The equivalent capacitance across \(A\) and \(B\) in the given figure is:

  
1. \( \frac{3}{2}C\)
2. \(C\)
3. \( \frac{2}{3}C\)
4. \( \frac{5}{3}C\)

Surface charge density on the positive plate of a charged parallel plate capacitor is $\sigma$. Energy density in the electric field of the capacitor is:

1. $\frac{{\sigma }^2}{{\epsilon }_0}$

2. $\frac{{\sigma }^2}{2{\epsilon }_0}$

3. $\frac{\sigma }{{\epsilon }_0}$

4. $2{\sigma }^2{\epsilon }_0$

Two capacitors of capacity $2$ $\mu F$ and $3$ $\mu F$ are charged to the same potential difference of 6 V. Now they are connected with opposite polarity as shown. After closing switches $S_1$ $and$ $S_2$, their final potential difference becomes:

How many capacitors each of $8$ $\mu F$ and 250 V are required to form a composite capacitor of $16$ $\mu F$ and 1 kV?

A positive charge q and a negative charge -q are placed at x= -a and x= +a respectively. The variation of V along x-axis is represented by the graph:

1.		2.
3.		4.

Which of the following statements is correct regarding electrostatics of conductors?

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.  $3$ $\times {10}^{-\mathrm{3 }}C$ 

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.  $7.8 \times {10}^{-10}$

Two concentric metallic spherical shells A and B of radii a and b respectively (b>a) are arranged such that outer shell is earthed and inner shell is charged to Q. Charge on the outer surface of outer shell will be:

1. $-\frac{Qa}{b}$

2. $Q\left(1-\begin{array}{c}\frac{a}{b}\end{array}\right)$

3. -Q

4. zero

In a circuit, 5 C of charge is passed through a battery in a given time. The plates of the battery are maintained at a potential difference of 12 V. The work done by the battery is: