Question 1

The capacitance of a parallel-plate capacitor

Accepted Answer

A) is defined as the amount of work required to move a charge from one plate to the other. 
B) decreases if a dielectric is placed between its plates. 
C) is independent of the distance between the plates. 
D) has units of J/C. 
E) is independent of the charge on the capacitor. 
A) is defined as the amount of work required to move a charge from one plate to the other. 
B) decreases if a dielectric is placed between its plates. 
C) is independent of the distance between the plates. 
D) has units of J/C. 
E) is independent of the charge on the capacitor.

Question 2

You connect two capacitors C1 = 15 pF and C2 = 30 pF in series across a 1.5-V battery.The potential difference across capacitor C1 is approximately

Accepted Answer

A) 0.50 V 
B) 1.0 V 
C) 1.5 V 
D) 0.33 V 
E) 0.67 V 
A) 0.50 V 
B) 1.0 V 
C) 1.5 V 
D) 0.33 V 
E) 0.67 V

Question 3

If a dielectric is inserted between the plates of a parallel-plate capacitor that is connected to a 100-V battery,the

Accepted Answer

A) voltage across the capacitor decreases. 
B) electric field between the plates decreases. 
C) electric field between the plates increases. 
D) charge on the capacitor plates decreases. 
E) charge on the capacitor plates increases. 
A) voltage across the capacitor decreases. 
B) electric field between the plates decreases. 
C) electric field between the plates increases. 
D) charge on the capacitor plates decreases. 
E) charge on the capacitor plates increases.

Question 4

The charge on each capacitor in a set of capacitors in parallel 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.

Question 5

A parallel-plate capacitor has square plates of side 12 cm and a separation of 6.0 mm.A dielectric slab of constant $\kappa$ = 2.0 has the same area as the plates but has a thickness of 3.0 mm.What is the capacitance of this capacitor with the dielectric slab between its plates?

Accepted Answer

A) 28 pF 
B) 21 pF 
C) 16 pF 
D) 37 pF 
E) 53 pF 
A) 28 pF 
B) 21 pF 
C) 16 pF 
D) 37 pF 
E) 53 pF

Question 6

Which of the following statements about parallel plate capacitor is false?

Accepted Answer

A) The two plates have equal charges. 
B) The capacitor store charges on the plates. 
C) The capacitance is proportional to the area. 
D) The capacitance is inversely proportional to the separation between the plates. 
E) A charged capacitor stores energy. 
A) The two plates have equal charges. 
B) The capacitor store charges on the plates. 
C) The capacitance is proportional to the area. 
D) The capacitance is inversely proportional to the separation between the plates. 
E) A charged capacitor stores energy.

Question 7

A parallel plate capacitor of area A = 30 cm2 and separation d = 5 mm is charged by a battery of 60-V.If the air between the plates is replaced by a dielectric of $\kappa$ = 4 with the battery still connected,then what is the ratio of the initial charge on the plates divided by the final charge on the plates?

Accepted Answer

A) 4.3 
B) 1 
C) 16 
D) 0.25 
E) 4.0 
A) 4.3 
B) 1 
C) 16 
D) 0.25 
E) 4.0

Question 8

An electric field,E,is applied to a dielectric.Which of the following statements is true?

Accepted Answer

A) The electric field within the dielectric is less than E. 
B) The dielectric produces an electric field in the opposite direction to E. 
C) The molecules in the dielectric become polarized. 
D) The electric field will produce a torque on molecules in dielectrics which have permanent dipoles. 
E) All the above statements are true. 
A) The electric field within the dielectric is less than E. 
B) The dielectric produces an electric field in the opposite direction to E. 
C) The molecules in the dielectric become polarized. 
D) The electric field will produce a torque on molecules in dielectrics which have permanent dipoles. 
E) All the above statements are true.

Question 9

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 per meter of the cable?

