Question 1

Three capacitors are connected as shown in the figure. What is the equivalent capacitance between points a and b?

Accepted Answer

A)  1.7 µF 
B)  4.0 µF 
C)  7.1 µF 
D)  12 µF 
E)  8.0 µF 
A)  1.7 µF 
B)  4.0 µF 
C)  7.1 µF 
D)  12 µF 
E)  8.0 µF A

Question 2

The network shown in the figure is assembled with uncharged capacitors X, Y, and Z, with CX = 7.0 μF, CY = 7.0 μF, and CZ = 6.0 μF, and open switches, S1 and S2. A potential difference Vab = +120 V is applied between points a and b. After the network is assembled, switch S1 is closed for a long time, but switch S2 is kept open. Then switch S1 is opened and switch S2 is closed. What is the final voltage across capacitor X?

Accepted Answer

A)  94 V 
B)  87 V 
C)  79 V 
D)  71 V 
E)  63 V 
A)  94 V 
B)  87 V 
C)  79 V 
D)  71 V 
E)  63 V A

Question 3

Equal but opposite charges Q are placed on the square plates of an air-filled parallel-plate capacitor. The plates are then pulled apart to twice their original separation, which is small compared to the dimensions of the plates. Which of the following statements about this capacitor are true? (There may be more than one correct choice.)

Accepted Answer

A)  The energy stored in the capacitor has doubled. 
B)  The energy density in the capacitor has increased. 
C)  The electric field between the plates has increased. 
D)  The potential difference across the plates has doubled. 
E)  The capacitance has doubled. 
A)  The energy stored in the capacitor has doubled. 
B)  The energy density in the capacitor has increased. 
C)  The electric field between the plates has increased. 
D)  The potential difference across the plates has doubled. 
E)  The capacitance has doubled. A, D

Question 4

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates. All the geometric parameters of the capacitor (plate diameter and plate separation) are now DOUBLED. If the original capacitance was C0, what is the new capacitance?

Accepted Answer

A)  4C0 
B)  2C0 
C)  C0 
D)  C0/2 
E)  C0/4 
A)  4C0 
B)  2C0 
C)  C0 
D)  C0/2 
E)  C0/4

Question 5

In the circuit shown in the figure, all the capacitors are air-filled. With the switch S open, the 40.0-µF capacitor has an initial charge of 5.00 µC while the other three capacitors are uncharged. The switch is then closed and left closed for a long time. Calculate the initial and final values of the total electrical energy stored in these four capacitors.

Accepted Answer

U_i= 0.313 µ

Question 6

An ideal parallel-plate capacitor consists of a set of two parallel plates of area A separated by a very small distance d. When this capacitor is connected to a battery that maintains a constant potential difference between the plates, the energy stored in the capacitor is U0. If the separation between the plates is doubled, how much energy is stored in the capacitor?

Accepted Answer

A)  4U0 
B)  2U0 
C)  U0 
D)  U0/2 
E)  U0/4 
A)  4U0 
B)  2U0 
C)  U0 
D)  U0/2 
E)  U0/4

Question 7

A parallel-plate capacitor with plate separation of 1.0 cm has square plates, each with an area of 6.0 × 10-2 m2. What is the capacitance of this capacitor if a dielectric material with a dielectric constant of 2.4 is placed between the plates, completely filling them? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

Accepted Answer

A)  15 × 10-12 F 
B)  15 × 10-14 F 
C)  64 × 10-14 F 
D)  1.3 × 10-12 F 
E)  1.3 × 10-10 F 
A)  15 × 10-12 F 
B)  15 × 10-14 F 
C)  64 × 10-14 F 
D)  1.3 × 10-12 F 
E)  1.3 × 10-10 F

Question 8

The capacitive network shown in the figure is assembled with initially uncharged capacitors. A potential difference, Vab = +100V, is applied across the network. The switch S in the network is kept open. Assume that all the capacitances shown are accurate to two significant figures. What is potential difference Vcd across the open switch S?

Accepted Answer

A)  0 V 
B)  40 V 
C)  50 V 
D)  60 V 
E)  70 V 
A)  0 V 
B)  40 V 
C)  50 V 
D)  60 V 
E)  70 V

Question 9

A charge of 2.00 μC flows onto the plates of a capacitor when it is connected to a 12.0-V potential source. What is the minimum amount of work that must be done in charging this capacitor?

Accepted Answer

A)  6.00 µJ 
B)  24.0 µJ 
C)  12.0 µJ 
D)  144 µJ 
E)  576 µJ 
A)  6.00 µJ 
B)  24.0 µJ 
C)  12.0 µJ 
D)  144 µJ 
E)  576 µJ

Question 10

A 1.0-μF and a 2.0-μF capacitor are connected in series across a 3.0-V voltage source.
(a) What is the charge on the 1.0-μF capacitor?
(b) What is the voltage across the 2.0-μF capacitor?

Accepted Answer

(a) 2.0 µC

Question 11

Five capacitors are connected across a potential difference Vab as shown in the figure. Because of the dielectrics used, each capacitor will break down if the potential across it exceeds 30.0 V. The largest that Vab can be without damaging any of the capacitors is closest to

Accepted Answer

A)  6.0 V. 
B)  30 V. 
C)  64 V. 
D)  150 V. 
E)  580 V. 
A)  6.0 V. 
B)  30 V. 
C)  64 V. 
D)  150 V. 
E)  580 V.

Question 12

A parallel-plate capacitor has a capacitance of 10 mF and is charged with a 20-V power supply. The power supply is then removed and a dielectric material of dielectric constant 4.0 is used to fill the space between the plates. What is the voltage now across the capacitor?

Accepted Answer

A)  80 V 
B)  20 V 
C)  10 V 
D)  5.0 V 
E)  2.5 V 
A)  80 V 
B)  20 V 
C)  10 V 
D)  5.0 V 
E)  2.5 V

Question 13

A 1.0 m long piece of coaxial cable has a wire with a radius of 1.1 mm and a concentric conductor with inner radius 1.3 mm. The area between the cable and the conductor is filled with a dielectric. If the voltage drop across the capacitor is 6000 V when the line charge density is
8)8 μC/m, find the value of the dielectric constant. (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Accepted Answer

A)  4.4 
B)  4.8 
C)  5.3 
D)  5.7 
A)  4.4 
B)  4.8 
C)  5.3 
D)  5.7

Question 14

Three capacitors, of capacitance 5.00 μF, 10.0 μF, and 50.0 μF, are connected in series across a 12.0-V voltage source.
(a) How much charge is stored in the 5.00-μF capacitor?
(b) What is the potential difference across the 10.0-μF capacitor?

Accepted Answer

(a) 37.5 µ

Question 15

The capacitive network shown in the figure is assembled with initially uncharged capacitors. A potential difference, Vab = +100V, is applied across the network. The switch S in the network is kept open. Assume that all the capacitances shown are accurate to two significant figures. What is the total energy stored in the seven capacitors?

Accepted Answer

A)  48 mJ 
B)  72 mJ 
C)  96 mJ 
D)  120 mJ 
E)  144 mJ 
A)  48 mJ 
B)  72 mJ 
C)  96 mJ 
D)  120 mJ 
E)  144 mJ

Question 16

A cylindrical capacitor is made of two thin-walled concentric cylinders. The inner cylinder has radius r1 = 4.0 mm, and the outer one a radius r2 = 8.0 mm. The common length of the cylinders is L = 150 m. What is the potential energy stored in this capacitor when a potential difference 4.0 V is applied between the inner and outer cylinder? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Accepted Answer

A)  9.6 × 10-8 J 
B)  1.3 × 10-8 J 
C)  6.3 × 10-8 J 
D)  0.34 × 10-8 J 
E)  4.6 × 10-8 J 
A)  9.6 × 10-8 J 
B)  1.3 × 10-8 J 
C)  6.3 × 10-8 J 
D)  0.34 × 10-8 J 
E)  4.6 × 10-8 J

Question 17

The capacitive network shown in the figure is assembled with initially uncharged capacitors. A potential difference, Vab = +100V, is applied across the network. The switch S in the network is initially open but is then closed. Assume that all the capacitances shown are accurate to two significant figures. What is the equivalent capacitance between ab
(a) with the switch S open?
(b) with the switch S closed?

