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64 charged drops of capacity C and potential V are put together to form a bigger drop. If each small drop had a charge q, then the charge on bigger drop will be
(1) q                         
(2) 4q
(3) 16q                     
(4) 64q

A positively charged pendulum is oscillating in a uniform electric field as shown in figure. Its time period as compared to that when it was uncharged

(a) will increase                           (b) will decrease
(c) will not change                       (d) will first increase then decrease

A thin metal plate P is inserted between the plates of a parallel-plate capacitor of capacitance C in such a ways that its edges touch the two plates (see the figure). The capacitance now becomes

(a) C/2            (b) 2C
(c) 0                (d) $\infty$

Two charged metal spheres of capacitances C₁ and C₂ are brought in contact and then separated. The final charges Q₁ and Q₂ on them will satisfy the condition
(1) Q₁C₁ = Q₂C₂             
(2) Q₁C₂ > Q₂C₁
(3) Q₁C₂ < Q₂C₁             
(4) Q₁C₂ = Q₂C₁

The charge on a drop of water is \(3\times10^{-8}\) C. If its surface potential is 500 V, its radius must be equal to:
1.  81 cm
2.  54 cm
3.  27 cm
4.  108 cm

A and B are two thin concentric hollow conductors having radii a and b and charges Q₁ and Q₂ respectively. Given that a > b and P is a point between the two spheres and distance of P from the common centre is r (b < r < a). The potential at P is proportional to
(1) $\frac{{\mathrm{Q}}_1+{\mathrm{Q}}_2}{\mathrm{r}}$
(2)$\frac{{\mathrm{Q}}_1}{\mathrm{a}}+\frac{{\mathrm{Q}}_2}{\mathrm{r}}$
(3)$\frac{{\mathrm{Q}}_1}{\mathrm{a}}+\frac{{\mathrm{Q}}_2}{b }$
(4) $\frac{{\mathrm{Q}}_1}{b }+\frac{{\mathrm{Q}}_2}{a}$

How should 5 capacitors each of value 1 $\mathrm{\mu }$F be connected so as to produce a total capacitance $\frac{3}{7}\mathrm{\mu }$F?
(1) Two capacitors in parallel and the combination in series with other three capacitors
(2) Three capacitors in parallel and the combination in series with other two capacitors
(3) Four capacitors in parallel and combination in series with fifth capacitor
(4) All capacitors in parallel

The equivalent capacitance of the combination shown in figure is

(1) $\frac{\mathrm{C}}{2}$
(2)  C
(3) 2C
(4) zero

Four plates of area A are arranged as shown. The equivalent capacitance between A and B is

(a) $\frac{2{\mathrm{A\epsilon }}_0}{3\mathrm{d}}$
(b) $\frac{3{\mathrm{A\epsilon }}_0}{2\mathrm{d}}$
(c) $\frac{4{\mathrm{A\epsilon }}_0}{3\mathrm{d}}$
(d) none

One plate of a capacitor having charge Q, and plate area A, is pulled by a man keeping one plate at fix position, as shown in the figure. What force should be applied by the man such that, the plate moves with constant velocity?

(a) $\frac{{\mathrm{Q}}^2}{{\mathrm{A\epsilon }}_0}$
(b) $\frac{2}{3}\frac{{\mathrm{Q}}^2}{{\mathrm{A\epsilon }}_0}$
(c) zero
(d) $\frac{{\mathrm{Q}}^2}{2{\mathrm{A\epsilon }}_0}$

In the circuit shown, a potential difference of 60 V is applied across AB. The potential difference between the points M and N is

(1) 10 V             
(2) 15 V
(3) 20 V             
(4) 30 V

Two thin different dielectrics are inserted between a parallel plate capacitor. Then electric field verses separation graph is (k₁ < k₂)

An electron having a charge – e located at A in the presence of a point charge +Q located at B is moved to a point C so that ABC is an equilateral triangle. The work done in this process is
1. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{\mathrm{Q}}{\mathrm{AC}}$
2. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{\mathrm{Qe}}{\mathrm{AC}}$
3. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{-\mathrm{Qe}}{\mathrm{AB}}$
4. zero

