Capacitors $C_1=10\mu F<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>C_2=30\mu F$ are connected in series across a source of emf 20KV. The potential difference across $C_1$ will be

1. 5 KV

2. 15 KV

3. 10 KV

4. 20 KV

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 new capacitance become

1. $\frac{KC}{2\left(K+1\right)}$

2. $\frac{2KC}{K+1}$

3. $\frac{5KC}{4K+1}$

4. $\frac{4KC}{3K+1}$

In the circuit shown in the figure, the energy stored in \(6~\mu\text{F}\) capacitor will be:
      

The electric potential at a point at distance 'r' from a short dipole is proportional to

1. $r^2$

2. ${\mathrm{r}}^{-1}$

3. $r^{-2}$

4. $r^1$

Two metallic spheres of radii 2cm and 3cm are given charges 6mC and 4mC respectively. The final charge on the smaller sphere will be if they are connected by a conducting wire

1. 4mC

2.6mC

3. 5mC

4. 10mC

A hollow charged metal spherical shell has radius R. If the potential difference between its surface and a point at a distance 3R from the center is V, then the value of electric field intensity at a point at distance 4R from the center is

1.  $\frac{3\mathrm{V}}{19\mathrm{R}}$

2.  $\frac{\mathrm{V}}{6\mathrm{R}}$

3.  $\frac{3\mathrm{V}}{32\mathrm{R}}$

4.  $\frac{3\mathrm{V}}{16\mathrm{R}}$

The equivalent capacitance between A and B is as the given figure:

 
1. \(16 \pi \epsilon_ 0 r\)
2. \(4 \pi \epsilon_ 0 r\)
3. \(8 \pi \epsilon_ 0 r\)
4. None of these

The electric potential at the surface of a charged solid sphere of insulator is 20V. The value of electric potential at its centre will be

1.  30V

2.  20V

3.  40V

4.  Zero