CAPACITANCE 1.
A parallel plate capacitor A is filled with a dielectric whose dielectric constant varies with applied voltage as K = V. An identical capacitor B of capacitance C 0 with air as dielectric is connected to voltage source V0 = 30V and then connected to the first capacitor after disconnecting the voltage source. The charge and voltage on capacitor (a) A are 25C0 and 25V (b) A are 25C0 5 V (c) B are 5C0 and 5V (d) B are 5C0 and 25 V
2.
Two capacitors of 2 F and 3 F are charges to 150 volt and 120 volt respectively. The plates of capacitor are connected as shown in the figure. A discharged capacitor of capacity 1.5 F falls to the free ends of the wire. Then 150V (a) charge on the 1.5 F capacitors is 180 C (b) charge on the 2F capacitor is 120 C (c) charge flows through A from right to left (d) charge flows through A from left to right
3.
4.
In the circuit shown, each capacitor has a capacitance C. The emf of the cell is E. IF the switch s is closed (a) positive charge will flow out of the positive terminal of the cell (b) positive charge will enter the positive terminal of the cell (c) the amount of charge flowing through the cell will be CE (d) the amount of charge flowing through the cell will be 4/3 CE In the circuit shown initially C1, C2 are uncharged. After closing the switch (a) the charge on C2 is greater that on C1 (b) the charge on C1 and C2 are the same (c) the potential drops across C1 and C2 are the same (d) the potential drops across C2 is greater than that across C1
1 .5 F
2F
3F
120V
A
S C C C E
C 1= 4 F
12V
C 2= 8 F
6V
5.
A parallel plate air–core capacitor is connected across a source of constant potential difference. When a dielectric plate is introduced between the two plates then (a) some charge from the capacitor will flow back into the source (b) some extra charge from the source will flow back into the capacitor (c) the electric field intensity between the two plate does not change (d) the electric field intensity between the two plates will decrease.
6.
A parallel plate capacitor has a parallel sheet of copper inserted between and parallel to the two plates, without touching the plates. The capacity of the capacitor after the introduction of the copper sheet is (a) minimum when the copper sheet touches one of the plates (b) maximum when the copper sheet touches one of the plates (c) invariant for all positions of the sheet between the plates (d) greater than that before introducing the sheet
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7.
8.
9.
In the circuit shown in the figure, the switch S is initially open and the capacitor is initially uncharged. I1, I2 and I3 represent the current in the resistance 2, 4 and 8 respectively. 6V (a) just after the switch S is closed, I1 = 3A, I2 = 3A and I3 = 0 (b) just after the switch S is closed, I1 = 3A, I2 = 0 and I3 = 0 (c) long time after the switch S is closed, I1 = 0.6A, I2 = 0 and I3 = 0 (d) long after the switch S is closed, I1 = I2 = I3 = 0.6 A.
4 F
2F I3
R The circuit shown in the figure consists of a battery of emf = 10V; capacitor of capacitance C = 1.0 F and three resistor of R values R1 = 2, R2 = 2 and R3 = 1. Initially the capacitor is completely uncharged and the switch s is open. The switch S is closed at t = 0 (a) the current through resistor R3 at the moment the switch closed is zero (b) the current through resistor R3 a long time after the switch closed is 5A. (c) the ratio of current through R1 and R2 is always constant (d) the maximum charge on the capacitor during the operation is 5C.
In the circuit shown in figure C1 = C2 = 2F. Then charge stored in (a) capacitor C1 is zero (b) capacitor C2 is zero (c) both capacitor is zero (d) capacitor C1 is 40 C
2 I1
I2
1
S 2
R
C
3
lo g I
(2 ) (1 )
O
10.
A capacitor of capacity C is charged to a steady potential difference V and connected in series with an open key and a pure resistor 'R'. At time t = 0, the key is closed. If I = current at time t, a plot a log I against t is as shown (1) in the graph. Later one of the parameters i.e., V,R or C is changed keeping the other two constant, and the graph (2) is recorded. Then (a) C is reduced (b) C is increased (c) R is reduced (d) R is increased.
Question No. 11 to 12 (2 Questions) The charge across the capacitor in two different RC circuits 1 and 2 are plotted as shown in figure.
q q m ax
1
O
11.
Choose the correct statement(s) related to the two circuits. (a) Both the capacitors are charged to the same charge. (b) The emf’s of cells in both the circuit are equal. (c) The emf’s of the cells may be different. (d) The emf E1 is more than E2.
12.
Identify the correct statement(s) related to the R1, R2, C1 and C2 of the two RC circuits. (a) R1 > R2 if E1 = E2 (b) C1 < C2 if E1 = E2
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2 t
(c) R1C1 > R2C2
(d)
R1 C 2 . R 2 C1
13.
A parallel plate capacitor is charged by connecting it to a battery. The battery is disconnected and the plates of the capacitor are pulled apart to make the separation between the plates twice. Again the capacitor is connected to the battery (with same polarity) then (a) Charge from the battery flows into the capacitor after reconnection. (b) Charge from capacitor flows into the battery after reconnection. (c) The potential difference between the plates increases when the plates are pulled apart. (d) After reconnection of battery potential difference between the plates will immediately becomes half of the initial potential difference. (Just after disconnecting the battery)
14.
The plates of a parallel plate capacitor with no dielectric are connected to a voltage source. Now a dielectric of dielectric constant K is inserted to fill the whole space between the plates with voltage source remaining connected to the capacitor. (a) The energy stored in the capacitor will become K–times. (b) The electric field inside the capacitor will decrease to K–times. (c) The force of attraction between the plates will increase to K2–times. (d) The charge on the capacitor will increase to K–times.
15.
Four capacitors and a battery are connected as shown. The potential drop across the 7F capacitor is 6V. Then the : (a) Potential difference across the 3F capacitor is 10V. (b) Charge on the 3F capacitor is 42C. (c) emf of the battery is 30 V. (d) Potential difference across the 12F capacitor is 10 V.
16.
F E
A circuit shown in the figure consists of a battery of emf 10 V and A C 1 two capacitance C1 and C2 of capacitances 1.0 F and 2.0 F respectively. The potential difference VA – VB is 5V. (a) Charge on capacitor C1 is equal to charge on capacitor C2. (b) Voltage across capacitor C1 is 5V. (c) Voltage across capacitor C2 is 10 V. (d) Energy stored in capacitor C1 is two times the energy stored in capacitor C2.
7 F
3 .9 F
3F
B C
2
17.
A capacitor C is charged to a potential difference V and battery is disconnected. Now if the capacitor plates are brought close slowly by some distance : (a) Some +ve work is done by external agent. (b) Energy of capacitor will decrease. (c) Energy of capacitor will increase. (d) None of these.
18.
The capacitance of a parallel plate capacitor is C when the region between the plate has air. This region is now filled with a dielectric slab of dielectric constant k. The capacitor is connected to a cell of emf E, and the slab is taken out (a) Charge CE (k – 1) flows through the cell. (b) Energy E2C(k – 2) is absorbed by the cell.
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(c) The energy stored in the capacitor is reduced by E2C(k – 1). 1 2 (d) The external agent has to do E C(k 1) amount of work to take the slab out. 2 19.
Two capacitors of capacitances 1F and 3F are charge to the same voltages 5V. They are connected in parallel with oppositely charged plates connected together. Then : (a) Final common voltage will be 5 V. (b) Final common voltage will be 2.5 V. (c) Heat produced in the circuit will be zero. (d) Heat produced in the circuit will be 37.5 J.
20.
The two plates X and Y of a parallel plate capacitor of capacitance C are given a charge of amount Q each. X is now joined to the positive terminal and Y to the negative terminal of a cell of emf E = Q/C. (a) Charge of amount Q will flow from the negative terminal to the positive terminal of the cell inside it. (b) The total charge on the plate X will be 2Q. (c) The total charge on the plate Y will be zero. (d) The cell will supply CE2 amount of energy.
