A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants k₁, k₂, k₃ and k₄ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by 

1.  $\mathrm{K}={\mathrm{k}}_1+{\mathrm{k}}_2+{\mathrm{k}}_3+3{\mathrm{k}}_4$

2.  $\mathrm{k}=\frac{2}{3}{\mathrm{k}}_4\left(\frac{{\mathrm{k}}_1}{{\mathrm{k}}_1+{\mathrm{K}}_4}+\frac{{\mathrm{k}}_2}{{\mathrm{k}}_2+{\mathrm{k}}_4}+\frac{{\mathrm{k}}_3}{{\mathrm{k}}_3+{\mathrm{k}}_4}\right)$

3.  $\frac{2}{\mathrm{k}}=\frac{3}{{\mathrm{k}}_1+{\mathrm{k}}_2+{\mathrm{k}}_3}+\frac{1}{{\mathrm{k}}_4}$

4.  $\frac{1}{\mathrm{k}}=\frac{1}{{\mathrm{k}}_1}+\frac{1}{{\mathrm{k}}_2}+\frac{1}{{\mathrm{k}}_3}+\frac{3}{2{\mathrm{k}}_4}$

A series combination of n1 capacitors, each of value C₁, is charged by a source of potential difference 4V. When another parallel combination of n₂ capacitors, each of value C₂, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of C₂ , in terms of C₁, is then

1. $\frac{2C_1}{n_1{n}_2}$

2. $16\frac{n_2}{n_1}{C}_1$

3. $2\frac{n_2}{n_1}{C}_1$

4. $\frac{16C_1}{n_1{n}_2}$

Four point charges –Q, -q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the center of the square is zero, is

1. Q=-q

2. Q= -2q

3. Q=q

4. Q=2q

A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are:

1. Zero and $\frac{Q}{4{\mathrm{\pi \epsilon }}_0{\mathrm{R}}^2}$

2. $\frac{Q}{4{\mathrm{\pi \epsilon }}_0\mathrm{R}}$ and zero

3. $\frac{Q}{4{\mathrm{\pi \epsilon }}_0\mathrm{R}}$ and $\frac{Q}{4{\mathrm{\pi \epsilon }}_0{\mathrm{R}}^2}$

4. Both are zero.

An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\theta =90°$, the torque and the potential energy of the dipole will respectively be

1. $pE \sin \theta ,-pE \cos \theta$

2. $pE \sin \theta ,-2pE \cos \theta$

3. $pE \sin \theta , 2pE \cos \theta$

4. $pE \cos \theta ,-pE \sin \theta$

The diagrams below show regions of equipotential. 
 
A positive charge is moved from A to B in each diagram.

1. In all the four cases , the work done is the same

2. Minimum work is required to move q in figure(a)

3. Maximum work is required to move q in figure (b)

4. Maximum work is required to move q in figure (c)

A parallel plate capacitor of capacitance 20 $\mu$F is being charged by a voltage source whose potential is charging at the rate of 3 V/s. The conduction current through the connecting wires, and the displacement current through the plates of the capacitor, would be, respectively:

1. zero, zero

2. zero, 60$\mu$A

3. 60$\mu$A, 60$\mu$A

4. 60$\mu$A, zero

A parallel plate condenser has a uniform electric field E (V/m) in the space between the plates. If the distance between the plates is d(m) and area of each plate is A(m²) , the energy (joule) stored in the condenser is

1.  $\frac{1}{2}\left({\mathrm{\epsilon }}_{\mathrm{o}}\right){\left(\mathrm{E}\right)}^2$

2.  $\frac{{\mathrm{E}}^2 \mathrm{Ad}}{{\mathrm{\epsilon }}_{\mathrm{o}}}$

3.  $\frac{1}{2}\left({\mathrm{\epsilon }}_{\mathrm{o}}\right) {\mathrm{E}}^2 \mathrm{Ad}$

4.  $\left({\mathrm{\epsilon }}_{\mathrm{o}}\right) \mathrm{EAd}$