RAINBOW CLASSES BY ER WAKHATWER ALI

Nawabganj, Bareilly

COMBINATIONS OF CAPACITOR
Class 12 - Physics
Time Allowed: 3 hours Maximum Marks: 70

Section A
Question No. 1 to 5 are based on the given text. Read the text carefully and answer the questions: [4]
If two or more capacitors are connected in series, the overall effect is that of a single (equivalent) capacitor having the
sum total of the plate spacing of the individual capacitors. If two or more capacitors are connected in parallel, the
overall effect is that of a single equivalent capacitor having the sum total of the plate areas of the individual capacitors.
(figure (a) shows parallel combination and (b) shows series combination)

1. Which quantities in capacitors will remain the same if capacitors are connected in the series?
2. How capacitors should be joined in order to increase the capacity?
3. Three capacitors having a capacitance equal to 2F, 4F and 6F are connected in series. Calculate the effective capacitance
of the combination.:
4. The plates of a parallel plate capacitor are 10 cm apart and have an area equal to 2m2. If the charge on each plate is 8.85

× 10-10 C, what will be the electric field at a point inside the plates of capacitor?

5. Four 10 F capacitors are connected in parallel, calculate the equivalent capacitance of the combination.

Question No. 6 to 10 are based on the given text. Read the text carefully and answer the questions: [5]
If two or more capacitors are connected in series, the overall effect is that of a single (equivalent) capacitor having the
sum total of the plate spacing of the individual capacitors. If two or more capacitors are connected in parallel, the
overall effect is that of a single equivalent capacitor having the sum total of the plate areas of the individual capacitors.

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(figure (a) shows parallel combination and (b) shows series combination)

6. When capacitors are connected in the series ________ remains the same.

a) charge b) resistance

c) capacitance d) voltage
7. Capacity can be increased by connecting capacitors in:

a) none of these b) both parallel and series

c) series d) parallel
8. Three capacitors having a capacitance equal to 2F, 4F and 6F are connected in parallel. Calculate the effective parallel
capacitance:

a) 10 F b) 13 F

c) 11 F d) 12 F

9. The plates of a parallel plate capacitor are 10 cm apart and have an area equal to 2m2. If the charge on each plate is 8.85

× 10-10 C , the electric field at a point:

a) between the plates will change from point to b) outside the plates will be zero
point

c) between the plates will be 25 NC-1 d) between the plates will be zero

10. Four 10 F capacitors are connected in series, calculate the equivalent capacitance.

a) 4.5 F b) 3.5 F

c) 2.5 F d) 1.5 F
Section B
11. The equivalent capacity of two capacitors in series is 3 μ F and in parallel is 16 μ F. Their individual capacities [1]
are

a) 12, 2 b) 12, 4

c) 8, 8 d) 10, 16
12. A capacitor of 20 μ F is charged up to 500 V is connected in parallel with another capacitor of 10 μ F which is [1]

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 charged up to 200 V. The common potential is:

a) 500 V b) 400 V

c) 300 V d) 200 V
13. How many 1μ F capacitors must be connected in parallel to store a charge of 1C with a potential of 110 V across [1]
the capacitors?

a) 9090 b) 909

c) 990 d) 900
14. A capacitor of capacitance C1 is charged upto potential V and then connected in parallel to an uncharged [1]

capacitor of capacitance C2. The final potential difference across each capacitor will be:

a) (1 + C2
)V b) (1 −
C2
)V
C1 C1

C1 V C2 V
c) C1 +C2
d) C1 +C2

15. Three capacitors of 2.0, 3.0 and 6.0 μ F are connected in series to a 10 V source. The charge on the 3.0 μ F: [1]

a) 5μ C b) 10μ C

c) 12μ C d) 15μ C
16. The equivalent capacity between points A and B shown in the figure is: [1]

a) ( 5

6
)C b) C

c) 30 C d)
6
( )C
5

Section C
17. In the circuit shown in the figure, the potential difference across the 4.5 μ F capacitor is: [1]

a) 8 volt b) volt
8

c) 6 volt d) 4 volt
18. A network of four capacitors of capacitances equal to C1 = C, C2 = 2C, C3 = 3C and C4 = 4C are connected to a [1]

battery as shown in the figure. The ratio of the charges on C2 and C4 is:

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 a) b)
3 4

22 7

c) 7

4
d) 22

19. What is the effective capacitance between points X and Y? [1]

a) 12 μ F b) 24 μ F

c) 6 μ F d) 18 μ F
20. What would be the voltage across C3? [1]

C3 V
a) (C1 +C2 )V
b)
C1 +C2 +C3 C1 +C2 +C3

C2 V C1 V
c) C1 +C2 +C3
d) C1 +C2 +C3

21. For circuit, the equivalent capacitance between P and Q is: [1]

a) 4C b)
6C

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c) 3C

4
d) 6C
Section D
22. Find the equivalent capacitance between the points A and B of the network of capacitors shown in Fig [1]

23. Calculate the capacitance of the capacitor in Fig. if the equivalent capacitance of the combination between A and [1]
B is 15 μ F.

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24. Find the charge on the capacitor as shown in the circuit. [1]

25. Two capacitors have a capacitance 5μ F when connected in parallel and 1.2 μ F when connected in series. [1]
Calculate their capacitances.
26. The capacities of three capacitors are in the ratio 1 : 2 : 3. Their equivalent capacity in parallel is greater than the [1]
equivalent capacity in series by pF. Calculate the individual capacitances.
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27. If C1 = 3 pF and C2 = 2 pF, calculate the equivalent capacitance of the given network between points A and B. [2]

28. Find the equivalent capacitance between the points P and Q as shown in Fig. Given C = 18 μ F and C1 = 12 μ F [2]

29. Calculate the potential difference and the energy stored in the capacitor C2 in the circuit shown in the figure. [2]

Given potential at A is 90 V, C1 = 20 µF, C2 = 30 µF and C3 = 15µF.

30. A network of four capacitors each of 12 μ F. Capacitance is connected to a 500 V supply as shown in Fig. [2]
Determine:
a. equivalent capacitance of the network, and
b. charge on each capacitor

31. Find the total energy stored in the capacitors in the network shown below. [2]

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32. What is the capacitance of arrangement of 4 plates of area A at distance d in the air in the given figure? [2]

33. Four capacitors of values 6 µF, 6 µF, 6 µF and 2 µF are connected to a 6 V battery as shown in the figure. [2]

Determine the
i. equivalent capacitance of the network.
ii. charge on each capacitor.
34. Obtain the equivalent capacitance of the network in figure. For a 300 V supply, determine the charge and voltage [3]
across each capacitor.

35. In the following arrangement of capacitors, the energy stored in the 6µF capacitor is E. Find the value of the [3]
following:
i. energy stored in 12µF capacitor
ii. energy stored in 3µF capacitor
iii. total energy drawn from the battery

36. Two parallel plate capacitors X and Y have the same area of the plates and same separation between them. X has [3]
air between the plates while Y contains a dielectric medium of ε r = 4 .

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 i. Calculate the capacitance of each capacitor if equivalent of the combination is 4 µF.
ii. Calculate the potential difference between the plates of X and Y.
iii. What is the ratio of electrostatic energy stored in X and Y?
37. Three capacitors C1, C2 and C3 are connected ’ to a 6 V battery, as shown in Fig. Find the charges on the three [3]
capacitors.

38. Find the equivalent capacitance of the combination of capacitors between points A and B as shown in Fig. Also [3]
calculate the total charge that flows in the circuit when a 100 V battery is connected between points A and B.

39. In the following arrangement of capacitors, the energy stored in the 6 μ F capacitor is E. Find the value of the [3]
following:

i. Energy stored in 12 μ F capacitor.

41. From the network shown in Fig. find the value of the capacitance C if the equivalent capacitance between points [5]
A and B is to be 1 μ F. All the capacitances are in μ F.

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42. In the circuit shown in Fig. If the point C is earthed and point A is given a potential of +1200 V, find the charge [5]
on each capacitor and the potential at point B.

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