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

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

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. \(\frac{\sigma^2}{\varepsilon_0}\)
2. \(\frac{\sigma^2}{2\varepsilon_0}\)
3. \(\frac{\sigma}{\varepsilon_0}\)
4. \(2\sigma^2 \varepsilon_0\)

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

A positive charge \(q\) and a negative charge \(-q\) are placed at \(x=-a\) and \(x=+a\) respectively. The variation of \(V\) along \(x\text-\)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 \(E = 3\times 10^{6}~\text{V/m}\). The maximum charge that can be given to a sphere of diameter \(5\) m is approximately:
1. \(2\times 10^{-5}~\text{C}\)
2. \(2\times 10^{-4}~\text{C}\)
3. \(2\times 10^{-3}~\text{C}\)
4. \(3\times 10^{-3}~\text{C}\)

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. \(- \frac{Q a}{b}\)
2. \(Q \left[1 - \frac{a}{b}\right]\)
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: