Two condensers of capacity \(0.3~\mu\text{F}\) and \(0.6~\mu\text{F}\) are connected in series. The combination is connected across a potential of \(6\) V. The ratio of energies stored by the condensers will be:
1. \(\frac{1}{2}\)
2. \(2\)
3. \(\frac{1}{4}\)
4. \(4\)

A parallel plate air capacitor is charged to potential difference \(V\). After disconnecting the battery, the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates:
1. decreases.
2. increases.
3. becomes zero.
4. does not change.

In a certain region of space with volume \(0.2\) m³, the electric potential is found to be \(5\) V throughout. The magnitude of electric field in this region is:
1. \(0.5\) N/C
2. \(1\) N/C
3. \(5\) N/C
4. zero

A short electric dipole has a dipole moment of \(16 \times 10^{-9} ~\text{C-}\text{m}\). The electric potential due to the dipole at a point at a distance of \(0.6~\text{m}\) from the centre of the dipole situated on a line making an angle of \(60^{\circ}\) with the dipole axis is: \(\left( \frac{1}{4\pi \varepsilon_0}= 9\times 10^{9}~\text{N-m}^2/\text{C}^2\right)\)
1. \(200~\text{V}\)
2. \(400~\text{V}\)
3. zero
4. \(50~\text{V}\)

The capacitance of a parallel plate capacitor with air as a medium is \(6~\mu\text{F}\). With the introduction of a dielectric medium, the capacitance becomes \(30~\mu\text{F}\)$$. The permittivity of the medium is:\(\left(\varepsilon_0=8.85 \times 10^{-12} ~\text{C}^2 \text{N}^{-1} \text{m}^{-2}\right )\)

The increasing order of the electrostatic potential energies for the given system of charges is given by:

A charge \(q_1=5 \times 10^{-8} ~\text{C}\) is kept at \(3\) cm from a charge \(q_2=-2 \times 10^{-8} ~\text{C}\). The potential energy of the system relative to the potential energy at infinite separation is:
1. \(3\times 10^{-4}~\text{J}\)
2. \(-3\times 10^{-4}~\text{J}\)
3. \(9\times 10^{-6}~\text{J}\)
4. \(-9\times 10^{-6}~\text{J}\)

A circuit has section \(AB\) as shown in figure. The emf of the cell is \(10\) V. The potential difference \(V_{AB}= 5~\text{V}\). The charge on the capacitor \(C_1\) is: