁ and dielectric constant K₁ and the other has thickness d₂ and dielectric constant K₂, as shown in the figure. This arrangement can be thought of as a dielectric slab of thickness d = d₁ + d₂ and effective dielectric constant K. K is:  

A parallel plate capacitor has capacitance \(C\). If it is equally filled with parallel layers of materials of dielectric constants \(K_1\) and \(K_2\), its capacity becomes \(C_1\). The ratio of \(C_1\) to \(C\) is:

The dielectric constant of pure water is 81. Its permittivity will be: (in MKS units)

1.  $1.02 \times {10}^{-13}$

2.  $8.86 \times {10}^{-12}$

3.  $7.17 \times {10}^{-10}$

4.  $7.8 \times {10}^{-10}$

The insulation property of air breaks down at $E$ $=$ $3$ $\times$ ${10}^6$ V/m. The maximum charge that can be given to a sphere of diameter 5 m is approximately:

1.  $2$ $\times {10}^{-5}$ $C$

2.  $2$ $\times {10}^{-4}$ $C$

3.  $2$ $\times {10}^{-3}$ $C$

4.  $3$ $\times {10}^{-\mathrm{3 }}C$ 

A parallel plate condenser is filled with two dielectrics as shown. Area of each plate is A metre² and the separation is t metre. The dielectric constants are k₁ and k₂ respectively. Its capacitance in farad will be:

1. $\frac{{\epsilon }_{0}A}{t}(k_1+k_2)$

2. $\frac{{\epsilon }_{0}A}{t}.\frac{k_1+k_2}{2}$

3. $\frac{2{\epsilon }_{0}A}{t}(k_1+k_2)$

4. $\frac{{\epsilon }_{0}A}{t}.\frac{k_1-k_2}{2}$