The variation of potential with distance \(x\) from a fixed point is shown in the figure. The electric field at \(x=13\) m is:

1.	\(7.5\) volt/meter	2.	\(-7.5\) volt/meter
3.	\(5\) volt/meter	4.	\(-5\) volt/meter

In the circuit diagram shown all the capacitors are in  \(\mu \text{F} \).  The equivalent capacitance between points, \(A\) & \(B\) is (in \(\mu \text{F} \)):

1. \(\frac{14}{5}\)

2. \(7.5\)

3. \(\frac{3}{7}\)

4. None of these

An electric dipole with dipole moment \(\vec{p} = \left(3 \hat{i} + 4 \hat{j}\right) \times 10^{- 30}~\text{C-m}\) is placed in an electric field \(\vec{E} = 4000 \hat{i} ~\text{N/C}\). An external agent turns the dipole slowly until its electric dipole moment becomes \(\left(- 4 \hat{i} + 3 \hat{j}\right) \times 10^{- 30}~\text{C-m}\). The work done by the external agent is equal to:
1. \(4\times 10^{-28}~\text{J}\)
2. \(-4\times 10^{-28}~\text{J}\)
3. \(2.8\times 10^{-26}~\text{J}\)
4. \(-2.8\times 10^{-26}~\text{J}\)

Two identical parallel plate capacitors are placed in series and connected to a constant voltage source of \(V_0\) volt. If one of the capacitors is completely immersed in a liquid with dielectric constant \(K\), the potential difference between the plates of the other capacitor will change to:

1. \(\frac{K +   1}{K} V_{0}\)

2. \(\frac{K}{K +   1} V_{0}\)

3. \(\frac{K +   1}{2 K} V_{0}\)

4. \(\frac{2 K}{K +   1} V_{0}\)

Five equal capacitors connected in series have a resultant capacitance of \(4~\mu\text{F}\). The total energy stored in these when these are connected in parallel and charged to \(400\) V is:
1. \(1~\text{J}\)
2. \(8~\text{J}\)
3. \(16~\text{J}\)
4. \(4~\text{J}\)

Two concentric conducting spherical shells carry charge \(Q\) each. The inner shell is earthed. The charge that flows into the earth is:

1. \(Q\)
2. \(\frac{3Q}{2}\)
3. \(\frac{-Q}{2}\)
4. \(\frac{-3Q}{2}\)

The equivalent capacitance between the points \(A\) and \(B\) in the given network is:

1. \(25~\mu\text{F}\)
2. \(16~\mu\text{F}\)
3. \(21~\mu\text{F}\)
4. \(12~\mu\text{F}\)

An electric dipole of moment \(\vec {p} \) is lying along a uniform electric field \(\vec{E}\). The work done in rotating the dipole by \(90^{\circ}\) is:
1. \(\sqrt{2}pE\)
2. \(\frac{pE}{2}\)
3. \(2pE\)
4. \(pE\)

Two condensers, one of capacity \(C\) and the other of capacity \(\frac{C}2\) are connected to a \(V\) volt battery, as shown in the figure. 
          
The energy stored in the capacitors when both condensers are fully charged will be:
1. \(2CV^2\)
2. \({1 \over4}CV^2\)
3. \({3 \over4}CV^2\)
4. \({1 \over2}CV^2\)

A parallel plate air capacitor has a capacity of \(C\), the distance of separation between plates is \(d\) and potential difference \(V\) is applied between the plates. The force of attraction between the plates of the parallel plate air capacitor is:
1. \(\frac{C^{2} V^{2}}{2 d}\)
2. \(\frac{C V^{2}}{2 d}\)
3. \(\frac{C V^{2}}{d}\)
4. \(\frac{C^{2} V^{2}}{2 d^{2}}\)