Question 1

What is the total energy stored in the capacitors in the circuit shown?

Accepted Answer

A) 1/2 CV2 
B) 3/2 CV2 
C) 2/3 CV2 
D) 1/3 CV2 
E) 5/2 CV2 
A) 1/2 CV2 
B) 3/2 CV2 
C) 2/3 CV2 
D) 1/3 CV2 
E) 5/2 CV2

Question 2

Which of the following statements is TRUE?

Accepted Answer

A) A capacitor has its air gap doubled and its area halved.The capacitance is unchanged. 
B) If the charge on one side of a capacitor is +Q,and the other side it is -Q,then the energy in the capacitor is Q2/C. 
C) Two capacitors in series always have a lower capacitance than the capacitance of either of the two alone. 
D) Two capacitors in parallel always have a lower capacitance than the capacitance of either of the two alone. 
E) Two capacitors differ only in the dielectric material that fills them.For the same voltage,the one with the higher dielectric constant holds less charge. 
A) A capacitor has its air gap doubled and its area halved.The capacitance is unchanged. 
B) If the charge on one side of a capacitor is +Q,and the other side it is -Q,then the energy in the capacitor is Q2/C. 
C) Two capacitors in series always have a lower capacitance than the capacitance of either of the two alone. 
D) Two capacitors in parallel always have a lower capacitance than the capacitance of either of the two alone. 
E) Two capacitors differ only in the dielectric material that fills them.For the same voltage,the one with the higher dielectric constant holds less charge.

Question 3

A 1.00-nF capacitor initially charged to 30.0 V and a 2.00-nF capacitor charged to 40.0 V are connected to each other with the negative plate of each connected to the negative plate of the other.What is the final charge on the 2.00-nF capacitor?

Accepted Answer

A) 33.3 nC 
B) 73.3 nC 
C) 86.2 nC 
D) 100 nC 
E) 365 nC 
A) 33.3 nC 
B) 73.3 nC 
C) 86.2 nC 
D) 100 nC 
E) 365 nC

Question 4

In the circuit shown,what would be the equivalent single capacitor which would replace the three?

Accepted Answer

A) 3 C 
B) C/3 
C) 2 C/3 
D) 4 C/3 
E) 2 C 
A) 3 C 
B) C/3 
C) 2 C/3 
D) 4 C/3 
E) 2 C

Question 5

A 1.00-nF capacitor initially charged to 30.0 V and a 2.00-nF capacitor charged to 40.0 V are connected to each other with the negative plate of each connected to the negative plate of the other.What is the electric potential across the 1.00-nF capacitor?

Accepted Answer

A) 36.7 V 
B) 40.0 V 
C) 30.0 V 
D) 38.9 V 
E) 34.1 V 
A) 36.7 V 
B) 40.0 V 
C) 30.0 V 
D) 38.9 V 
E) 34.1 V

Question 6

A parallel plate capacitor is made of two circular thin plates of radius 15 cm separated by 2.5 mm of air.If they are charged to a potential difference of 22 V,what is the charge resident on each plate?

Accepted Answer

A) 1.8 nC 
B) 5.5 nC 
C) 7.0 nC 
D) 22 nC 
E) 36 nC 
A) 1.8 nC 
B) 5.5 nC 
C) 7.0 nC 
D) 22 nC 
E) 36 nC

Question 7

An air-filled parallel plate capacitor is connected to a battery of voltage Vo.There is charge Qo on each plate,energy Uo stored between the plates and an electric field of Eo between the plates.The capacitor is then removed from the battery and then a dielectric material with a dielectric constant of K is then placed between the plates of the capacitor.What are the new values of V,Q,U,and E?

Accepted Answer

A) Vo/K,KQo,Uo,Eo/K 
B) KVo,Qo,K2Uo,Eo/K 
C) Vo/K,Qo,Uo/K,Eo/K 
D) Vo,Qo/K,Uo/K,Eo 
E) Vo,KQo,KUo,Eo 
A) Vo/K,KQo,Uo,Eo/K 
B) KVo,Qo,K2Uo,Eo/K 
C) Vo/K,Qo,Uo/K,Eo/K 
D) Vo,Qo/K,Uo/K,Eo 
E) Vo,KQo,KUo,Eo

Question 8

A dielectric with a dielectric constant of 3 is inserted into a parallel plate capacitor,filling one-half of the volume as shown in the figure.If the capacitance of the capacitor without the dielectric is C,what is the capacitance of the capacitor with the dielectric?

Accepted Answer

A) 0.5 C 
B) 1 C 
C) 2 C 
D) 3 C 
E) 4 C 
A) 0.5 C 
B) 1 C 
C) 2 C 
D) 3 C 
E) 4 C

Question 9

When a capacitor has a charge of absolute value 40.0 µC on each plate the potential difference across the plates is 15.0 V.What is the potential difference across its plates when the energy is stored in this capacitor is 50.0 mJ?

Accepted Answer

A) 137 V 
B) 0.516 mV 
C) 194 V 
D) 0.360 mV 
E) 0.155 V 
A) 137 V 
B) 0.516 mV 
C) 194 V 
D) 0.360 mV 
E) 0.155 V

Question 10

When N identical capacitors are connected in series across a battery,the energy stored is U.If the same capacitors were connected in parallel across the same battery,then how much energy would be stored?

Accepted Answer

A) U/N 
B) U 
C) NU 
D) N2U 
A) U/N 
B) U 
C) NU 
D) N2U

Question 11

Consider an isolated spherical conductor of radius R = 30 m,kept in a medium of permittivity 1.What is its capacitance?

Accepted Answer

A) 0.29 nF 
B) 1.53 nF 
C) 3.34 nF 
D) 7.35 nF 
E) 53.5 nF 
A) 0.29 nF 
B) 1.53 nF 
C) 3.34 nF 
D) 7.35 nF 
E) 53.5 nF

Question 12

A parallel plate capacitor of capacitance C has plates of area A with separation d between them.When it is connected to a battery of voltage V,it has charge of magnitude Qon its plates.While it is connected to the battery,the distance between the plates is increased by a factor of 2 and the magnitude of the charge on the plates and the new capacitance are

Accepted Answer

A)    Q,
  C 
B)    Q,2C 
C) 2Q,2C 
D) 2Q,   
A)    Q,
  C 
B)    Q,2C 
C) 2Q,2C 
D) 2Q,

Question 13

A 1.00-nF capacitor initially charged to 30.0 V and a 2.00-nF capacitor charged to 40.0 V are connected to each other with the negative plate of each connected to the negative plate of the other.What is the final charge on the 1.00-nF capacitor?

Accepted Answer

A) 100 nC 
B) 86.2 nC 
C) 36.7 nC 
D) 365 nC 
E) 73.3 nC 
A) 100 nC 
B) 86.2 nC 
C) 36.7 nC 
D) 365 nC 
E) 73.3 nC

Question 14

In the circuit shown,three capacitors with C1 = C2 = C3 = 10.00 $\mu$F are connected to a battery with voltage V = 194 V.What is the voltage across capacitor C1 (in V)?

Accepted Answer

A) 129.3 
B) 146.1 
C) 165.1 
D) 186.6 
E) 210.9 
A) 129.3 
B) 146.1 
C) 165.1 
D) 186.6 
E) 210.9

Question 15

What is the capacitance of a steel sphere of radius 5 mm?

Accepted Answer

A) 0.4 pF 
B) 1 pF 
C) 0.8 pF 
D) 0.6 pF 
E) 1.5 pF 
A) 0.4 pF 
B) 1 pF 
C) 0.8 pF 
D) 0.6 pF 
E) 1.5 pF

Question 16

When a capacitor has a charge of absolute value 80 µC on each plate the potential difference across the plates is 10 V.How much energy is stored in this capacitor when the potential difference across its plates is 120 V?

Accepted Answer

A) 0.36 J 
B) 58 mJ 
C) 0.90 GJ 
D) 0.48 mJ 
E) 0.12 J 
A) 0.36 J 
B) 58 mJ 
C) 0.90 GJ 
D) 0.48 mJ 
E) 0.12 J

Question 17

A 6-V battery is connected across a capacitor through a switch which is initially open.The 90 µC charge flows from the battery to the capacitor when the switch is closed.The capacitance of the capacitor is

Accepted Answer

A) 0.67 µF. 
B) 15 µF 
C) 20 µF 
D) 54 µF. 
E) 30 µF. 
A) 0.67 µF. 
B) 15 µF 
C) 20 µF 
D) 54 µF. 
E) 30 µF.

Question 18

Two metal plates,as shown in the figure,extend 5 cm into the page.The plates are machined in this shape to serve as electrodes in electrical equipment.The capacitance of this machined capacitor is

Accepted Answer

A) 2.53 pF. 
B) 6.20 pF. 
C) 9.89 pF. 
D) 12.39 pF. 
E) 29.24 pF. 
A) 2.53 pF. 
B) 6.20 pF. 
C) 9.89 pF. 
D) 12.39 pF. 
E) 29.24 pF.

Exam 24: Capacitors

What is the total energy stored in the capacitors in the circuit shown?

Which of the following statements is TRUE?

A 1.00-nF capacitor initially charged to 30.0 V and a 2.00-nF capacitor charged to 40.0 V are connected to each other with the negative plate of each connected to the negative plate of the other.What is the final charge on the 2.00-nF capacitor?

In the circuit shown,what would be the equivalent single capacitor which would replace the three?

A 1.00-nF capacitor initially charged to 30.0 V and a 2.00-nF capacitor charged to 40.0 V are connected to each other with the negative plate of each connected to the negative plate of the other.What is the electric potential across the 1.00-nF capacitor?

A parallel plate capacitor is made of two circular thin plates of radius 15 cm separated by 2.5 mm of air.If they are charged to a potential difference of 22 V,what is the charge resident on each plate?

A dielectric with a dielectric constant of 3 is inserted into a parallel plate capacitor,filling one-half of the volume as shown in the figure.If the capacitance of the capacitor without the dielectric is C,what is the capacitance of the capacitor with the dielectric?

When a capacitor has a charge of absolute value 40.0 µC on each plate the potential difference across the plates is 15.0 V.What is the potential difference across its plates when the energy is stored in this capacitor is 50.0 mJ?

When N identical capacitors are connected in series across a battery,the energy stored is U.If the same capacitors were connected in parallel across the same battery,then how much energy would be stored?

Consider an isolated spherical conductor of radius R = 30 m,kept in a medium of permittivity 1.What is its capacitance?

A 1.00-nF capacitor initially charged to 30.0 V and a 2.00-nF capacitor charged to 40.0 V are connected to each other with the negative plate of each connected to the negative plate of the other.What is the final charge on the 1.00-nF capacitor?

In the circuit shown,three capacitors with C1 = C2 = C3 = 10.00 μ\muμ F are connected to a battery with voltage V = 194 V.What is the voltage across capacitor C1 (in V)?

What is the capacitance of a steel sphere of radius 5 mm?

When a capacitor has a charge of absolute value 80 µC on each plate the potential difference across the plates is 10 V.How much energy is stored in this capacitor when the potential difference across its plates is 120 V?

A 6-V battery is connected across a capacitor through a switch which is initially open.The 90 µC charge flows from the battery to the capacitor when the switch is closed.The capacitance of the capacitor is

Two metal plates,as shown in the figure,extend 5 cm into the page.The plates are machined in this shape to serve as electrodes in electrical equipment.The capacitance of this machined capacitor is

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