A capacitor of \(1~\mu\text{F}\) withstands a maximum voltage of \(6\) kilovolts while another capacitor of \(2~\mu\text{F}\) withstands a maximum voltage of \(4\) kilovolts. If the two capacitors are connected in series, the system will withstand a maximum voltage of:

1.	\(2\) kV	2.	\(4\) kV
3.	\(6\) kV	4.	\(9\) kV

The potential at a certain point in an electric field is 200 V. The work done in carrying an electron upto that point will be.

1.  $3.2\times {10}^{-17} \mathrm{J}$                      

2.  $-3.2\times {10}^{-17} \mathrm{J}$

3.  $200 \mathrm{J}$                                     

4.  $-200 \mathrm{J}$

Two charged conducting spheres of radii ${\mathrm{r}}_1$ and ${\mathrm{r}}_2$ are at the same potential. The ratio of their surface charge densities will be -

1.  ${\mathrm{r}}_1/{\mathrm{r}}_2$                               

2.  ${\mathrm{r}}_2/{\mathrm{r}}_1$

3.  ${{\mathrm{r}}_1}^2/{{\mathrm{r}}_2}^2$                           

4.  ${{\mathrm{r}}_2}^2/{{\mathrm{r}}_1}^2$

At the mid point of a line joining an electron and a proton, the values of E and V will be.

1. $\mathrm{E}=0, \mathrm{V}\ne 0$                   

2. $\mathrm{E}\ne 0, \mathrm{V}=0$

3. $\mathrm{E}\ne 0, \mathrm{V}\ne 0$                   

4. $\mathrm{E}=0, \mathrm{V}=0$

A charge of $10\mu \mathrm{C}$ is kept at the origin of $\mathrm{X}–\mathrm{Y}$ coordinate system. The potential difference in volts between two points (a, 0) and $\left(\mathrm{a}/\sqrt{2} , \mathrm{a}/\sqrt{2}\right)$ will be.

1.  Zero                             

2.  $9\times {10}^4$

3.  $\frac{9\times {10}^4}{\mathrm{a}}$                           

4.  $\frac{9\times {10}^4}{\sqrt{2}}$

Find equivalent capacitance between $\mathrm{X}$ and $\mathrm{Y}$ if each capacitor is $4 \mathrm{\mu F}$.

1.  $4 \mathrm{\mu F}$                                     

2.  $2 \mathrm{\mu F}$

3.  $12 \mathrm{\mu F}$                                   

4.  $1 \mathrm{\mu F}$

Two point charge of $8 \mathrm{\mu C}$ and $12 \mathrm{\mu C}$ are kept in air at a distance of 10 cm from each other. The work required to change the distance between them to 6 cm will be.

1.  $5.8 \mathrm{J}$                       

2.  $4.8 \mathrm{J}$

3.  $3.8 \mathrm{J}$                       

4.  $2.8 \mathrm{J}$

Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to a potential difference V. The battery is then disconnected and the region between the plates of the capacitor C is completely filled with a material of dielectric constant K. The potential difference across the capacitors now becomes –

1.  $\frac{3\mathrm{V}}{\mathrm{K}+2}$                             

2.  $\mathrm{KV}$

3.  $\frac{\mathrm{V}}{\mathrm{K}}$                                 

4.  $\frac{3}{\mathrm{KV}}$

Maximum charge stored on a metal sphere of radius $15$ cm may be $7.5 \mu \mathrm{C}$. The potential energy of the sphere in this case is :

1.  $9.67 \mathrm{J}$                   

2.  $0.25 \mathrm{J}$ 

3.  $3.25 \mathrm{J}$                    

4.  $1.69 \mathrm{J}$

Four identical particles each of mass m and charge q are kept at the four corners of a square of length L. The final velocity of these particles after setting them free will be.

1. ${\left[\frac{{\mathrm{Kq}}^2}{\mathrm{mL}}\left(5.4\right)\right]}^{1/2}$                           

2. ${\left[\frac{{\mathrm{Kq}}^2}{\mathrm{mL}}\left(1.35\right)\right]}^{1/2}$

3. ${\left[\frac{{\mathrm{Kq}}^2}{\mathrm{mL}}\left(2.7\right)\right]}^{1/2}$                           

4. Zero