21.
A dielectric slab is inserted between the plates of an isolated charge capacitor. Which of the following quantities will remain the same ? (a) The electric field in the capacitor. (b) The charge on the capacitor. (c) The potential difference between the plates. (d) The stored energy in the capacitor.
22.
The separation between the plates of a isolated charged parallel plate capacitor is increased. Which of the following quantities will charge ? (a) Charge on the capacitor (b) Potential difference across the capacitor (c) Energy of the capacitor (d) Energy density between the plates.
23.
Each plate of a parallel plate capacitor has a charge q on it. The capacitor is not connected to a battery. Now, (a) The facing surface of the capacitor have equal and opposite charges. (b) The two plates of the capacitor have equal and opposite charges. (c) The battery supplies equal and opposite charges to the two plates. (d) The other surfaces of the plates have equal charges.
24.
Following operation can be performed on a capacitor : X – connect the capacitor to a battery of emf E. Y – disconnect the battery. Z – reconnect the battery with polarity reversed. W – insert a dielectric slab in the capacitor. (a) In XYZ (perform X, then Y, then Z) the stored electric energy remains uncharged and no thermal energy is developed. (b) The charge appearing on the capacitor is greater after the action XWY than after the action XYW.
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(c) The electric energy stored in the capacitor is greater after the action WXY than after the action XYW. (d) The electric field in the capacitor after the action XW is the same as that after WX. 25.
A parallel plate capacitor is charged and then disconnected from the source of potential difference. If the plates of the condenser are then moved farther apart by the use of insulated handle, which one of the following is true ? (a) The charge on the capacitor increases. (b) The charge on the capacitor decreases. (c) The capacitance of the capacitor increases. (d) The potential difference across the plate increases.
26.
A parallel plate capacitor is charged and then disconnected from the source steady emf. The plates are then drawn apart farther. Again it is connected to the same source. Then : (a) The potential difference across the plate increases, while the plates are being drawn apart. (b) The charge from the capacitor flows into the source, when the capacitor is reconnected. (c) More charge is drawn to the capacitor from the source, during the reconnection. (d) The electric intensity between the plates remains constant during the drawing apart of plates.
27.
When a parallel plates capacitor is connected to a source of constant potential difference, (a) All the charge drawn from the source is stored in the capacitor. (b) All the energy drawn from the source is stored in the capacitor. (c) The potential difference across the capacitor grows very rapidly initially and this rate decreases to zero eventually. (d) The capacity of the capacitor increases with the increase of the charge in the capacitor.
28.
When two identical capacitors are charged individually to different potentials and connected parallel to each other, after disconnecting them from the source : (a) Net charge on connected plates is less than the sum of initial individual charges. (b) Net charge on connected plates equals the sum of initial charges. (c) The net potential difference across them is different from the sum of the individual initial potential differences. (d) The net energy stored in the two capacitors is less than the sum of the initial individual energies.
29.
A parallel plate capacitor of plate area A and plate separation d is charged to potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates. If Q, E and W denote respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted) and the work done on the system, in question, in the process of inserting the slab, then AV KAV (a) Q 0 (b) Q 0 d d 0 AV 2 V 1 E W (c) (d) 1 . Kd 2d K
30.
A parallel plate capacitor is connected to a battery. The quantities charge, voltage, electric field and energy associated with the capacitor are given by Q0, V0, E0 and U0 respectively. A dielectric PARTH IITJEE 304/305 AARON ELEGANCE CHANDKHEDA
slab is introduced between plates of capacitor but battery is still in connection. The corresponding quantities now given by Q, V, E and U related to previous ones are (a) Q > Q0 (b) V > V0 (c) E > E0 (d) U < U0. 31.
A parallel plate capacitor is connected to a cell. Its positive plate A and its negative plate B have charges +Q and –Q respectively. A third plate C, identical to A and B, with charge +Q, is now introduced midway between A and B, parallel to them. Which of the following are correct ? 3Q (a) The charge on the inner face of B is now . 2 (b) There is no change in the potential difference between A and B. (c) The potential difference between A and C is one–third of the potential difference between B and C. (d) The charge on the inner face of A is now Q/2.
