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Infinite charges, each of q coulomb are lying on the x-axis at x = 1m, 2m, 4m, 8m, --------.The electric potential due to these charges at x = 0 will be – 
1. $\mathrm{Kq}$                   
2. $\frac{\mathrm{Kq}}{2}$ 
3. $2<mspace\; width="1em"></mspace>\mathrm{Kq}$                 
4. $\frac{\mathrm{Kq}}{3}$

From a supply of identical capacitors rated $8<mspace\; width="1em"></mspace>\mathrm{mF}$, $250<mspace\; width="1em"></mspace>\mathrm{V}$, the minimum number of capacitors required to form a composite $16<mspace\; width="1em"></mspace>\mathrm{mF}$, $1000<mspace\; width="1em"></mspace>\mathrm{V}$ is : 
1.  $2$                     
2.  $4$
3.  $16$                   
4.  $32$

A parallel plate capacitor of area ‘A’ , plate separation ‘d’ is filled with two dielectrics as shown. What is the capacitance of the arrangement ?

1.  $\frac{3{\mathrm{K\epsilon }}_0\mathrm{A}}{4\mathrm{d}}$                             
2. $\frac{4{\mathrm{K\epsilon }}_0\mathrm{A}}{3\mathrm{d}}$
3. $\frac{\left(\mathrm{K}+1\right){\mathrm{\epsilon }}_0\mathrm{A}}{2\mathrm{d}}$                       
4.$\frac{\mathrm{K}\left(\mathrm{K}+3\right){\mathrm{\epsilon }}_0\mathrm{A}}{2\left(\mathrm{K}+1\right)\mathrm{d}}$

If E be the electric field inside a parallel plate capacitor due to Q and -Q charges on the two plates, then electrostatic force on plate having charge -Q due to the plate having charge +Q will be
1. -QE
2. $\frac{-QE}{2}$
3. QE
4. $\frac{-QE}{4}$

The electric potential at the surface of a charged solid sphere of insulator is 20V. The value of electric potential at its centre will be
1.  30V
2.  20V
3.  40V
4.  Zero

Two identical metal plates are given charges $Q_1 and Q_2\left(<Q_1\right)$ respectively. If they are now brought close to form a parallel plate capacitor with capacitance $C$, the potential difference between them is :
1. $\frac{Q_1+Q_2}{2C}$
2. $\frac{Q_1+Q_2}{C}$
3. $\frac{Q_1-Q_2}{C}$
4. $\frac{Q_1-Q_2}{2C}$

An electron of mass m and charge e is accelerated from rest through a potential difference V in vacuum. The final speed of the electron will be 
(1) $V\sqrt{e/m}$
(2) $\sqrt{eV/m}$
(3) $\sqrt{2eV/m}$
(4) $2eV/m$

Two charged spheres of radii 10 cm and 15 cm are connected by a thin wire. No current will flow, if they have -
1. The same charge on each
2. The same potential
3. The same energy
4. The same field on their surfaces

In the electric field of a point charge q, a certain charge is carried from point A to B, C, D and E. Then the work done

1. Is least along the path AB
2. Is least along the path AD
3. Is zero along all the paths AB, AC, AD and AE
4. Is least along AE

A conductor with a positive charge:

If a charged spherical conductor of radius 10 cm has potential V at a point distant 5 cm from its centre, then the potential at a point distant 15 cm from the centre will be -
1. $\frac{1}{3}V$
2. $\frac{2}{3}V$
3. $\frac{3}{2}V$
4. 3 V

The ratio of momenta of an electron and an $\alpha$-particle which are accelerated from rest by a potential difference of 100 volt is 
1. 1
2. $\sqrt{\frac{2m_e}{m_{\alpha }}}$
3. $\sqrt{\frac{m_e}{m_{\alpha }}}$
4. $\sqrt{\frac{m_e}{2m_{\alpha }}}$

A proton is about 1840 times heavier than an electron. When it is accelerated by a potential difference of 1 kV, its kinetic energy will be -
1. 1840 keV
2. 1/1840 keV
3. 1 keV
4. 920 keV

As per this diagram a point charge +q is placed at the origin O. Work done in taking another point charge –Q from the point A [co-ordinates (0, a)] to another point B [co-ordinates (a, 0)] along the straight path AB is