Accepted Answer

(a) 14 µF

Question 18

An isolated air-filled parallel-plate capacitor that is no longer connected to anything has been charged up to Q = 2.9 nC. The separation between the plates initially is 1.20 mm, and for this separation the capacitance is 31 pF. Calculate the work that must be done to pull the plates apart until their separation becomes 5.30 mm, if the charge on the plates remains constant. (ε0 = 8.85 × 10-12 C2/N ∙ m2)

Accepted Answer

Question 19

The capacitance per unit length of a very long coaxial cable, made of two concentric cylinders, is 50 pF/m. What is the radius of the outer cylinder if the radius of the inner one is 1.0 mm? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

Accepted Answer

A)  3.0 mm 
B)  2.0 mm 
C)  4.0 mm 
D)  1.0 mm 
E)  0.50 mm 
A)  3.0 mm 
B)  2.0 mm 
C)  4.0 mm 
D)  1.0 mm 
E)  0.50 mm

Question 20

A 6.0-μF air-filled capacitor is connected across a 100-V voltage source. After the source fully charges the capacitor, the capacitor is immersed in transformer oil (of dielectric constant 4.5). How much ADDITIONAL charge flows from the voltage source, which remained connected during the process?

Accepted Answer

A)  1.2 mC 
B)  1.5 mC 
C)  1.7 mC 
D)  2.1 mC 
E)  2.5 mC 
A)  1.2 mC 
B)  1.5 mC 
C)  1.7 mC 
D)  2.1 mC 
E)  2.5 mC

Exam 23: Capacitance and Dielectrics

Three capacitors are connected as shown in the figure. What is the equivalent capacitance between points a and b?

An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates. All the geometric parameters of the capacitor (plate diameter and plate separation) are now DOUBLED. If the original capacitance was C0, what is the new capacitance?

A charge of 2.00 μC flows onto the plates of a capacitor when it is connected to a 12.0-V potential source. What is the minimum amount of work that must be done in charging this capacitor?

A 1.0-μF and a 2.0-μF capacitor are connected in series across a 3.0-V voltage source. (a) What is the charge on the 1.0-μF capacitor? (b) What is the voltage across the 2.0-μF capacitor?

Five capacitors are connected across a potential difference Vab as shown in the figure. Because of the dielectrics used, each capacitor will break down if the potential across it exceeds 30.0 V. The largest that Vab can be without damaging any of the capacitors is closest to

A parallel-plate capacitor has a capacitance of 10 mF and is charged with a 20-V power supply. The power supply is then removed and a dielectric material of dielectric constant 4.0 is used to fill the space between the plates. What is the voltage now across the capacitor?

Three capacitors, of capacitance 5.00 μF, 10.0 μF, and 50.0 μF, are connected in series across a 12.0-V voltage source. (a) How much charge is stored in the 5.00-μF capacitor? (b) What is the potential difference across the 10.0-μF capacitor?

The capacitance per unit length of a very long coaxial cable, made of two concentric cylinders, is 50 pF/m. What is the radius of the outer cylinder if the radius of the inner one is 1.0 mm? (k = 1/4πε0 = 8.99 × 109 N ∙ m2/C2)

A 6.0-μF air-filled capacitor is connected across a 100-V voltage source. After the source fully charges the capacitor, the capacitor is immersed in transformer oil (of dielectric constant 4.5). How much ADDITIONAL charge flows from the voltage source, which remained connected during the process?

Units, Physical Quantities, and Vectors

Motion Along a Straight Line

Motion in Two or Three Dimensions

Newtons Laws of Motion

Applying Newtons Laws

Work and Kinetic Energy

Potential Energy and Energy Conservation

Momentum, Impulse, and Collisions

Rotation of Rigid Bodies

Equilibrium and Elasticity

Fluid Mechanics

Gravitation

Periodic Motion

Mechanical Waves

Sound and Hearing

Temperature and Heat

Thermal Properties of Matter

The First Law of Thermodynamics

The Second Law of Thermodynamics

Electric Charge and Electric Field

Gausss Law

Electric Potential

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Magnetic Field and Magnetic Forces

Sources of Magnetic Field

Electromagnetic Induction

Inductance

Alternating Current

Electromagnetic Waves

The Nature and Propagation of Light

Geometric Optics

Interference

Diffraction

Relativity

Photons: Light Waves Behaving As Particles

Particles Behaving As Waves

Quantum Mechanics

Atomic Structure

Molecules and Condensed Matter

Nuclear Physics

Particle Physics and Cosmology

Filters

Five capacitors are connected across a potential difference V_ab as shown in the figure. Because of the dielectrics used, each capacitor will break down if the potential across it exceeds 30.0 V. The largest that V_ab can be without damaging any of the capacitors is closest to

The capacitance per unit length of a very long coaxial cable, made of two concentric cylinders, is 50 pF/m. What is the radius of the outer cylinder if the radius of the inner one is 1.0 mm? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)