Question 1: Palette 1/125

Allen 2000 MCQ

A number of capacitors, each of capacitance 1 $\mu$ F and each one of which gets punctured if a potential difference just exceeding 500 volt is applied, are provided. Then an arrangement suitable for giving a capacitor of capacitance 3 $\mu$ F across which 2000 volt may be applied requires at least:

A

4 component capacitors

B

12 component capacitors

C

48 component capacitors

D

16 component capacitors

Question 2: Palette 2/125

Allen MCQ

The capacitance C of a capacitor is :-

A

independent of the charge and potential of the capacitor.

B

dependent on the charge and independent of potential.

C

independent of the geometrical configuration of the capacitor.

D

independent of the dielectric medium between the two conducting surfaces of the capacitor.

Question 3: Palette 3/125

Allen MCQ

To increase the charge on the plate of a capacitor implies to :-

A

decrease the potential difference between the plates.

B

decrease the capacitance of the capacitor.

C

increase the capacitance of the capacitor.

D

increase the potential difference between the plates.

Question 4: Palette 4/125

Allen MCQ

The net charge on a capacitor is :-

A

2q

B

q/2

C

0

D

infinity

Question 5: Palette 5/125

Allen MCQ

The earth has Volume 'V' and Surface area 'A'; then its capacitance would be:

A

$4\pi \in_{0} \frac{A}{V}$

B

$4\pi \in_{0} \frac{V}{A}$

C

$12\pi \in_{0} \frac{V}{A}$

D

$12\pi \in_{0} \frac{A}{V}$

Question 6: Palette 6/125

Allen MCQ

Capacitors are used in electrical circuits where appliances need rapid :

A

Current

B

Voltage

C

Watt

D

Resistance

Question 7: Palette 7/125

Allen MCQ

Which of the following is called electrical energy tank?

A

Resistor

B

Inductance

C

Capacitor

D

Motor

Question 8: Palette 8/125

Allen MCQ

If the maximum circumference of a sphere is 2 m, then its capacitance in water would be :-(Dielectric constant of water = 81)

A

27.65 pF

B

2385 pF

C

236.5 pF

D

2865 pF

Question 9: Palette 9/125

Allen MCQ

The two parallel plates of a condenser have been connected to a battery of 300 V and the charge collected at each plate is 1 $\mu$ C. The energy supplied by the battery is:

A

$6 \times 10^{-4}$ J

B

$3 \times 10^{-4}$ J

C

$1.5 \times 10^{-4}$ J

D

$4.5 \times 10^{-4}$ J

Question 10: Palette 10/125

Allen MCQ

When a capacitor of value 200 $\mu$ F charged to 200V is discharged separately through resistance of 2 ohms and 8 ohms, then heat produced in joule will respectively be:

A

4 and 16

B

16 and 4

C

4 and 8

D

4 and 4

Question 11: Palette 11/125

Allen MCQ

The potential to which a conductor is raised, depends on :-

A

the amount of charge

B

the geometry and size of the conductor

C

both (1) and (2)

D

None of these

Question 12: Palette 12/125

Allen MCQ

The charge q on a capacitor varies with voltage as shown in figure. The area of the triangle AOB represents :

A

electric field between the plates

B

electric flux between the plates

C

energy density

D

energy stored by the capacitor.

Question 13: Palette 13/125

Allen MCQ

An uncharged capacitor is connected to a battery. On charging the capacitor :-

A

all the energy supplied is stored in the capacitor.

B

half the energy supplied is stored in the capacitor.

C

the energy stored depends upon the capacity of the capacitor only.

D

the energy stored depends upon the time for which the capacitor is charged.

Question 14: Palette 14/125

Allen MCQ

The capacity of parallel plate condenser depends on:

A

the type of metal used

B

the thickness of plates

C

the potential difference applied across the plates

D

the separation between the plates.

Question 15: Palette 15/125

Allen MCQ

A parallel plate capacitor has rectangular plates of $400 \, cm^{2}$ area and are separated by a distance of 2 mm with air as the medium. What charge will appear on the plates if a 200 volt potential difference is applied across the capacitor?

A

$3.54 \times 10^{-6}$ C

B

$3.54 \times 10^{-8}$ C

C

$3.54 \times 10^{-10}$ C

D

$1770.8 \times 10^{-13}$ C

Question 16: Palette 16/125

Allen MCQ

There are two metallic plates of a parallel plate capacitor. One plate is given a charge +q while the other is earthed as shown. Points P, $P_{1}$ and $P_{2}$ are taken as shown in adjoining figure. Then the electric intensity is not zero at:

A

P only

B

$P_{1}$ only

C

$P_{2}$ only

D

P, $P_{1}$ and $P_{2}$

Question 17: Palette 17/125

Allen MCQ

The distance between the plates of a circular parallel plate capacitor of diameter 40 mm, whose capacity is equal to that of a metallic sphere of radius 1m will be:

A

0.01 mm

B

0.1 mm

C

1.0 mm

D

10 mm

Question 18: Palette 18/125

Allen MCQ

The energy density in a parallel plate capacitor is given as $2.1 \times 10^{-9}$ J/m $^{3}$ . The value of the electric field in the region between the plates is:

A

2.1 NC $^{-1}$

B

21.6 NC $^{-1}$

C

72 NC $^{-1}$

D

8.4 NC $^{-1}$

Question 19: Palette 19/125

Allen MCQ

A charged parallel plate capacitor of distance (d) has $U_{0}$ energy. A slab of dielectric constant (K) and thickness (d) is then introduced between the plates of the capacitor. The new energy of the system is given by:

A

$KU_{0}$

B

$K^{2}U_{0}$

C

$\frac{U_{0}}{K}$

D

$\frac{U_{0}}{K^{2}}$

Question 20: Palette 20/125

Allen MCQ

The energy and capacity of a charged parallel plate capacitor are U and C respectively. Now a dielectric slab of $\in_{r}=6$ is inserted in it then energy and capacity becomes: (Assuming charge on plates remains constant)

A

6U, 6C

B

U, C

C

$\frac{U}{6}$ , 6C

D

U, 6C

Question 21: Palette 21/125

Allen MCQ

Distance between the plates of a parallel plate capacitor is 'd' and area of each plate is A. When a slab of dielectric constant K and thickness t is placed between the plates, its capacity becomes:

A

$\frac{\varepsilon_{0}A}{\left[d+t\left\{1-\frac{1}{K}\right\}\right]}$

B

$\frac{\varepsilon_{0}A}{\left[d+t\left\{1+\frac{1}{K}\right\}\right]}$

C

$\frac{\varepsilon_{0}A}{\left[d-t\left\{1+\frac{1}{K}\right\}\right]}$

D

$\frac{\varepsilon_{0}A}{\left[d-t\left\{1-\frac{1}{K}\right\}\right]}$

Question 22: Palette 22/125

Allen MCQ

When a slab of dielectric medium is placed between the plates of a parallel plate capacitor which is connected with a battery, then the charge on plates in comparison with earlier charge:

A

is less

B

is same

C

is more

D

depends on the nature of the material inserted

Question 23: Palette 23/125

Allen MCQ

A glass slab is put within the plates of a charged parallel plate condenser. Which of the following quantities does not change?

A

energy of the condenser

B

capacity

C

intensity of electric field

D

charge

Question 24: Palette 24/125

Allen MCQ

A parallel plate capacitor is connected to a battery and a dielectric slab is inserted between the plates, then which quantity increase:

A

potential difference

B

electric field

C

stored energy

D

E.M.F. of battery

Question 25: Palette 25/125

Allen MCQ

A parallel plate capacitor is charged by a battery. After charging the capacitor, battery is disconnected and a dielectric plate is inserted between the plates. Then which of the following statements is not correct there is a/an?

A

increase in the stored energy

B

decrease in the potential difference

C

decrease in the electric field

D

increase in the capacitance

Question 26: Palette 26/125

Allen MCQ

A parallel plate capacitor is charged by a battery. After charging the capacitor, battery is disconnected and distance between the plates is decreased then which of the following statement is correct?

A

electric field does not remain constant

B

potential difference is increased

C

the capacitance decreases

D

the stored energy decreases

Question 27: Palette 27/125

Allen MCQ

A parallel plate capacitor is connected with a battery whose potential difference remains constant. If the plates of the capacitor are shifted apart then the intensity of electric field:

A

decreases and charge on plates also decreases.

B

remains constant but charge on plates decreases.

C

remains constant but charge on the plates increases.

D

increases but charge on the plates decreases.

Question 28: Palette 28/125

Allen MCQ

A parallel plate capacitor is charged with a battery and afterwards the battery is removed. if now, with the help of insulating handles, the distance between the plates is increased, then

A

charge on capacitor increases and capacity decreases.

B

potential difference between the plates increases.

C

capacity of capacitor increases.

D

value of energy stored in capacitor decreases.

Question 29: Palette 29/125

Allen MCQ

Can a metal be used as a medium for dielectric?

A

Yes

B

No

C

Depends on its shape

D

Depends on dielectric

Question 30: Palette 30/125

Allen MCQ

A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be :-

A

400%

B

66.6%

C

33.3%

D

200%

Question 31: Palette 31/125

Allen MCQ

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

A

$8\mu \mathrm{F}$

B

$6\mu \mathrm{F}$

C

$\frac{8}{3}\mu \mathrm{F}$

D

$\frac{3}{8}\mu \mathrm{F}$

Question 32: Palette 32/125

Allen MCQ

In an adjoining figure three capacitors $C_{1}$ , $C_{2}$ and $C_{3}$ are joined to a battery. The correct condition will be :

A

$Q_{1} = Q_{2} = Q_{3}$ and $V_{1} = V_{2} = V_{3} = V$

B

$Q_{1} = Q_{2} + Q_{3}$ and $V = V_{1} + V_{2} + V_{3}$

C

$Q_{1} = Q_{2} + Q_{3}$ and $V = V_{1} + V_{2}$

D

$Q_{2} = Q_{3}$ and $V_{2} = V_{3}$
(Symbols have their usual meanings)

Question 33: Palette 33/125

Allen MCQ

The effective capacity of the network between terminals A and B is :

A

$6\mu \mathrm{F}$

B

$20\mu \mathrm{F}$

C

$3\mu \mathrm{F}$

D

$10\mu \mathrm{F}$

Question 34: Palette 34/125

Allen MCQ

A series combination of two capacitances of value 0.1 μF and 1μF is connected with a source of voltage 500 volts. The potential difference in volts across the capacitor of value 0.1 μF will be:

A

50

B

500

C

45.5

D

454.5

Question 35: Palette 35/125

Allen MCQ

The value of equivalent capacitance of the combination shown in figure, between the points P and Q is :

A

3C

B

2C

C

C

D

C/3

Question 36: Palette 36/125

Allen MCQ

The equivalent capacitance between points A and B of the circuit shown will be :

A

$\frac{2}{3} \mu \mathrm{F}$

B

$\frac{5}{3}$ μF

C

$\frac{8}{3} \mu \mathrm{F}$

D

$\frac{7}{3} \mu \mathrm{F}$

Question 37: Palette 37/125

Allen MCQ

The effective capacitance between the points P and Q of the arrangement shown in the figure is :

