CAPACITORS

CAPACITORS
1. A parallel plate condenser is connected with the terminals of a battery. The

distance between the plates is6𝑚𝑚. If a glass plate (dielectric constant 𝐾 = 9) of
thickness 4.5𝑚𝑚 is introduced between them, then the capacity will become
(a) 2 times (b) The same
(c) 3 times (d) 4 times
2. In a parallel plate condenser, the radius of each circular plate is 12𝑐𝑚 and the
distance between the plates is5𝑚𝑚. There is a glass slab of 3𝑚𝑚 thick and of
radius 12𝑐𝑚 with dielectric constant 6 between its plates. The capacity of the
condenser will be
(a) 144 × 10 𝐹 (b) 40𝑝𝐹
(c) 160𝑝𝐹 (d) 1.44𝜇𝐹
3. A capacitor of capacity 𝐶 has charge 𝑄 and stored energy is 𝑊. If the charge is
increased to 2𝑄, the stored energy will be
(a) 2𝑊 (b) 𝑊/2
(c) 4𝑊 (d) 𝑊/4
4. There is an air filled 1𝑝𝐹 parallel plate capacitor. When the plate separation is
doubled and the space is filled with wax, the capacitance increases to2𝑝𝐹. The
dielectric constant of wax is
(a) 2 (b) 4
(c) 6 (d) 8
5. The capacity and the energy stored in a parallel plate condenser with air between
its plates are respectively 𝐶 and 𝑊 . If the air is replaced by glass (dielectric
constant = 5) between the plates, the capacity of the plates and the energy stored
in it will respectively be
(a) 5𝐶 , 5𝑊 (b) 5𝐶 ,
(c) , 5𝑊 (d) ,
6. In a parallel plate capacitor with air between the plates, each plate has an area
of 6 × 10-3 m2 and the distance between the plates is 3 mm. Calculate the
capacitance of the capacitor. If this capacitor is connected to a 100 V supply, what
is the charge on each plate of the capacitor? (Take 0 =9x10-12 S.I unit)
Ans. 18pF, 1.8x10-9 C
7. A 12pF capacitor is connected to a 50V battery. How much electrostatic energy is
stored in the capacitor?
Ans. 1.5x10-8J
8. A 600pF capacitor is charged by a 200V supply. It is then disconnected from the
supply and is connected to another uncharged 600 pF capacitor. How much
electrostatic energy is lost in the process?
Ans. 6x10-6J
9. The parallel plates of a capacitor have an area 0.2 m2 and are 10-2m apart. The
original potential difference between them is 3000 volts and it decreases to 1000 volts
when a sheet of dielectric is inserted between the plates. Compute:
(a) Original capacitance (b) the charge q on each plate
(c)Capacitance after insertion of the dielectric. (d) dielectric constant
(e) permittivity of dielectric. (f) the original field E0 between the plates &
(g) the electric field E after insertion of the dielectric . (Take 0 =9x10-12 S.I unit)
[Ans. 180 pF, 54x10-8C, 540pF, 3, 27x10-12C2N-1m-2, 3x105 V/m, 105V/m]
10. A parallel plate capacitor in which the area of each plate is 6.2x10-3 m2 is filled with
mica with dielectric constant =6. The separation between the plates is 2mm and each
carries a charge of 4x10-8C. Determine :(a) Capacitance
(b) p.d across the plates
(c) electric field in the capacitor
(d) Force of mutual attraction of the plates.
[Ans. 156pF, 256 V, 1.28x105V/m, 2.56x10-3N]
11. The given graph shows variation of charge ‘q’ versus potential difference ‘V’ for
two capacitors C1 and C2. Both the capacitors have same plate separation but plate
area of C2 is greater than that of C1. Which line (A or B) corresponds to C1 and why?
Ans. B represent C1
12. A network of four capacitors, each of capacitance 15 µF, is connected across a

battery of 100 V, as shown in the figure. Find the net capacitance and the charge
on the capacitor C4.
Ans. 20μF, 1500μC

13. 1 mF capacitance connected to a battery of 6 V. Initially switch S is closed. After
sometime S is left open and dielectric slabs of dielectric constant K = 3 are
inserted to fill completely the space between the plates of the two capacitors.
How will the (i) charge and (ii) potential difference between the plates of the
capacitors be affected after the slabs are inserted?
Ans. 𝑞 , = 18𝜇𝐶, 𝑉 , = 6𝑉; 𝑞, = 6𝜇𝐶, 𝑉 , = 2𝑉
14. In Fig. the capacitances are 𝐶1 = 1.0 𝜇𝐹 and 𝐶2 = 3.0 𝜇𝐹, and both capacitors
are charged to a potential difference of V = 100 V but with opposite polarity as
shown. Switches S1 and S2 are now closed.
(a) What is now the potential difference between points a and b?
(b) What now is the charge on capacitor C1 and C2?
Ans. (a) 50V (b) 5x10-5C, 1.5x10-4C
15. Calculate the potential difference and the energy stored in the capacitor C2 in the
circuit shown in the figure. Given potential at A is 90 V, C1 = 20 µF, C2 = 30 µF
and C3 = 15 µF.
Ans. 20V, 6x10-3J
16. Net capacitance of three identical capacitors in series is 1 µF. What will be their
net capacitance if connected in parallel?
Find the ratio of energy stored in the two configurations if they are both connected
to the same source.
Ans. 9μF, 1:9
17. (i) Find the equivalent capacitance between A and B in the combination given
below. Each capacitor is of 2 µF capacitance.
(ii) If a dc source of 7 V is connected across AB, how much charge is drawn

