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  \(\mu F\).  The equivalent capacitance between points, A & B is (in $\mathrm{\mu }$F):

1. 14/5 

2. 7.5

3. 3/7 

4. None of these

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

1. 4 × 10^–28  J 

2. –4 × 10^–28  J

3. 2.8 × 10^–26  J 

4. –2.8 × 10^–26  J

Two identical parallel plate capacitors are placed in series and connected to a constant voltage source of V₀ 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 $\mathrm{4 }\mu F$. The total energy stored in these when these are connected in parallel and charged to 400 V is:
1. 1 J
2. 8 J
3. 16 J
4. 4 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. $\frac{3\mathrm{Q}}{2}$

3. $\frac{-\mathrm{Q}}{2}$

4. $\frac{-3\mathrm{Q}}{2}$

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

1. 25 $\mathrm{\mu F}$

2. 16 $\mathrm{\mu F}$

3. 21 $\mathrm{\mu F}$

4. 12 $\mathrm{\mu F}$

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. $\frac{C^2{V}^2}{2d}$

2. $\frac{C{V}^2}{2d}$

3. $\frac{C{V}^2}{d}$

4. $\frac{C^2{V}^2}{2d^2}$