A

$(1 / 2)\mu \mathrm{F}$

B

$1 \mu \mathrm{F}$

C

$2\mu \mathrm{F}$

D

$1.33\mu \mathrm{F}$

Question 38: Palette 38/125

Allen MCQ

Two spheres of radii $R_{1}$ and $R_{2}$ having equal charges are joined together with a copper wire. If V is the potential of each sphere after they are separated from each other, then the initial charge on both spheres was:

A

$\frac{V}{k}(R_{1}+R_{2})$

B

$\frac{V}{2k}(R_{1}+R_{2})$

C

$\frac{V}{3k}(R_{1}+R_{2})$

D

$\frac{V}{k}\frac{(R_{1}R_{2})}{(R_{1}+R_{2})}$

Question 39: Palette 39/125

Allen MCQ

Two spheres of radii 1 cm and 2 cm have been charged with $1.5 \times 10^{-8}$ and $0.3 \times 10^{-7}$ coulombs of positive charge. When they are connected with a wire, charge:

A

will flow from the first to the second

B

will flow from the second to the first

C

will not flow at all

D

may flow either from first to second, or from the second to first, depending upon the length of the connecting wire

Question 40: Palette 40/125

Allen MCQ

Half of the space between a parallel plate capacitor is filled with a medium of dielectric constant K parallel to the plates. If initially the capacity was C, then the new capacity will be:

A

2KC/(1+K)

B

C (K+1)/2

C

CK/(1+K)

D

KC

Question 41: Palette 41/125

Allen MCQ

Two capacitances $C_{1}$ and $C_{2}$ in a circuit are joined as shown in figure The potential of point A is $V_{1}$ and that of B is $V_{2}$ . The potential of point D will be :

A

$\frac{1}{2} (V_1 + V_2)$

B

$\frac{\mathrm{C}_2\mathrm{V}_1 + \mathrm{C}_1\mathrm{V}_2}{\mathrm{C}_1 + \mathrm{C}_2}$

C

$\frac{\mathrm{C}_1\mathrm{V}_1 + \mathrm{C}_2\mathrm{V}_2}{\mathrm{C}_1 + \mathrm{C}_2}$

D

$\frac{\mathrm{C}_2\mathrm{V}_1 - \mathrm{C}_1\mathrm{V}_2}{\mathrm{C}_1 + \mathrm{C}_2}$

Question 42: Palette 42/125

Allen MCQ

A circuit has a section AB as shown in the figure with E = 10 V, $C_{1} = 1.0 \mu F$ , $C_{2} = 2.0 \mu F$ and the potential difference $V_{A} - V_{B} = 5 V$ . The voltage across $C_{1}$ is :

A

Zero

B

$5\mathrm{V}$

C

$10\mathrm{V}$

D

$15\mathrm{V}$

Question 43: Palette 43/125

Allen MCQ

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

A

$14 / 5$

C

$3 / 7$

D

None of these

Question 44: Palette 44/125

Allen MCQ

Two capacitances $C_{1}$ and $C_{2}$ are connected in series; assume that $C_{1} < C_{2}$ . The equivalent capacitance of this arrangement is C, where:

A

$C < C_{1}/2$

B

$C_{1}/2 < C < C_{1}$

C

$C_{1} < C < C_{2}$

D

$C_{2} < C < 2C_{2}$

Question 45: Palette 45/125

Allen MCQ

In the following circuit the resultant capacitance between A & B is $1\mu F$ . Find the value of C :

A

$\frac{23}{32}\mu \mathrm{F}$

B

$\frac{32}{23}\mu \mathrm{F}$

C

$\frac{13}{23}\mu \mathrm{F}$

D

$\frac{23}{13}\mu \mathrm{F}$

Question 46: Palette 46/125

Allen MCQ

A capacitor of capacitance 5 $\mu$ F is connected as shown in the figure. The internal resistance of the cell is 0.5 $\Omega$ . The amount of charge on the capacitor plate is :

A

0

B

$5\mu \mathrm{C}$

C

$10\mu \mathrm{C}$

D

$25\mu \mathrm{C}$

Question 47: Palette 47/125

Allen MCQ

In the given circuit, the potential difference across 3 $\mu$ F capacitor will be :

A

$16\mathrm{V}$

B

$10\mathrm{V}$

C

$6\mathrm{V}$

D

4 V

Question 48: Palette 48/125

Allen MCQ

If potential of A is 10 V, then potential of B is :

A

$25 / 3\mathrm{V}$

B

$50 / 3\mathrm{V}$

C

$100 / 3\mathrm{V}$

D

$50\mathrm{V}$

Question 49: Palette 49/125

Allen MCQ

Capacitance $C_{1} = 2C_{2} = 2C_{3}$ and potential difference across $C_{1}$ , $C_{2}$ and $C_{3}$ are $V_{1}$ , $V_{2}$ and $V_{3}$ respectively then :

A

$V_{1} = V_{2} = V_{3}$

B

$V_{1} = 2V_{2} = 2V_{3}$

C

$2V_{1} = V_{2} = V_{3}$

D

$2V_{1} = 2V_{2} = V_{3}$

Question 50: Palette 50/125

Allen MCQ

In the circuit shown in figure, the battery is an ideal one with emf V. The capacitor is initially uncharged. Switch S is closed at time t = 0. The final charge Q on the capacitor is:

A

$\frac{CV}{2}$

B

$\frac{CV}{3}$

C

CV

D

$\frac{CV}{6}$

Question 51: Palette 51/125

Allen MCQ

In previous question, what is the current in the steady state is?

A

$\frac{V}{2R}$

B

$\frac{V}{R}$

C

$\frac{2V}{R}$

D

$\frac{V}{3R}$

Question 52: Palette 52/125

Allen MCQ

A bulb, a capacitor and a battery are connected together as shown here, with switch S initially open. When the switch S is closed, which one of the following is true?

A

The bulb will light up for an instant when the capacitor starts charging.

B

The bulb will light up when the capacitor is fully charged

C

The bulb will not light up at all

D

The bulb will light up and go off at regular intervals.

Question 53: Palette 53/125

Allen MCQ

The capacity of a parallel plate air capacitor is $10 \mu F$ . As shown in the figure this capacitor is divided into two equal parts; these parts are filled by media of dielectric constants $K_{1}=2$ and $K_{2}=4$ . Capacity of this arrangement will be :

A

$20\mu \mathrm{F}$

B

$30\mu \mathrm{F}$

C

$10\mu \mathrm{F}$

D

$40\mu \mathrm{F}$

Question 54: Palette 54/125

Allen MCQ

Three capacitors, each of value 1 $\mu$ F are so combined that the resultant capacity is 1.5 $\mu$ F. Then :

A

All three capacitors are connected in parallel.

B

All three capacitors are connected in series.

C

Third capacitor is in series with a parallel combination of the other two.

D

Third capacitor is in parallel with a series combination of the other two.

Question 55: Palette 55/125

Allen MCQ

Two conducting spheres of radii $R_{1}$ and $R_{2}$ are charged with charges $Q_{1}$ and $Q_{2}$ respectively. On bringing them in contact there is:

A

no change in the energy of the system

B

an increase in the energy of the system if $Q_{1}R_{2} \neq Q_{2}R_{1}$

C

always a decrease in the energy of the system

D

a decrease in the energy of the system if $Q_{1}R_{2} \neq Q_{2}R_{1}$

Question 56: Palette 56/125

Allen MCQ

A capacitor is charged with a battery and energy stored is U. After disconnecting the battery another capacitor of same capacity is connected in parallel with it. The energy stored in each capacitor is:

A

U/2

B

U/4

C

4 U

D

2 U

Question 57: Palette 57/125

Allen MCQ

Three capacitors of capacitances 3 μF, 10 μF and 15 μF are connected in series to a voltage source of 100 V. The charge on 15 μF is :

A

50 μC

B

160 μC

C

200 μC

D

280 μC

Question 58: Palette 58/125

Allen MCQ

Two capacitors A and B are connected in series with a battery as shown in the figure. When the switch S is closed and the two capacitors get charged fully, then :

A

the potential difference across the plates of A is 4 V and across the plates of B is 6 V

B

the p.d. across the plates of A is 6 V and across the plates of B is 4 V

C

the ratio of electrical energies stored in A and B is 2:3

D

the ratio of charges on A and B is 3:2

Question 59: Palette 59/125

Allen MCQ

An automobile spring extends 0.2 m for 5000 N load. The ratio of potential energy stored in this spring when it has been compressed by 0.2 m to the potential energy stored in a 10 $\mu$ F capacitor at a potential difference of 10000 V will be :

A

$\frac{1}{4}$

B

1

C

$\frac{1}{2}$

D

2

Question 60: Palette 60/125

Allen MCQ

The charge on each capacitors shown in figure and the potential difference across them will be respectively :-

A

240μC, 80μC, 160μC and 80 V, 40 V, 40 V

B

300μC, 75μC, 150μC and 40 V, 80 V, 60 V

C

220μC, 70μC, 140μC and 60 V, 50 V, 40 V

D

none of these

Question 61: Palette 61/125

Allen MCQ

Three capacitance 2 μF, 3 μF and 6 μF are connected in series with a 10 volt battery, then charge on 3 μF capacitor is:

A

5 μC

B

10μC

C

11μC

D

15μC

Question 62: Palette 62/125

Allen MCQ

Two charged spheres having radii a and b are joined with a wire then the ratio of electric field $E_{a}/E_{b}$ on their respective surfaces is:

A

a/b

B

b/a

C

$a^{2}/b^{2}$

D

$b^{2}/a^{2}$

Question 63: Palette 63/125

Allen MCQ

A solid conducting sphere of radius $R_{1}$ is surrounded by another concentric hollow conducting sphere of radius $R_{2}$ . The capacitance of this assembly is proportional to:

A

$\frac{R_{2}-R_{1}}{R_{1}R_{2}}$

B

$\frac{R_{2}+R_{1}}{R_{1}R_{2}}$

C

$\frac{R_{1}R_{2}}{R_{1}+R_{2}}$

D

$\frac{R_{1}R_{2}}{R_{2}-R_{1}}$

Question 64: Palette 64/125

Allen MCQ

Two spherical conductors A and B of radius a and b (b > a) are placed in air concentrically. B is given a charge + Q coulombs and A is grounded. The equivalent capacitance of these is:

A

$4\pi \in_{0} \frac{ab}{(b - a)}$

B

$4\pi \in_{0} (a + b)$

C

$4\pi \in_{0} b$

D

$4\pi \in_{0} \frac{b^{2}}{(b - a)}$

Question 65: Palette 65/125

Allen MCQ

Time constant of a series R-C circuit is:-

A

+RC

B

-RC

C

$\frac{R}{C}$

D

$\frac{C}{R}$

Question 66: Palette 66/125

Allen MCQ

Energy per unit volume for a capacitor having area A and separation d kept at potential difference V is given by:

A

$\frac{1}{2} \in_{0} \frac{V^{2}}{d^{2}}$

B

$\frac{1}{2 \in_{0}} \frac{V^{2}}{d^{2}}$

C

$\frac{\varepsilon_{0} V^{2} A^{2}}{2 d^{2}}$

D

$\frac{1}{2} \frac{V^{2} A^{2}}{\varepsilon_{0} d^{2}}$

Question 67: Palette 67/125

Allen MCQ

A capacitor of capacity $C_{1}$ charged up to a voltage V and then connected to an uncharged capacitor of capacity $C_{2}$ . Then final potential difference across each will be:

A

$\frac{C_{2}V}{C_{1}+C_{2}}$

B

$\frac{C_{1}V}{C_{1}+C_{2}}$

C

$\left(1+\frac{C_{2}}{C_{1}}\right)V$

D

$\left(1-\frac{C_{2}}{C_{1}}\right)V$

Question 68: Palette 68/125

Allen MCQ

A conducting sphere of radius 10 cm is charged with 10 $\mu$ C. Another uncharged sphere of radius 20 cm is allowed to touch it for some time. After that, if the spheres are separated, then surface density of charge on the spheres will be in the ratio of:

A

1:4

B

1:3

C

2:1

D

1:1

Question 69: Palette 69/125

Allen MCQ

In the given figure, the capacitors $C_{1}$ , $C_{3}$ , $C_{4}$ , $C_{5}$ have a capacitance 4 $\mu$ F each. If the capacitor $C_{2}$ has a capacitance 10 $\mu$ F, then effective capacitance between A and B will be:

A

$2\mu \mathrm{F}$

B

$4\mu \mathrm{F}$

C

$6\mu \mathrm{F}$

D

$8\mu \mathrm{F}$

Question 70: Palette 70/125

Allen MCQ

Two capacitors of capacitances 3 $\mu$ F and 6 $\mu$ F are charged to a potential of 12 V each. They are now connected to each other with the positive plate of one joined to the negative plate of the other. The potential difference across each will be

A

3 V

B

Zero

C

6 V

D

4 V

Question 71: Palette 71/125

Allen MCQ

A capacitor of 0.2 μF capacitance is charged to 600 V. After removing the battery, it is connected with a 1.0 μF capacitor in parallel, then the potential difference across each capacitor will become:

A

300 V

B

600 V

C

100 V

D

120 V

Question 72: Palette 72/125

Allen MCQ

Mean electric energy density between the plates of a charged capacitor is: Here q = Charge on capacitor A = Area of each plate of the capacitor

A

$q^{2}/(2 \in_{0} A^{2})$

B

$q/(2 \in_{0} A^{2})$

C

$q^{2}/(2 \in_{0} A)$

D

None of these

Question 73: Palette 73/125

Allen MCQ

If potential difference across a capacitor is changed from 15 V to 30 V, work done is W. The work done when potential difference is changed from 30 V to 60 V, will be :

A

W

B

4W

C

3 W

D

2 W

Question 74: Palette 74/125

Allen MCQ

Three capacitors each of capacity $4 \mu F$ are to be connected in such a way that the effective capacitance is $6 \mu F$ . This can be done by:

A

connecting all of them in series

B

connecting all of them in parallel

C

connecting two in series and one in parallel

D

connecting two in parallel and one in series

Question 75: Palette 75/125

Allen MCQ

A capacitor is connected to a 10 V battery. The charge on plates is 40 μC when medium between plates is air. The charge on the plates become 100 μC when the space between the plates is filled with oil. The dielectric constant of oil is:

A

2.5

B

4

C

6.25

D

10

Question 76: Palette 76/125

Allen MCQ

Two capacitor each having a capacitance C and breakdown voltage V are joined in series. The effective capacitance and maximum working voltage of the combination is :-

A

2C, 2V

B

$\frac{C}{2}, \frac{V}{2}$

C

2C, V

D

$\frac{C}{2}, 2V$

Question 77: Palette 77/125

Allen MCQ

The charge (in $\mu$ C) on any one of the 2 $\mu$ F capacitor and 1 $\mu$ F capacitor will be given respectively as :

A

1,2

B

2,1

C

1,1

D

2,2

Question 78: Palette 78/125

Allen MCQ

The electric field between the plates of a parallel plate capacitor when connected to a certain battery is $E_{0}$ . If the space between the plates of the capacitor is filled by introducing a material of dielectric constant K without disturbing the battery connections; the field between the plates will be:

A

$KE_{0}$

B

$E_{0}$

C

$\frac{E_{0}}{K}$

D

None of the above

Question 79: Palette 79/125

Allen MCQ

A 40 μF capacitor in a defibrillator is charged to 3000 V. The energy stored in the capacitor is sent through the patient during a pulse of duration 2 ms. The power delivered to the patient is:

A

45 kW

B

90 kW

C

180 kW

D

360 kW

Question 80: Palette 80/125

Allen MCQ

Two capacitors with capacity $C_{1}$ and $C_{2}$ , when connected in series, have a capacitance $C_{s}$ and when connected in parallel have a capacitance $C_{p}$ . Which of the following is true?

