Physics 72: Chapter 24 Problem Set Summer 2010

Name: Score:

Lecturer: Mr Carlos Baldo III Section: X7-7

Encircle the letter of the correct answer. Solve each problem clearly and completely for full credit.

1. Which of the following is correct about the capacitance of a parallel-plate capacitor?

A. It depends on the amount of charge on the capacitor plates.

B. It is directly proportional to the separation distance of the plates

C. It is directly proportional to the area of the plates

D. A and B

E. A and C

2. A 3-μF capacitor is initially connected to a 3V power supply. The voltage is later increased to 6V, what will be the new

capacitance of the capacitor?

A. 1 μF

B. 2 μF

C. 3 μF

D. 6 μF

E. 9 μF

3. Consider two capacitors C1 = 3-uF and C2 = 6-uF capacitor are connected in parallel to a 9-V battery. Which of the

following statements is TRUE about the charge stored and voltage across each capacitor?

A. VC1 < VC2 ; QC1 < QC2

B. VC1 < VC2 ; QC1 > QC2

C. VC1 = VC2 ; QC1 < QC2

D. VC1 = VC2 ; QC1 > QC2

E. VC1 > VC2 ; QC1 = QC2

4. Five identical capacitors of capacitance C are connected as shown. The equivalent

capacitance across points A and B if a dielectric (κ = 2) fills the space between the

plates of C2 is _______.

A. (1/2) C

B. (3/2) C

C. (5/2) C

D. (7/2) C

E. (11/2) C

For the next three numbers, consider a 2-µF parallel-plate capacitor that is initially connected to a 4-V dc battery

5. What is the net charge on the plates of the capacitor?

A. zero

B. ½ µC

C. 4 µC

D. 8 µC

E. 16 µC

6. If the voltage is increased to 8 V, what will be the new capacitance?

A. 1-µF

B. 2-µF

C. 4-µF

D. 6-µF

E. 8-µF

Physics 72: Chapter 24 Problem Set Summer 2010

7. While the capacitor is connected to 8V, the area of the plates of the capacitor is doubled. What will be the value of the

stored energy in the capacitor?

A. 16 µJ

B. 32 µJ

C. 64 µJ

D. 128 µJ

E. 256 µJ

For the next three numbers, consider the capacitor network consists of C1, C2 and C3 connected to an

ideal battery with terminal voltage Vab = 12V.

8. What is the charge stored in C1?

A. 6 µC

B. 12 µC

C. 24 µC

D. 48 µC

E. 96 µC

9. An isolated capacitor has an initial charge Q. What will happen to the energy density when a dielectric (к = 2) is inserted

in the capacitor?

A. Remains the same

B. Decreases by a factor of 2

C. Increases by a factor of 2

D. Decreases by a factor of 4

E. Increases by a factor of 4

10. What is the new charge stored in C3 if a dielectric (к = 2) is inserted in C1?

A. 6 µC

B. 12 µC

C. 24 µC

D. 48 µC

E. 96 µC

11. A 4μF parallel-plate capacitor is connected to a 1.5V battery. While connected, the separation between the plates of the

capacitor is doubled. How much charge will be measured at the plates of the capacitor?

A. 1.5 μC

B. 2.0 μC

C. 3.0 μC

D. 4.0 μC

E. 6.0 μC

12. Shown below are four different arrangements of capacitors with equal individual capacitances. Which of the following

arrangements could store the largest total charge when a dc battery is connected across terminals X and Y?

Physics 72: Chapter 24 Problem Set Summer 2010

13. An isolated parallel-plate capacitor is carrying some charge on its plate. What will happen to the electric field across the

capacitor if the area of the plates is halved?

A. Halved

B. Doubled

C. Quartered

D. Quadrupled

E. Remains the same

For the next three questions, consider the circuit below, where C1 = C2 = 2 µF and C3 = 1 µF. The applied potential is Vab = 4 V

14. A parallel plate capacitor has the space between the plates (with area A) filled

with three slabs of dielectric, with constants shown in the figure. What is its

capacitance?

A. 7 εoA / 4d

B. 11 εoA / 4d

C. 4 εoA / d

D. 7 εoA / d

E. εoA / d

15. What is the equivalent capacitance of the network between points a and b?

A. 1/2 μF

B. 4/5 μF

C. 2 μF

D. 3 μF

E. 5 μF

16. What is the charge on C3?

A. 0.25 μC

B. 0.75 μC

C. 1.5 μC

D. 2 μC

E. 4 μC

17. What is the potential difference across C1?

A. 1 V

B. 2 V

C. 3 V

D. 4 V

E. 5 V

For the next two questions, a constants potential difference of 24V is maintained between the terminals of a 0.2μF parallel-

plate air capacitor.

18. Dielectric. A sheet of Mylar-like material (K = 3.0) is inserted between the plates of the capacitor, completely filling the

space between the plates. When this is done, what is the total charge that flows onto the positive plate of the capacitor?

A. zero

B. 0.4 μC

C. 1.6 μC

D. 2.4 μC

E. 3.6 μC

Physics 72: Chapter 24 Problem Set Summer 2010

19. What effect does the Mylar-like material have on the electric field between the plates while it is connected to a constant

potential difference?

A. The electric field will increase 3 times.

B. The electric field will decrease 3 times.

C. The electric field will increase 9 times.

D. The electric field will decrease 9 times.

E. The electric field will not be affected.

20. A parallel plate capacitor with vacuum between plates has a surface charge density of magnitude σ in each plate. What is

the energy density stored between the plates?

A. εoσ2

B. 2 εoσ2

C. σ2/ εo

D. σ2/ 2εo

E. σ2/ 4 εo

21. An air capacitor is made by using two flat plates, each with area A, separated by a

distance d. Then a metal slab having thickness t (t < d) and the same shape and size as

the plates is placed exactly in between them, parallel to the plates and not touching

either plate. What is the capacitance of this arrangement?

A. εoA/t

B. εoA/d

C. εoA/(d + t)

D. εoA/(d - t)

E. εoA/2(d + t)

22. A parallel-plate capacitor has capacitance Co, with no dielectric. It is then filled with a dielectric κ. When a second

capacitor of capacitance C’ is connected in series with the first one, the capacitance of the series combination is Co. What

is the value of C’?

A. κCo

B. Co (1 + κ)

C. Co (1 - κ)

D. κCo / (κ - 1)

E. κCo / (κ + 1)

23. What is/are TRUE regarding the effect of the presence of a dielectric between the plates of a capacitor if the charge is

kept constant?

I. The electric field between the plates strengthened.

II. The capacitance is increased by a factor equal to the dielectric constant.

III. The energy stored in the capacitor is decreased.

IV. The potential difference between the plates is increased.

A. I and II

B. II and III

C. II and IV

D. I, II and III

E. II, III and IV

< SAND PRINCE >