Question 1

The voltage across each capacitor in a set of capacitors in series is

Accepted Answer

A) directly proportional to its capacitance. 
B) inversely proportional to its capacitance. 
C) independent of its capacitance. 
D) the same. 
E) None of these is correct. 
A) directly proportional to its capacitance. 
B) inversely proportional to its capacitance. 
C) independent of its capacitance. 
D) the same. 
E) None of these is correct. B

Question 2

You attach a 30-pF capacitor across a 1.5-V battery.How much energy is stored in the capacitor?

Accepted Answer

A) 3.4 $\times$ 10-11 J 
B) 4.5 $\times$ 10-11 J 
C) 6.7 $\times$ 10-11 J 
D) 3.4 $\times$ 10-8 J 
E) 4.5 $\times$ 10-8 J 
A) 3.4 $\times$ 10-11 J 
B) 4.5 $\times$ 10-11 J 
C) 6.7 $\times$ 10-11 J 
D) 3.4 $\times$ 10-8 J 
E) 4.5 $\times$ 10-8 J A

Question 3

The charge on each capacitor in a set of capacitors in series is

Accepted Answer

A) directly proportional to its capacitance. 
B) inversely proportional to its capacitance. 
C) independent of its capacitance. 
D) the same. 
E) None of these is correct. 
A) directly proportional to its capacitance. 
B) inversely proportional to its capacitance. 
C) independent of its capacitance. 
D) the same. 
E) None of these is correct. D

Question 4

Use the following figure to answer the next  problem:  
-You connect three capacitors as shown in the diagram below.The effective capacitance of this combination when C1 = 5.0 $\mu$F,C2 = 4.0 $\mu$F,and C3 = 3.0 $\mu$F is approximately

Accepted Answer

A) 0.44 $\mu$F 
B) 2.3 $\mu$F 
C) 3.5 $\mu$F 
D) 5.2 $\mu$F 
E) 12 $\mu$F 
A) 0.44 $\mu$F 
B) 2.3 $\mu$F 
C) 3.5 $\mu$F 
D) 5.2 $\mu$F 
E) 12 $\mu$F

Question 5

When you insert a piece of paper ($\kappa$ = 3.7)into the air between the plates of a capacitor,the capacitance

Accepted Answer

A) increases. 
B) decreases. 
C) does not change. 
D) could increase,decrease,or not change depending on the dielectric constant of the paper. 
E) does none of these. 
A) increases. 
B) decreases. 
C) does not change. 
D) could increase,decrease,or not change depending on the dielectric constant of the paper. 
E) does none of these.

Question 6

The space between the inner wire of radius a = 1 mm of a co-axial cable and the conducting shield of radius b = 8 mm is made of nylon ($\kappa$ = 4.2).A potential difference of 20 V is maintained between the wire and the shield.The energy stored per meter of the cable is

Accepted Answer

A) 1.12 nJ/m 
B) 22.5 nJ/m 
C) 44.9 nJ/m 
D) 5.36 nJ/m 
E) 2.68 nJ/m 
A) 1.12 nJ/m 
B) 22.5 nJ/m 
C) 44.9 nJ/m 
D) 5.36 nJ/m 
E) 2.68 nJ/m

Question 7

Doubling the potential difference across a capacitor

Accepted Answer

A) doubles its capacitance. 
B) halves its capacitance. 
C) quadruples the charge stored on the capacitor. 
D) doubles the charge stored on the capacitor. 
E) produces none of the above results. 
A) doubles its capacitance. 
B) halves its capacitance. 
C) quadruples the charge stored on the capacitor. 
D) doubles the charge stored on the capacitor. 
E) produces none of the above results.

Question 8

A capacitor is made with two strips of metal foil,each 2.5 cm wide by 50 cm long,with a 0.70-$\mu$m thick strip of paper ($\kappa$ = 3.7)sandwiched between them.The capacitor is rolled up to save space.What is the capacitance of this device? (The permittivity of free space $\varepsilon$0 = 8.85 $\times$ 10-12 F/m.)

Accepted Answer

A) 43 nF 
B) 0.16 $\mu$F 
C) 0.58 $\mu$F 
D) 2.0 $\mu$F 
E) 7.3 $\mu$F 
A) 43 nF 
B) 0.16 $\mu$F 
C) 0.58 $\mu$F 
D) 2.0 $\mu$F 
E) 7.3 $\mu$F

Question 9

Three capacitors 2 $\mu$F,4 $\mu$F and 8 $\mu$F are connected in parallel across a 120-V source.The charge on the 4 $\mu$F capacitor is

Accepted Answer

A) 2.4 $\times$ 10-4 C 
B) 9.6 $\times$ 10-4 C 
C) 2.1 $\times$ 103 C 
D) 1.7 $\times$ 10-3 C 
E) 4.8 $\times$ 10-4 C 
A) 2.4 $\times$ 10-4 C 
B) 9.6 $\times$ 10-4 C 
C) 2.1 $\times$ 103 C 
D) 1.7 $\times$ 10-3 C 
E) 4.8 $\times$ 10-4 C

Question 10

Which of the following statements is false?