A

$C_{s} = C_{1} + C_{2}$

B

$C_{p} = \frac{C_{1}C_{2}}{C_{1} + C_{2}}$

C

$\frac{C_{s}}{C_{p}} = \frac{C_{1}}{C_{2}}$

D

$C_{s}C_{p} = C_{1}C_{2}$

Question 81: Palette 81/125

Allen MCQ

Two metallic spheres of radii $R_{1}$ and $R_{2}$ are connected by a thin wire. If $+q_{1}$ and $+q_{2}$ are the charges on the two spheres then:

A

$\frac{q_{1}}{q_{2}} = \frac{R_{1}^{2}}{R_{2}^{2}}$

B

$\frac{q_{1}}{q_{2}} = \frac{R_{1}}{R_{2}}$

C

$\frac{q_{1}}{q_{2}} = \frac{R_{1}^{3}}{R_{2}^{3}}$

D

$\frac{q_{1}}{q_{2}} = \frac{\left(R_{1}^{2} - R_{2}^{2}\right)}{\left(R_{1}^{2} + R_{2}^{2}\right)}$

Question 82: Palette 82/125

Allen MCQ

Two spheres have radii 10 cm & 20 cm. One of the sphere is given 150 $\mu$ C charge and connected by a wire. Their common potential will be -

A

$9 \times 10^{6}$ volts

B

$4 \cdot 5 \times 10^{6}$ volts

C

$1 \cdot 8 \times 10^{6}$ volts

D

$1 \cdot 35 \times 10^{9}$ volts

Question 83: Palette 83/125

Allen MCQ

Total energy stored in a 900 $\mu$ F capacitor at 100 volts is transferred into a 100 $\mu$ F capacitor. The potential drop across the new capacitor is (in volts)

A

900

B

200

C

100

D

300

Question 84: Palette 84/125

Allen MCQ

Two thin dielectric slabs of dielectric constants $K_{1}$ and $K_{2}$ ( $K_{1} < K_{2}$ ) are inserted between the plates of a parallel plate capacitor, as shown in the figure. The variation of electric field 'E' between the plates with distance 'd' as measured from plate P is correctly shown by :-

A

B

C

D

Question 85: Palette 85/125

Allen MCQ

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?

A

The energy stored in the capacitor decreases K times.

B

The change in energy stored is $\frac{1}{2}\mathrm{CV}^2\left(\frac{1}{\mathrm{K}} -1\right)$ .

C

The charge on the capacitor is not conserved.

D

The potential difference between the plates decreases K times.

Question 86: Palette 86/125

Allen MCQ

A parallel plate air capacitor has capacity 'C' and separation between the plates is 'd'. A potential difference 'V' is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is :-

A

$\frac{C^2V^2}{2d^2}$

B

$\frac{C^2V^2}{2d}$

C

$\frac{CV^2}{2d}$

D

$\frac{CV^2}{d}$

Question 87: Palette 87/125

Allen MCQ

A capacitor of $2\mu F$ is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is:

A

$0\%$

B

$20\%$

C

$75\%$

D

$80\%$

Question 88: Palette 88/125

Allen MCQ

A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system :-

A

Decreases by a factor of 2

B

Remains the same

C

Increases by a factor of 2

D

Increases by a factor of 4

Question 89: Palette 89/125

Allen MCQ

The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is :-

A

independent of the distance between the plates.

B

linearly proportional to the distance between the plates

C

proportional to the square root of the distance between the plates.

D

inversely proportional to the distance between the plates.

Question 90: Palette 90/125

Allen MCQ

Two identical capacitors $C_{1}$ and $C_{2}$ of equal capacitance are connected as shown in the circuit. Terminals a and b of the key k are connected to charge capacitor $C_{1}$ using battery of emf V volt. Now disconnecting a and b the terminals b and c are connected. Due to this, what will be the percentage loss of energy?

A

75%

B

0%

C

50%

D

25%

Question 91: Palette 91/125

Allen MCQ

Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density $\sigma$ . They are brought in contact and separated. What will be the new surface charge densities on them?

A

$\sigma_{1} = \frac{5}{6}\sigma$ , $\sigma_{2} = \frac{5}{2}\sigma$

B

$\sigma_{1} = \frac{5}{2}\sigma$ , $\sigma_{2} = \frac{5}{6}\sigma$

C

$\sigma_{1} = \frac{5}{2}\sigma$ , $\sigma_{2} = \frac{5}{3}\sigma$

D

$\sigma_{1} = \frac{5}{3}\sigma$ , $\sigma_{2} = \frac{5}{6}\sigma$

Question 92: Palette 92/125

Allen MCQ

The capacitance of a parallel plate capacitor with air as medium is 6 μF. With the introduction of a dielectric medium, the capacitance becomes 30 μF. The permittivity of the medium is: (ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²)

A

5.00 C² N⁻¹ m⁻²

B

0.44 × 10⁻¹³ C² N⁻¹ m⁻²

C

1.77 × 10⁻¹² C² N⁻¹ m⁻²

D

0.44 × 10⁻¹⁰ C² N⁻¹ m⁻²

Question 93: Palette 93/125

Allen MCQ

A parallel plate capacitor having cross-sectional area A and separation d has air in between the plates. Now an insulating slab of same area but thickness d/2 is inserted between the plates as shown in figure having dielectric constant K(= 4). The ratio of new capacitance to its original capacitance will be,

A

2:1

B

8:5

C

6:5

D

4:1

Question 94: Palette 94/125

Allen MCQ

The equivalent capacitance of the combination shown in the figure is :

A

3C

B

2C

C

C/2

D

3C/2

Question 95: Palette 95/125

Allen MCQ

A parallel plate capacitor has a uniform electric field 'E' in the space between the plates. If the distance between the plates is 'd' and the area of each plate is 'A', the energy stored in the capacitor is: ($\varepsilon_{0}$ = permittivity of free space)

A

$\frac{1}{2}\varepsilon_{0}E^{2}$

B

$\varepsilon_{0}EAd$

C

$\frac{1}{2}\varepsilon_{0}E^{2}Ad$

D

$\frac{E^{2}Ad}{\varepsilon_{0}}$

Question 96: Palette 96/125

Allen MCQ

Polar molecules are the molecules :

A

having zero dipole moment.