Accepted Answer

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

Question 10

A capacitor,C1 = 5.0 $\mu$F,is charged up to 8 V.It is then connected to a second uncharged capacitor C2 = 2.5 $\mu$F.The charge on C2 after the system has come to equilibrium is

Accepted Answer

A) 26.7 $\mu$C 
B) 13.3 $\mu$C 
C) 20.0 $\mu$C 
D) 40.0 $\mu$C 
E) 6.67 $\mu$C 
A) 26.7 $\mu$C 
B) 13.3 $\mu$C 
C) 20.0 $\mu$C 
D) 40.0 $\mu$C 
E) 6.67 $\mu$C

Question 11

If the potential difference of a capacitor is reduced by one-half,the energy stored in that capacitor is

Accepted Answer

A) reduced to one-half. 
B) reduced to one-quarter. 
C) increased by a factor of 2. 
D) increased by a factor of 4. 
E) not changed. 
A) reduced to one-half. 
B) reduced to one-quarter. 
C) increased by a factor of 2. 
D) increased by a factor of 4. 
E) not changed.

Question 12

If the area of the plates of a parallel plate capacitor is halved and the separation between the plates tripled,while the charge on the capacitor remains constant,then by what factor does the energy stored in the capacitor change?

Accepted Answer

A) increase by a factor of 2 
B) decrease by a factor of 2/3 
C) increase by a factor of 6 
D) increase by a factor of 3/2 
E) decrease by a factor of 1/6 
A) increase by a factor of 2 
B) decrease by a factor of 2/3 
C) increase by a factor of 6 
D) increase by a factor of 3/2 
E) decrease by a factor of 1/6

Question 13

A capacitor is constructed by placing a conducting sphere of radius a concentrically inside a thin conducting spherical shell of radius b.Derive an expression for the capacitance of such a capacitor.

Accepted Answer

A)    
B)    
C)    
D)    
E) It is not possible to construct such a capacitor. 
A)    
B)    
C)    
D)    
E) It is not possible to construct such a capacitor.

Question 14

If you decrease the charge on a parallel-plate capacitor from 12 µC to 4 µC and increase the plate separation from 1 mm to 3 mm,the energy stored in the capacitor changes by a factor of

Accepted Answer

A) 27 
B) 1/3 
C) 3 
D) 8 
E) 1/4 
A) 27 
B) 1/3 
C) 3 
D) 8 
E) 1/4

Question 15

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 voltage across on capacitor C3 is approximately

Accepted Answer

A) 1.2 V 
B) 7.9 V 
C) 3.2 V 
D) 5.4 V 
E) 6.8 V 
A) 1.2 V 
B) 7.9 V 
C) 3.2 V 
D) 5.4 V 
E) 6.8 V

Question 16

A capacitor,C1 = 5.0 $\mu$F,is charged up to 8 V.It is then connected to a second uncharged capacitor C2 = 2.5 $\mu$F.The voltage across the capacitor C1 after the system has come to equilibrium is

Accepted Answer

A) 2.67 V 
B) 4.0 V 
C) 5.33 V 
D) 8.0 V 
E) 12.0 V 
A) 2.67 V 
B) 4.0 V 
C) 5.33 V 
D) 8.0 V 
E) 12.0 V

Question 17

A parallel-plate capacitor has square plates of side 8.0 cm separated by 0.80 mm.If you charge this capacitor to 15 V,the amount of charge transferred from one plate to the other is

Accepted Answer

A) 71 nC 
B) 7.1 nC 
C) 1.1 pC 
D) 1.1 nC 
E) 7.1 pC 
A) 71 nC 
B) 7.1 nC 
C) 1.1 pC 
D) 1.1 nC 
E) 7.1 pC

Question 18

A coaxial cable consists of a wire of radius 0.30 mm and an outer conducting shell of radius 1.0 mm.Its capacitance per unit length is approximately

Accepted Answer

A) 17 nF/m 
B) 0.11 nF/m 
C) 92 pF/m 
D) 23 pF/m 
E) 46 pF/m 
A) 17 nF/m 
B) 0.11 nF/m 
C) 92 pF/m 
D) 23 pF/m 
E) 46 pF/m

Question 19

A parallel plate capacitor is constructed using two square metal sheets,each of side L = 10 cm.The plates are separated by a distance d = 2 mm and a voltage applied between the plates.The electric field strength within the plates is E = 4000 V/m.The energy stored in the capacitor is