from the source and what is the energy stored in the network?
Ans. (i) 6/7μF, (ii) 6μC, 21μJ
18. A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy
is stored in the capacitor? If another capacitor of 6 pF is connected in series with
it with the same battery connected across the combination, find the charge stored
and potential difference across each capacitor.
Ans. 1.5x10-8J, 2x10-10C, 16.67V, 33.33V
19. Two identical parallel plate capacitors A and B are connected to a battery of V
volt with the switch S closed. The switch is now opened and the free space
between the plates of the capacitors is filled with a dielectric of dielectric constant
K. Find the ratio of the total electrostatic energy stored in both capacitors before
and after the introduction of the dielectric.
Ans.
20. Two parallel plate capacitors X and Y have the same area of plates and same
separation between them. X has air between the plates while 7 contains a
dielectric of 𝜀 = 4.
(i) Calculate capacitance of each capacitor if equivalent capacitance of the

combination is 4 µF.
(ii) Calculate the potential difference between the plates of X and Y.
(iii) Estimate the ratio of electrostatic energy stored in X and Y.
Ans. (i) 5μF, 20μF; (ii) 12V, 3V; (iii) 4:1
21. In the following arrangement of capacitors, the energy stored in the 6 µF
capacitor is E. Find the value of the following
(i) Energy stored in 12 µF capacitor
(ii) Energy stored in 3 µF capacitor
(iii) Total energy drawn from the battery
Ans. (i) 2E; (ii) 18E; (iii) 21E

22. A capacitor of unknown capacitance is connected across a battery of V volts. The
charge stored in it is 360 µC. When potential across the capacitor is reduced by
120 V, the charge stored in it becomes 120 µC.
Calculate:
(i) The potential V and the unknown capacitance C.
(ii) What will be the charge stored in the capacitor, if the voltage applied had
increased by 120 V?
Ans. (i) 180V, 2μF; (ii) 600μC
23. A capacitor of 200 pF is charged by a 300 V battery. The battery is then

disconnected and the charged capacitor is connected to another uncharged
capacitor of 100 pF. Calculate the difference between the final energy stored in
the combined system and the initial energy stored in the single capacitor.
Ans. 6x10-6-9x10-6=-3x10-6J
24. A parallel plate capacitor is charged by a battery. After sometime the battery is
disconnected and a dielectric slab with its thickness equal to the plate separation
is inserted between the plates. How will (i) the capacitance of the capacitor, (ii)
potential difference between the plates and (iii) the energy stored in the capacitor
be affected? Justify your answer in each case.
Ans. Capacitance will increase, Potential will decrease, Energy will decrease.
25. When a slab of insulating material 4mm thick is introduced between the plates of
a parallel plate capacitor, it is found that the distance between the plates has to be
increased by 3.2mm to restore the capacity to its original value. Calculate dielectric
constant of the material.
Ans. 5
26. A parallel plate capacitor with plate separation 5 mm is charged by a battery. It is

found that on introducing a mica sheet 2 mm thick, while keeping the battery
connections intact, the capacitor draws 25% more charge from the battery than
before. Find the dielectric constant of mica.
Ans. 2
ANSWERS
1. (c) 𝐶 ∝  = = . = =3
.
( . )
2. (c) 𝐶 = = × ×
.
2 × 144 × 10
= = 160𝑝𝐹
36 × 5
3. (c) 𝑊 =  𝑊′ = 4𝑊
4. (b) 𝐶 = = 1𝑝𝐹 and 𝐶′ = = 2𝑝𝐹  K = 4.
5. (b) When a dielectric K is introduced in a parallel plate condenser its capacity
becomes K times. Hence 𝐶′ = 5𝐶 . Energy stored 𝑊 =
 𝑊′ = = ×
 𝑊′ =

CAPACITORS

Uploaded by

Copyright:

Available Formats

CAPACITORS

Uploaded by

Document Information

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

CAPACITORS

Uploaded by

Copyright:

Available Formats

CAPACITORS

1. A parallel plate condenser is connected with the terminals of a battery. The

12. A network of four capacitors, each of capacitance 15 µF, is connected across a

Ans. 20μF, 1500μC

Ans. (a) 50V (b) 5x10-5C, 1.5x10-4C

Ans. 20V, 6x10-3J

(ii) If a dc source of 7 V is connected across AB, how much charge is drawn

(i) Calculate capacitance of each capacitor if equivalent capacitance of the

Ans. (i) 2E; (ii) 18E; (iii) 21E

23. A capacitor of 200 pF is charged by a 300 V battery. The battery is then

26. A parallel plate capacitor with plate separation 5 mm is charged by a battery. It is

You might also like