B

acquire a dipole moment only in the presence of electric field due to displacement of charges.

C

acquire a dipole moment only when magnetic field is absent.

D

having a permanent electric dipole moment.

Question 97: Palette 97/125

Allen MCQ

A capacitor of capacitance C = 900 pF is charged fully by 100 V battery B as shown in figure (a). Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance C = 900 pF as shown in figure (b). The electrostatic energy stored by the system (b) is:
(a)

(b)

A

$3.25 \times 10^{-6} \mathrm{~J}$

B

$2.25 \times 10^{-6} \mathrm{~J}$

C

$1.5 \times 10^{-6} \mathrm{~J}$

D

$4.5 \times 10^{-6} \mathrm{~J}$

Question 98: Palette 98/125

Allen MCQ

The distance between the two plates of a parallel plate capacitor is doubled and the area of each plate is halved. If C is its initial capacitance, its final capacitance is equal to:

A

2C

B

C/2

C

4C

D

C/4

Question 99: Palette 99/125

Allen MCQ

The effective capacitances of two capacitors are $3\mu F$ and $16\mu F$ , when they are connected in series and parallel respectively. The capacitance of two capacitors are:

A

$10\mu F, 6\mu F$

B

$8\mu F, 8\mu F$

C

$12\mu F, 4\mu F$

D

$1.2\mu F, 1.8\mu F$

Question 100: Palette 100/125

Allen MCQ

The equivalent capacitance of the system shown in the following circuit is :

A

$3\mu \mathrm{F}$

B

$6\mu \mathrm{F}$

C

$9\mu \mathrm{F}$

D

$2\mu \mathrm{F}$

Question 101: Palette 101/125

Allen MCQ

The equivalent capacitance of the arrangement shown in figure is :

A

$30~\mu \mathrm{F}$

B

$15~\mu \mathrm{F}$

C

$25~\mu \mathrm{F}$

D

$20~\mu \mathrm{F}$

Question 102: Palette 102/125

Allen MCQ

In the following circuit, the equivalent capacitance between terminal A and terminal B is :

A

2μF

B

1μF

C

0.5μF

D

4μF

Question 103: Palette 103/125

Allen MCQ

If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then A. the charge stored in it, increases. B. the energy stored in it, decreases. C. its capacitance increases. D. the ratio of charge to its potential remains the same. E. the product of charge and voltage increases. Choose the most appropriate answer from the options given below:

A

A, B and E only

B

A, C and E only

C

B, D and E only

D

A, B and C only

Question 104: Palette 104/125

Allen MCQ

A 12 pF capacitor is connected to a 50V battery, the electrostatic energy stored in the capacitor in nJ is :

A

15

B

7.5

C

0.3

D

150

Question 105: Palette 105/125

Allen MCQ

The capacitance of a capacitor with charge q and a potential difference V depends on:

A

both q and V

B

the geometry of the capacitor

C

q only

D

V only

Question 106: Palette 106/125

Allen MCQ

The steady state current in the circuit shown below is:

A

0.67 A

B

1.5 A

C

2 A

D

1 A

Question 107: Palette 107/125

Allen MCQ

A parallel plate air capacitor is connected to a battery. The quantities charge, voltage, electric field and energy associated with the capacitor are given by $Q_{0}$ , $V_{0}$ , $E_{0}$ and $U_{0}$ respectively. A dielectric slab is now inserted to fill the space between the plates with battery still in connection. The corresponding quantities now given by Q, V E and U are related to the previous one as:
(a) $Q > Q_{0}$ (b) $V > V_{0}$ (c) $E > E_{0}$ (d) $U > U_{0}$

A

only a) is correct

B

only a & c are correct

C

only a & d are correct

D

all of above are correct

Question 108: Palette 108/125

Allen MCQ

A dielectric slab of thickness d is inserted in a parallel plate capacitor whose negative plate is at x = 0 and positive plate is at x = 3d. The slab is equidistant from the plates. The capacitor is given some charge. As one goes from 0 to 3d:
(a) The magnitude of the electric field remains the same
(b) The direction of the electric field remains the same
(c) The electric potential increases continuously
(d) The electric potential increases at first, then decreases and again increases

A

a and c are correct

B

b and c are correct

C

a, b and c are correct

D

All are correct

Question 109: Palette 109/125

Allen MCQ

The plates of a parallel plate capacitor are, not exactly parallel. The surface charge density therefore:
(a) Is higher at the closer end
(b) The surface charge density will not be uniform
(c) Each plate will have the same potential at each point
(d) The electric field is smallest where the plates are closest

A

only a is correct

B

only b & c are correct

C

a & c are correct

D

a, b & c are correct

Question 110: Palette 110/125

Allen MCQ

If at distance r from a positively charged particle, electric field strength and energy density are E and U, respectively, which of the following graphs is correct?
(a)

(b)

(c)

(d)

A

only a

B

only b

C

only c

D

a, b, d

Question 111: Palette 111/125

Allen MCQ

In the circuit shown in figure, match the following two columns.

Column-I	Column-II
(A) Charge given by battery (B) Charge of 4μF capacitor (C) Charge of 2 μF capacitor (D) Charge of 3 μF capacitor	(P) 20 μC (Q) 30 μC (R) 60 μC (S) 40 μC

A

A-P, B-S, C-Q, D-R

B

A-R, B-S, C-P, D-R

C

A-Q, B-P, C-R, D-S

D

A-T, B-S, C-R, D-P

Question 112: Palette 112/125

Allen Match the Columns

Three identical metal plates with large surface areas are kept parallel to each other as shown in fig. The leftmost plate is given charge Q, the rightmost given charge -2Q and the middle one remains neutral. Then Match Column-I with Column-II

Column-I	Column-II
(A) . The charge appearing on outer surface of the rightmost plate (B) The charge appearing on outer surface of the leftmost plate (C) The charge appearing on left surface of the middle plate (D) The charge appearing on right surface of the middle plate	(P) $+\frac{Q}{2}$ (Q) $-\frac{Q}{2}$ (R) $-\frac{3Q}{2}$ (S) $\frac{3Q}{2}$

A

A-Q, B-Q, C-S, D-R

B

A-R, B-Q, C-S, D-R

C

A-Q, B-P, C-R, D-S

D

A-Q, B-Q, C-R, D-S

Question 113: Palette 113/125

Allen MCQ

Match the following -

Column-I

Column-II

(A) $\frac{1}{8\pi\varepsilon_0} \frac{Q^2}{R}$ (B) $\frac{1}{4\pi\varepsilon_0} \frac{2Q^2}{R^2}$ (C) $\frac{1}{4\pi\varepsilon_0} \frac{Q^2}{R}$ (D) $\frac{1}{2}\varepsilon_0E^2$

(P) Self-energy of a uniformly charged spherical shell (Q) Energy stored per unit volume of a charged air filled capacitor (R) Force between two circular plates of a charged parallel plate capacitor, radius of the plates being R and separation R/32 (S) Work done by electric field in moving a point charge Q from the surface of a uniformly charged sphere of radius R and moving it to infinity, total charge on the sphere = Q

A

P-3, Q-1, R-4, S-2

B

P-2, Q-1, R-3, S-4

C

P-1, Q-4, R-2, S-3

D

P-4, Q-1, R-2, S-3

Question 114: Palette 114/125

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Mutual force of attraction between two plates of isolated capacitor is independent of presence of dielectric slab between plates.
Reason (R) : Force of interaction between two charged bodies is independent of medium.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 115: Palette 115/125

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): It is not possible to make a spherical conductor of capacitance one farad.
Reason (R): It is possible for earth as its radius is 6400 km.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 116: Palette 116/125

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): When two charged capacitors are connected in parallel, then total potential energy of system always decreases.
Reason (R): During recombination charge flow from one capacitor to another capacitor so energy is lost in the form of heat and electromagnetic radiation.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 117: Palette 117/125

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Circuits containing high capacity capacitors, charged to high voltage should be handled with caution, even when the current in the circuit is switched off.
Reason (R) : When an isolated capacitor is touched by hand or any other part of the human body, there is an easy path to the ground available for the discharge of the capacitor.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 118: Palette 118/125

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): If separation between plates of a parallel plate isolated charged capacitor is increased, its energy stored increases.
Reason (R): Work done to more separate the plates get converted in electrostatic potential energy.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 119: Palette 119/125

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): When a capacitor is charged by a battery, both the plates receive charge equal in magnitude, no matter size of plates are identical or not.
Reason (R) : The charge distribution on the plates of capacitor is in accordance with charge conservation principle.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 120: Palette 120/125

Allen MCQ

A network consisting of three resistors, three batteries, and a capacitor is shown in figure.

Column-I	Column-II
(A) Current in branch EB is (B) Current in branch CB is (C) Current in branch ED is (D) Charge on capacitor is	(P) 10 $\mu$ C (Q) 0.5 A (R) 1.5 A (S) $5\mu \mathrm{C}$ (T) None

A

A → R, B → Q, C → Q, D → P

B

A → R, B → Q, C → R, D → S

C

A → Q, B → R, C → R, D → P

D

A → R, B → Q, C → Q, D → S

Question 121: Palette 121/125

Allen MCQ

Statement-1: If capacitor is filled with, same thickness (t) of dielectric (t < d) and conducting sheet one after another, then capacitance are $C_1$ and $C_2$ respectively then $C_1 < C_2$ Statement-2 : Capacitance is more in presence of metal sheet in compare to dielectric sheet as $K_{Conduct} > K_{dielectric}$

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 122: Palette 122/125

Allen MCQ

For the given circuit, select the incorrect alternative

A

The equivalent capacitance between points $1 \& 2$ is $\frac{15C}{11}$

B

The equivalent capacitance between points 3 & 6 is $\frac{5C}{3}$

C

The equivalent capacitance between points 1 & 3 is $\frac{15\mathrm{C}}{14}$

D

The equivalent capacitance between points 3 & 5 is $\frac{14C}{15}$

Question 123: Palette 123/125

Allen MCQ

The equivalent capacitance between A and B is .... and charge on 5μF capacitor is ....

A

$4\mu \mathrm{F}\& 50~\mu \mathrm{C}$

B

5μF & 40 μC

C

8μF & 60 μC

D

None

Question 124: Palette 124/125

Allen MCQ

Write down the charge in $\mu \mathrm{C}$ on $10\mu \mathrm{F}$ capacitor in steady state.

A

100 μC

B

150 μC

C

180 μC

D

200 μC

Question 125: Palette 125/125

Allen MCQ

In the circuit shown in figure E=25V, L=2H, C=60 $\mu$ F, $R_{1}=5\Omega$ and $R_{2}=10\Omega$ . Switch S is closed at t=0.

Column-I	Column-II
(A) Current through $R_1$ at t = 0 (B) Current through $R_2$ at t = 0 (C) Current through $R_1$ at t = ∞ (D) Current through $R_2$ at t = ∞	(P) 0 (Q) 5A (R) 2.5 A (S) None of these

A

A → P, B → Q, C → P, D → R

B

A → Q, B → P, C → P, D → R

C

A → Q, B → P, C → R, D → P

D

A → P, B → R, C → P, D → Q