Accepted Answer

A) In the process of charging a capacitor,an electric field is produced between its plates. 
B) The work required to charge a capacitor can be thought of as the work required to create the electric field between its plates. 
C) The energy density in the space between the plates of a capacitor is directly proportional to the first power of the electric field. 
D) The potential difference between the plates of a capacitor is directly proportional to the electric field. 
E) All of these are true. 
A) In the process of charging a capacitor,an electric field is produced between its plates. 
B) The work required to charge a capacitor can be thought of as the work required to create the electric field between its plates. 
C) The energy density in the space between the plates of a capacitor is directly proportional to the first power of the electric field. 
D) The potential difference between the plates of a capacitor is directly proportional to the electric field. 
E) All of these are true.

Question 11

The energy stored in a capacitor is directly proportional to

Accepted Answer

A) the voltage across the capacitor. 
B) the charge on the capacitor. 
C) the reciprocal of the charge on the capacitor. 
D) the square of the voltage across the capacitor. 
E) None of these is correct. 
A) the voltage across the capacitor. 
B) the charge on the capacitor. 
C) the reciprocal of the charge on the capacitor. 
D) the square of the voltage across the capacitor. 
E) None of these is correct.

Question 12

The equivalent capacitance of two capacitors in series is

Accepted Answer

A) the sum of their capacitances. 
B) the sum of the reciprocals of their capacitances. 
C) always greater than the larger of their capacitances. 
D) always less than the smaller of the capacitances. 
E) described by none of the above. 
A) the sum of their capacitances. 
B) the sum of the reciprocals of their capacitances. 
C) always greater than the larger of their capacitances. 
D) always less than the smaller of the capacitances. 
E) described by none of the above.

Question 13

You connect two 12-$\mu$F capacitors and a 6-$\mu$F capacitor in parallel.The equivalent capacitance of the combination is

Accepted Answer

A) 18 $\mu$F 
B) 4 $\mu$F 
C) 3 $\mu$F 
D) 30 $\mu$F 
E) None of these is correct. 
A) 18 $\mu$F 
B) 4 $\mu$F 
C) 3 $\mu$F 
D) 30 $\mu$F 
E) None of these is correct.

Question 14

Use the following figure to answer the next  problem:  
-You connect three capacitors as shown in the diagram.C1 = 5.0 $\mu$F,C2 = 4.0 $\mu$F,and C3 = 3.0 $\mu$F.If you apply 12 V between points A and B,the energy stored in C3 will be approximately

Accepted Answer

A) 0.16 mJ 
B) 41 $\mu$J 
C) 0.12 mJ 
D) 0.41 mJ 
E) 16 mF 
A) 0.16 mJ 
B) 41 $\mu$J 
C) 0.12 mJ 
D) 0.41 mJ 
E) 16 mF

Question 15

A potential of 12 V is applied across a parallel-plate capacitor which is constructed of square plates of side 10 cm and separation of 4.0 mm.A dielectric slab of constant $\kappa$ = 2.5 is inserted between the plates so that it completely fills the space.What is the bound surface charge density on the dielectric?

Accepted Answer

A) 12.3 pC/m2 
B) 15.9 pC/m2 
C) 39.8 pC/m2 
D) 56.8 pC/m2 
E) 85.4 pC/m2 
A) 12.3 pC/m2 
B) 15.9 pC/m2 
C) 39.8 pC/m2 
D) 56.8 pC/m2 
E) 85.4 pC/m2

Question 16

An 80-nF capacitor is charged to a potential of 500 V.How much charge accumulates on each plate of the capacitor?

Accepted Answer

A) 4.0 $\times$ 10-4 C 
B) 4.0 $\times$ 10-5 C 
C) 4.0 $\times$ 10-10 C 
D) 1.6 $\times$ 10-10 C 
E) 1.6 $\times$ 10-7 C 
A) 4.0 $\times$ 10-4 C 
B) 4.0 $\times$ 10-5 C 
C) 4.0 $\times$ 10-10 C 
D) 1.6 $\times$ 10-10 C 
E) 1.6 $\times$ 10-7 C

Question 17

A coaxial cable consists of a wire of radius 1.0 mm and an outer conducting shell of radius 8 mm.A 20 V potential difference is applied between the wire and the shell.What is the energy stored in a 2 m length of the cable?