An infinite number of charges each equal to q are placed along the x-axis at x = 1, x =2,
x = 4, x = 8 and so on. The resultant potential at x = 0 will be
(a) $\frac{\mathrm{q}}{2{\mathrm{\pi \epsilon }}_0}$
(b) $\frac{\mathrm{q}}{4{\mathrm{\pi \epsilon }}_0}$
(c) $\frac{\mathrm{q}}{8{\mathrm{\pi \epsilon }}_0}$
(d) $\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}$

A solid conducting sphere of charge Q is surrounded by an uncharged concentric conducting spherical shell. The potential difference between the sphere and the shell is V. If the shell is now given a charge of –3Q, the new potential difference between them will be
(a) V                    (b) 2 V
(c) 4 V                 (d) –2 V

In a parallel plate capacitor, the plate separation of 10 mm is very small compared with the size of the plates. A potential difference of 5.0 kV is maintained across the plates. The electric field intensity between the plates is
(1) 500 V/m                             
(2) 2.5 $\times$ 10⁵ V/m
(3) 5 $\times$ 10⁵ V/m                       
(4) 2.5 $\times$ 10³ V/m

Three uncharged capacitors of capacities C₁ , C₂ , C₃ are connected as shown in figure to one another and to points A, B and C at potentials V₁ , V₂ and V₃ . Then the potential at O will be

(1) $\frac{{\mathrm{V}}_1{\mathrm{C}}_1+{\mathrm{V}}_2{\mathrm{C}}_2+{\mathrm{V}}_3{\mathrm{C}}_3}{{\mathrm{C}}_1+{\mathrm{C}}_2+{\mathrm{C}}_3}$
(2) $\frac{{\mathrm{V}}_1+{\mathrm{V}}_2+{\mathrm{V}}_3}{{\mathrm{C}}_1+{\mathrm{C}}_2+{\mathrm{C}}_3}$
(3) $\frac{{\mathrm{V}}_1({\mathrm{V}}_2+{\mathrm{V}}_3)}{{\mathrm{C}}_1({\mathrm{C}}_2+{\mathrm{C}}_3)}$
(4) $\frac{{\mathrm{V}}_1{\mathrm{V}}_2{\mathrm{V}}_3}{{\mathrm{C}}_1{\mathrm{C}}_2{\mathrm{C}}_3}$

Two capacitors A (2 $\mathrm{\mu }$F) and B(5 $\mathrm{\mu }$F) are connected to two batteries as shown in the figure. Then the potential difference in volts between the plates of A is

(1) 2                 
(2) 5
(3)11                 
(4)18

The effective capacitance between A and B is ( each capacitor is of 1 $\mathrm{\mu }$F)

(1) $\frac{15}{2}\mathrm{\mu F}$
(2) $\frac{17}{3}\mathrm{\mu F}$
(3) $\frac{13}{8}\mathrm{\mu F}$
(4) $\frac{19}{8}\mathrm{\mu F}$

Two identical thin rings, each of radius R metres are coaxially placed at a distance R metres apart. If Q₁ and Q₂ charges are spread uniformly on the two rings, the work done in moving a charge q from the centre of one ring to that of the other is

(a) zero
(b) $\mathrm{q}\left({\mathrm{Q}}_1-{\mathrm{Q}}_2\right)\left(\sqrt{2}-1\right)/\sqrt{2}\left(4{\mathrm{\pi \epsilon }}_0\mathrm{R}\right)$
(c) $\mathrm{q}\sqrt{2}\left({\mathrm{Q}}_1+{\mathrm{Q}}_2\right)/\left(4{\mathrm{\pi \epsilon }}_0\mathrm{R}\right)$
(d) $\mathrm{q}\left({\mathrm{Q}}_1+{\mathrm{Q}}_2\right)\left(\sqrt{2}+1\right)/\sqrt{2}\left(4{\mathrm{\pi \epsilon }}_0\mathrm{R}\right)$