Accepted Answer

A) 0.71 nJ 
B) 1.42 nJ 
C) 2.83 nJ 
D) 3.67 nJ 
E) zero 
A) 0.71 nJ 
B) 1.42 nJ 
C) 2.83 nJ 
D) 3.67 nJ 
E) zero

Question 20

A 2.0-µF capacitor has a potential difference of 5000 V.The work done in charging it was

Accepted Answer

A) 2.5 J 
B) 5.0 J 
C) 25 J 
D) 5.0 mJ 
E) 0.50 kJ 
A) 2.5 J 
B) 5.0 J 
C) 25 J 
D) 5.0 mJ 
E) 0.50 kJ

Exam 24: Capacitance

The capacitance of a parallel-plate capacitor

You connect two capacitors C1 = 15 pF and C2 = 30 pF in series across a 1.5-V battery.The potential difference across capacitor C1 is approximately

If a dielectric is inserted between the plates of a parallel-plate capacitor that is connected to a 100-V battery,the

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

A parallel-plate capacitor has square plates of side 12 cm and a separation of 6.0 mm.A dielectric slab of constant κ\kappaκ = 2.0 has the same area as the plates but has a thickness of 3.0 mm.What is the capacitance of this capacitor with the dielectric slab between its plates?

Which of the following statements about parallel plate capacitor is false?

An electric field,E,is applied to a dielectric.Which of the following statements is true?

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 per meter of the cable?

A capacitor,C1 = 5.0 μ\muμ F,is charged up to 8 V.It is then connected to a second uncharged capacitor C2 = 2.5 μ\muμ F.The charge on C2 after the system has come to equilibrium is

If the potential difference of a capacitor is reduced by one-half,the energy stored in that capacitor is

If the area of the plates of a parallel plate capacitor is halved and the separation between the plates tripled,while the charge on the capacitor remains constant,then by what factor does the energy stored in the capacitor change?

A capacitor is constructed by placing a conducting sphere of radius a concentrically inside a thin conducting spherical shell of radius b.Derive an expression for the capacitance of such a capacitor.

If you decrease the charge on a parallel-plate capacitor from 12 µC to 4 µC and increase the plate separation from 1 mm to 3 mm,the energy stored in the capacitor changes by a factor of

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 voltage across on capacitor C3 is approximately

A capacitor,C1 = 5.0 μ\muμ F,is charged up to 8 V.It is then connected to a second uncharged capacitor C2 = 2.5 μ\muμ F.The voltage across the capacitor C1 after the system has come to equilibrium is

A parallel-plate capacitor has square plates of side 8.0 cm separated by 0.80 mm.If you charge this capacitor to 15 V,the amount of charge transferred from one plate to the other is

A coaxial cable consists of a wire of radius 0.30 mm and an outer conducting shell of radius 1.0 mm.Its capacitance per unit length is approximately

A parallel plate capacitor is constructed using two square metal sheets,each of side L = 10 cm.The plates are separated by a distance d = 2 mm and a voltage applied between the plates.The electric field strength within the plates is E = 4000 V/m.The energy stored in the capacitor is

A 2.0-µF capacitor has a potential difference of 5000 V.The work done in charging it was

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You connect two capacitors C₁ = 15 pF and C₂ = 30 pF in series across a 1.5-V battery.The potential difference across capacitor C₁ is approximately

A parallel-plate capacitor has square plates of side 12 cm and a separation of 6.0 mm.A dielectric slab of constant $\kappa$ = 2.0 has the same area as the plates but has a thickness of 3.0 mm.What is the capacitance of this capacitor with the dielectric slab between its plates?

A capacitor,C₁ = 5.0 $\mu$ F,is charged up to 8 V.It is then connected to a second uncharged capacitor C₂ = 2.5 $\mu$ F.The charge on C₂ after the system has come to equilibrium is

A capacitor,C₁ = 5.0 $\mu$ F,is charged up to 8 V.It is then connected to a second uncharged capacitor C₂ = 2.5 $\mu$ F.The voltage across the capacitor C₁ after the system has come to equilibrium is