Accepted Answer

A) 5.35 nJ 
B) 10.7 nJ 
C) 2.67 nJ 
D) 61.6 pJ 
E) 123 pJ 
A) 5.35 nJ 
B) 10.7 nJ 
C) 2.67 nJ 
D) 61.6 pJ 
E) 123 pJ

Question 18

Use the following figure to answer the next  problem:  
-You connect three capacitors as shown in the diagram.C1 = C3 = 2.5 $\mu$F,and C2 = 5.0 $\mu$F.A potential difference of 9.0 V is maintained between the terminals A and B.The magnitude of the charge on capacitor C3 is approximately

Accepted Answer

A) 4.2 $\mu$C 
B) 4.8 $\mu$C 
C) 17 $\mu$C 
D) 37 $\mu$C 
E) 90 $\mu$C 
A) 4.2 $\mu$C 
B) 4.8 $\mu$C 
C) 17 $\mu$C 
D) 37 $\mu$C 
E) 90 $\mu$C

Question 19

A 1.0-$\mu$F capacitor and a 2.0-$\mu$F capacitor are connected in series across a 1200-V source.The charge on each capacitor is

Accepted Answer

A) 0.40 mC 
B) 0.80 mC 
C) 1.2 mC 
D) 1.8 mC 
E) 3.6 mC 
A) 0.40 mC 
B) 0.80 mC 
C) 1.2 mC 
D) 1.8 mC 
E) 3.6 mC

Question 20

If the area of the plates of a parallel-plate capacitor is doubled,the capacitance is

Accepted Answer

A) not changed. 
B) doubled. 
C) halved. 
D) increased by a factor of 4. 
E) decreased by a factor of 1/4. 
A) not changed. 
B) doubled. 
C) halved. 
D) increased by a factor of 4. 
E) decreased by a factor of 1/4.

Exam 24: Capacitance

The voltage across each capacitor in a set of capacitors in series is

You attach a 30-pF capacitor across a 1.5-V battery.How much energy is stored in the capacitor?

The charge on each capacitor in a set of capacitors in series is

Use the following figure to answer the next problem: -You connect three capacitors as shown in the diagram below.The effective capacitance of this combination when C1 = 5.0 μ\muμ F,C2 = 4.0 μ\muμ F,and C3 = 3.0 μ\muμ F is approximately

When you insert a piece of paper ( κ\kappaκ = 3.7)into the air between the plates of a capacitor,the capacitance

The space between the inner wire of radius a = 1 mm of a co-axial cable and the conducting shield of radius b = 8 mm is made of nylon ( κ\kappaκ = 4.2).A potential difference of 20 V is maintained between the wire and the shield.The energy stored per meter of the cable is

Doubling the potential difference across a capacitor

Three capacitors 2 μ\muμ F,4 μ\muμ F and 8 μ\muμ F are connected in parallel across a 120-V source.The charge on the 4 μ\muμ F capacitor is

Which of the following statements is false?

The energy stored in a capacitor is directly proportional to

The equivalent capacitance of two capacitors in series is

You connect two 12- μ\muμ F capacitors and a 6- μ\muμ F capacitor in parallel.The equivalent capacitance of the combination is

Use the following figure to answer the next problem: -You connect three capacitors as shown in the diagram.C1 = 5.0 μ\muμ F,C2 = 4.0 μ\muμ F,and C3 = 3.0 μ\muμ F.If you apply 12 V between points A and B,the energy stored in C3 will be approximately

An 80-nF capacitor is charged to a potential of 500 V.How much charge accumulates on each plate of the capacitor?

A coaxial cable consists of a wire of radius 1.0 mm and an outer conducting shell of radius 8 mm.A 20 V potential difference is applied between the wire and the shell.What is the energy stored in a 2 m length of the cable?

Use the following figure to answer the next problem: -You connect three capacitors as shown in the diagram.C1 = C3 = 2.5 μ\muμ F,and C2 = 5.0 μ\muμ F.A potential difference of 9.0 V is maintained between the terminals A and B.The magnitude of the charge on capacitor C3 is approximately

A 1.0- μ\muμ F capacitor and a 2.0- μ\muμ F capacitor are connected in series across a 1200-V source.The charge on each capacitor is

If the area of the plates of a parallel-plate capacitor is doubled,the capacitance is

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When you insert a piece of paper ( $\kappa$ = 3.7)into the air between the plates of a capacitor,the capacitance

The space between the inner wire of radius a = 1 mm of a co-axial cable and the conducting shield of radius b = 8 mm is made of nylon ( $\kappa$ = 4.2).A potential difference of 20 V is maintained between the wire and the shield.The energy stored per meter of the cable is

Three capacitors 2 $\mu$ F,4 $\mu$ F and 8 $\mu$ F are connected in parallel across a 120-V source.The charge on the 4 $\mu$ F capacitor is

You connect two 12- $\mu$ F capacitors and a 6- $\mu$ F capacitor in parallel.The equivalent capacitance of the combination is

A 1.0- $\mu$ F capacitor and a 2.0- $\mu$ F capacitor are connected in series across a 1200-V source.The charge on each capacitor is