32.
Two capacitor C1 = 4F and C2 = 2F are charged to same potential V = 500 volt, but with opposite polarity as shown in the figure. The switches S1 and S2 are closed. (a) The potential difference across the two capacitors are same and is 500 given by . 3V
+ S
–
C
1
1
(b) The potential difference across the two capacitors are same and is given by
–
+ C
S
2
2
1000 . 3V
1 . 9 4 (d) The ratio of final energy to initial energy of the system is . 9 (c) The ratio of final energy to initial energy of the system is
33.
A parallel plate capacitor is charged to a certain potential and the charging battery is then disconnected. Now, if the plates of the capacitor are moved apart then: (a) The stored energy of the capacitor increases. (b) Charge on the capacitor increases. (c) Voltage of the capacitor decreases. (d) The capacitance increases.
34.
If a battery of voltage V is connected across terminals I of the block box shown in the figure, an ideal voltmeter connected to terminals II gives a reading of V/2, while if the battery is connected to terminals II, a voltmeter across terminals I reads V. The black box may contain (a) I
R R
II
a (b) I
C R
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II
I
II
C
R
(c) I
R
II
(d) I
C
II .
R
35.
Two capacitors of equal capacitance (C1 = C2) are shown in the figure. Initially, while the switch S is open, one of the capacitors is uncharged and the other carries charge Q0. The energy stored in the charged capacitor is U0. Sometimes after the switch is closed, the capacitors C 1 and C2 carry charges Q1 and Q2, respectively, the voltages across the capacitors are V1 and V2; and the energies stored in the capacitors are U1 and U2. Which of the following statement is INCORRECT ? 1 (a) Q0 (Q1 Q 2 ) (b) Q1 = Q2 2 (c) V1 = V2 (d) U0 = U1 + U2.
S C
Question No. 36 to 39 (4 Questions) The figure shows a diagonal symmetric arrangement of capacitors and a battery
4F
C
1
2
2 F
B
2F A
2F
D
4 F
C
E=20V
36.
Identify the correct statement. (a) Both the 4F capacitors carry equal charges in opposites sense. (b) Both the 4F capacitors carry equal charges in same sense. (c) VB – VD > 0. (d) VD – VB > 0.
37.
If the potential of C is zero, then (a) VA = + 20V (c) 2(VA – VD) + 2(VB – VB) = 4VD
(b) 4(VA – VB) + 2(VD – VB) = 2VB (d) VA = VB + VD.
The potential of the point B and D are (a) VB = 8V (c) VD = 8V
(b) VB = 12V (d) VD = 12V.
38.
39.
The value of charge q1, q2 and q3 as shown in the figure are (a) q1 = 32 C; q2 = 24 C; q3 = – 8 C. (b) q1 = 48 C; q2 = 16 C; q3 = + 8 C (c) q1 = 32 C; q2 = 24 C; q3 = + 8 C. (d) q1 = 3 C; q2 = 4 C; q3 = + 2 C.
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q
1
q2
B q3
A
q2
D E=20V
q
C 1
40.
If Q is the charge on the plates of a capacitor of capacitance C, V the potential difference between the plates, A the area of each plate and d the distance between the plates, the force of attraction between the plates is 1 Q2 1 CV 2 (a) (b) 2 0 A 2 d 1 CV 2 (c) 2 A0
1 Q2 (d) . 4 0d 2
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ANSWER KEYS (CAPACITANCE) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
b, c a, b, c a, d b b, c c, d b a, b, c, d b, d b a, c d b, c a, c, d b, c, d a, d b a, b, d b, d a, b, c, d
21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40.
b b, c a, c, d b, c, d d a, c, d a, c b, c, d a, c, d a a, b, c, d a, c a d e b, c a, b, c, d b, c c a, b
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