1. Zero
2. $\left(\frac{{\displaystyle -qQ}}{{\displaystyle 4\pi {\epsilon }_0}}\frac{{\displaystyle 1}}{{\displaystyle a^2}}\right)\sqrt{2}a$
3. $\left(\frac{{\displaystyle qQ}}{{\displaystyle 4\pi {\epsilon }_0}}\frac{{\displaystyle 1}}{{\displaystyle a^2}}\right)\frac{a}{\sqrt{2}}$
4. $\left(\frac{{\displaystyle qQ}}{{\displaystyle 4\pi {\epsilon }_0}}\frac{{\displaystyle 1}}{{\displaystyle a^2}}\right)\sqrt{2}a$

The capacity of a condenser is 4 × 10^–6 farad and its potential is 100 volts. The energy released on discharging it fully will be -
1. 0.02 Joule
2. 0.04 Joule
3. 0.025 Joule
4. 0.05 Joule

The energy stored in a condenser of capacity C which has been raised to a potential V is given by -
1. $\frac{1}{2}CV$
2. $\frac{1}{2}C{V}^2$
3. CV
4. $\frac{1}{2VC}$

Eight drops of mercury of equal radii possessing equal charges combine to form a big drop. Then the capacitance of bigger drop compared to each individual small drop is 
1. 8 times
2. 4 times
3. 2 times
4. 32 times

The capacity of a parallel plate condenser is C. It's capacity when the separation between the plates is halved will be?
1. 4 C
2. 2 C
3. $\frac{C}{2}$
4. $\frac{C}{4}$

If the dielectric constant and dielectric strength be denoted by \(k\) and \(x\) respectively, then a material suitable for use as a dielectric in a capacitor must have:
1. high \(k\) and high \(x\).
2. high \(k\) and low \(x\).
3. low \(k\) and low \(x\).
4. low \(k\) and high \(x\).

64 drops each having the capacity C and potential V are combined to form a big drop. If the charge on the small drop is q, then the charge on the big drop will be 
1. 2q
2. 4q
3. 16q
4. 64q

The capacity of a parallel plate capacitor increases with the 
1. Decrease of its area
2. Increase of its distance
3. Increase of its area
4. None of the above

The true statement is, on increasing the distance between the plates of a parallel plate condenser -
1. The electric intensity between the plates will decrease
2. The electric intensity between the plates will increase
3. The electric intensity between the plates will remain unchanged
4. The P.D. between the plates will decrease

Force of attraction between the plates of a parallel plate capacitor whose dielectric constant is K will be -
1. $\frac{q^2}{2{\epsilon }_{0}AK}$
2. $\frac{q^2}{{\epsilon }_{0}AK}$
3. $\frac{q}{2{\epsilon }_{0}A}$
4. $\frac{q^2}{2{\epsilon }_0{A}^{2}K}$

A light bulb, a capacitor and a battery are connected together as shown below with the switch S initially open. When the switch S is closed, which one of the following is true?
      
1. The bulb will light up for an instant when
    the capacitor starts charging.
2. The bulb will light up when
    the capacitor is fully charged.
3. The bulb will not light up at all.
4. The bulb will light up and go off at regular intervals.

A parallel plate condenser with oil between the plates (dielectric constant of oil K = 2) has a capacitance C. If the oil is removed, then capacitance of the capacitor becomes 
1. $\sqrt{2}C$
2. 2C
3. $\frac{C}{\sqrt{2}}$
4. $\frac{C}{2}$

A 12pF capacitor is connected to a 50V battery. How much electrostatic energy is stored in the capacitor ?
1. 1.5 × 10^–8 Joule
2. 2.5 × 10^–7 Joule
3. 3.5 × 10^–5 Joule
4. 4.5 × 10^–2 Joule

The capacity of a parallel plate condenser is 10 μF, when the distance between its plates is 8 cm. If the distance between the plates is reduced to 4 cm, then the capacity of this parallel plate condenser will be 
1. 5 μF
2. 10 μF
3. 20 μF
4. 40 μF

The effective capacitance between points X and Y of figure shown in:

1. $6<mspace\; width="1em"></mspace>\mathrm{\mu F}$
2. $12<mspace\; width="1em"></mspace>\mathrm{\mu F}$
3. $18<mspace\; width="1em"></mspace>\mathrm{\mu F}$
4. $24<mspace\; width="1em"></mspace>\mathrm{\mu F}$

A capacitor is charged by connecting a battery across its plates. It stores energy U. Now the battery is disconnected and another identical capacitor is connected across it, then the energy stored by both capacitors of the system will be:
1. U
2. $\frac{U}{2}$
3. 2U
4. $\frac{3}{2}U$

A bullet of mass 2g is having a charge of $2\mathrm{\mu C}$. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of $10<mspace\; width="1em"></mspace>{\mathrm{ms}}^{-1}$ ?
1. 20 kV
2. 5 V
3. 50 kV
4. 5 kV

An electric dipole of moment $\overrightarrow{\mathrm{p}}$ is lying along a uniform electric field $\overrightarrow{\mathrm{E}}$. The work done in rotating the dipole by $90°$ is
1. $\sqrt{2}pE$
2. $\frac{\mathrm{pE}}{2}$
3. 2pE
4. pE

A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging 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. does not change
3. becomes zero
4. increases.

Charges +q and -q are placed at points  A and B respectively which are distance 2L apart, C is the midpoint between A and B. The work done in moving a charge +Q along the semicircle CRD is

1. $\frac{qQ}{2\pi {\epsilon }_{0}L}$
2. $\frac{qQ}{\mathit{6}\pi {\epsilon }_{0}L}$
3. $-\frac{qQ}{\mathit{6}\pi {\epsilon }_{0}L}$
4. $\frac{qQ}{\mathit{4}\pi {\epsilon }_{0}L}$

Two condensers one of capacity C and other of capacity C/2 are connected to a V-volt battery, as shown. The work done in charging fully both the condensers is

1. $\frac{1}{4}C{V}^2$
2. $\frac{3}{2}C{V}^2$
3. $\frac{1}{2}C{V}^2$
4. $2{\mathrm{CV}}^2$

Three capacitors each of capacitance C and of breakdown voltage V are joined in series. The capacitance and breakdown voltage of the combination will be
1. $3\mathrm{C},<mspace\; width="1em"></mspace>\frac{\mathrm{V}}{3}$
2. $\frac{\mathrm{C}}{3}$, 3V
3. 3C, 3V
4. $\frac{C}{3},<mspace\; width="1em"></mspace>\frac{V}{3}$

A parallel plate condenser has a uniform electric field E ($\mathrm{V}<mspace\; width="1em"></mspace>{\mathrm{m}}^{-1}$) in the space between the plates. If the distance between the plates is d (m) and area of each plate is A $\left({\mathrm{m}}^2\right)$, the energy (joules) stored in the condenser is
1. $\frac{1}{2}{\epsilon }_0{E}^{2}Ad$
2. $E^{2}Ad/{\epsilon }_0$
3. $\frac{1}{2}{\epsilon }_0{E}^2$
4. ${\mathrm{\epsilon }}_0\mathrm{EAd}$

Three charges each +q are placed at the corners of an isosceles triangle ABC of sides BC and AC equal to 2a. D and E are the midpoints of BC and CA. The work done in taking a charge Q from D to E is

1. $\frac{3qQ}{4\pi {\epsilon }_{0}a}$
2. $\frac{3qQ}{8\pi {\epsilon }_{0}a}$
3. $\frac{qQ}{4\pi {\epsilon }_{0}a}$
4. zero

A, B and C are three points in a uniform electric field. The electric potential is

1. maximum at A
2. maximum at B
3. maximum at C
4. same at all the three points A, B and C

A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?
1. The energy stored in the capacitor decreases K times.
2. The change in energy stored is $\frac{1}{2}C{V}^2\left(\frac{1}{K}-1\right)$
3. The charge on the capacitor is not conserved.
4. The potential difference between the plates decreases K times.

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

Three uncharged capacitors of capacities \(C_1, C_2~\text{and}~C_3\) are connected to one another as shown in the figure.

If points A, B, and D, are at potential \(V_1, V_2 ~\text{and}~V_3\) then the potential at O will be: