Question 1

Capacitors connected in series always have the same

Accepted Answer

A) capacitance. 
B) charge. 
C) potential difference. 
D) dielectric strength. 
A) capacitance. 
B) charge. 
C) potential difference. 
D) dielectric strength. B

Question 2

Suppose we have two capacitors connected in parallel with a 10 V battery.What is the energy stored in the circuit if the capacitance of one is C1 = 50 mF and the other is C2 = 100 mF?

Accepted Answer

A) 9.67 J 
B) 2.33 J 
C) 1.67 J 
D) 3.33 J 
E) 7.50 J 
A) 9.67 J 
B) 2.33 J 
C) 1.67 J 
D) 3.33 J 
E) 7.50 J E

Question 3

Which of the following capacitors have the smallest charge?

Accepted Answer

A) a parallel plate capacitor with an area of 10 cm2 and a plate separation of 2 mm connected to a 10-V battery 
B) a parallel plate capacitor with an area of 5 cm2 and a plate separation of 1 mm connected to a 10-V battery 
C) a parallel plate capacitor with an area of 10 cm2 and a plate separation of 4 mm connected to a 5-V battery 
D) A parallel plate capacitor with an area of 20 cm2 and a plate separation of 2 mm connected to a 20-V battery 
E) All of the choices have the same charge. 
A) a parallel plate capacitor with an area of 10 cm2 and a plate separation of 2 mm connected to a 10-V battery 
B) a parallel plate capacitor with an area of 5 cm2 and a plate separation of 1 mm connected to a 10-V battery 
C) a parallel plate capacitor with an area of 10 cm2 and a plate separation of 4 mm connected to a 5-V battery 
D) A parallel plate capacitor with an area of 20 cm2 and a plate separation of 2 mm connected to a 20-V battery 
E) All of the choices have the same charge. C

Question 4

A proton traveling at speed of 1.0 * 106 m/s enters the gap between the plates of a 2.0-cm-wide parallel-plate capacitor along x-axis.The surface charge densities on the plates are  $\sigma$ = $\pm$1.0 * 10-6 C/m2.How far has the proton been deflected sideways ($\Delta$y)when it reaches the far edge of the capacitor? Assume the electric field is uniform inside the capacitor and zero outside.

Accepted Answer

A) 1.33 mm 
B) 2.17 mm 
C) 4.7 mm 
D) 0.96 mm 
A) 1.33 mm 
B) 2.17 mm 
C) 4.7 mm 
D) 0.96 mm

Question 5

Consider the assembly of capacitors shown here.Let C1 = C2 = C3 = C4 = 20 mF.What is the equivalent capacitance of this circuit?

Accepted Answer

A) 10 mF 
B) 15 mF 
C) 30 mF 
D) 80 mF 
E) 40 mF 
A) 10 mF 
B) 15 mF 
C) 30 mF 
D) 80 mF 
E) 40 mF

Question 6

What is the radius of a steel sphere having a capacitance of radius 1.5 pF?

Accepted Answer

A) 9.0 mm 
B) 5.0 mm 
C) 170 mm 
D) 13 mm 
E) 6.0 mm 
A) 9.0 mm 
B) 5.0 mm 
C) 170 mm 
D) 13 mm 
E) 6.0 mm

Question 7

An uncharged parallel plate capacitor with an air gap is connected to a 6.0-V battery.After charging,the energy stored in the capacitor is 40 nJ.If each of the plates has an area of 10 cm2,what is the magnitude of the electric field between the plates?

Accepted Answer

A) 19 V/m 
B) 1.5 * 106 V/m 
C) 3.0 * 106 V/m 
D) 4.2 * 106 V/m 
E) 6.0 * 106 V/m 
A) 19 V/m 
B) 1.5 * 106 V/m 
C) 3.0 * 106 V/m 
D) 4.2 * 106 V/m 
E) 6.0 * 106 V/m

Question 8

Which of the following capacitors have the largest charge?

Accepted Answer

A) a parallel plate capacitor with an area of 10 cm2 and a plate separation of 2 mm connected to a 10-V battery 
B) a parallel plate capacitor with an area of 5 cm2 and a plate separation of 1 mm connected to a 10-V battery 
C) a parallel plate capacitor with an area of 10 cm2 and a plate separation of 4 mm connected to a 5-V battery 
D) A parallel plate capacitor with an area of 20 cm2 and a plate separation of 2 mm connected to a 20-V battery 
E) All of the choices have the same charge. 
A) a parallel plate capacitor with an area of 10 cm2 and a plate separation of 2 mm connected to a 10-V battery 
B) a parallel plate capacitor with an area of 5 cm2 and a plate separation of 1 mm connected to a 10-V battery 
C) a parallel plate capacitor with an area of 10 cm2 and a plate separation of 4 mm connected to a 5-V battery 
D) A parallel plate capacitor with an area of 20 cm2 and a plate separation of 2 mm connected to a 20-V battery 
E) All of the choices have the same charge.

Question 9

A 10-nF is connected in series with a 20-nF capacitor.This combination is then placed in parallel with a 30-nF capacitor.This combination is then placed parallel to a 9.0-V battery.What is the charge on the 20-nF capacitor.

Accepted Answer

A) 60 nC 
B) 90 nC 
C) 140 nC 
D) 180 nC 
E) 330 nC 
A) 60 nC 
B) 90 nC 
C) 140 nC 
D) 180 nC 
E) 330 nC

Question 10

A spherical shell capacitor is 1 cm in radius with the outside shell 1 mm beyond this.What is the capacitance of this combination?

Accepted Answer

A) 21.3 pF 
B) 16.8 pF 
C) 12.2 pF 
D) 8.7 pF 
E) 5.7 pF 
A) 21.3 pF 
B) 16.8 pF 
C) 12.2 pF 
D) 8.7 pF 
E) 5.7 pF

Question 11

A 1.50-µF capacitor charged to 40.0 V and a 2.40-µF capacitor charged to 15.0 V are connected to each other,with the positive plate of each connected to the negative plate of the other.What is the final electric potential across the 1.50-µF capacitor?

Accepted Answer

A) 12.5 V 
B) 6.15 V 
C) 40.0 V 
D) 25.0 V 
E) 8.13 V 
A) 12.5 V 
B) 6.15 V 
C) 40.0 V 
D) 25.0 V 
E) 8.13 V

Question 12

What is the capacitance of two parallel plates 0.9 mm apart with an area of 12 cm2 if the space between the plates is filled with a material with dielectric constant of 3.7?

Accepted Answer

A) 76 F 
B) 4.4 mF 
C) 130 $\mu$F 
D) 3.7 $\mu$F 
E) 44 pF 
A) 76 F 
B) 4.4 mF 
C) 130 $\mu$F 
D) 3.7 $\mu$F 
E) 44 pF

Question 13

In circuit shown,calculate the charge on C3,where $\varepsilon$ = 10 V,C1 = C2 = 6 $\mu$F and C3 = 3 $\mu$F.

Accepted Answer

A) 12 µC 
B) 36 µC 
C) 24 µC 
D) 9 µC 
A) 12 µC 
B) 36 µC 
C) 24 µC 
D) 9 µC

Question 14

A 1.50-µF capacitor charged to 40.0 V and a 2.40-µF capacitor charged to 15.0 V are connected to each other,with the positive plate of each connected to the negative plate of the other.What is the final charge on the 2.4-µF capacitor?

Accepted Answer

A) 9.23 µC 
B) 36.9 µC 
C) 14.8 µC 
D) 1.82 µC 
E) 5.74 µC 
A) 9.23 µC 
B) 36.9 µC 
C) 14.8 µC 
D) 1.82 µC 
E) 5.74 µC

Question 15

A parallel plate capacitor connected to a 2-V battery consists of two 1-cm square plates separated by 1 mm of air.How much work is done in inserting a sheet with a dielectric constant of 1.5 between the plates (in units of 10-13 J)?

Accepted Answer

A) 17.4 
B) 9.67 
C) 8.85 
D) 4.53 
E) 2.28 
A) 17.4 
B) 9.67 
C) 8.85 
D) 4.53 
E) 2.28

Question 16

Two capacitors C1 = 2.5 mF and C2 = 5.0 mF are connected in parallel.If a voltage of V = 120 volts is applied across the capacitors,what is the energy stored in the capacitors?

Accepted Answer

A) 4.0 J 
B) 36 J 
C) 54 J 
D) 12 J 
E) 0 
A) 4.0 J 
B) 36 J 
C) 54 J 
D) 12 J 
E) 0

Question 17

Three capacitors of capacity 4,6,and 8 µF are connected in series with a battery of 13 V.The potential difference across the 6-µF capacitance is

Accepted Answer

A) 4 V. 
B) 6 V. 
C) 8 V. 
D) 9 V. 
E) 10 V. 
A) 4 V. 
B) 6 V. 
C) 8 V. 
D) 9 V. 
E) 10 V.

Question 18

A 3.0-nF parallel plate capacitor with a sheet of mylar (k = 3.1)filling the space between the plates is connected to a 150-V battery.While it is still connected to the battery,the sheet of mylar is completely removed from the space between the two plates.Determine the change in energy stored in the capacitor?

Accepted Answer

A) -1.0 * 10-6 J 
B) -2.4 * 10-6 J 
C) -4.9 * 10-6 J 
D) -5.5 * 10-6 J 
A) -1.0 * 10-6 J 
B) -2.4 * 10-6 J 
C) -4.9 * 10-6 J 
D) -5.5 * 10-6 J

Question 19

A 1.50-µF capacitor charged to 40.0 V and a 2.40-µF capacitor charged to 15.0 V are connected to each other,with the positive plate of each connected to the negative plate of the other.What is the final charge on the 1.50-µF capacitor?

Accepted Answer

A) 1.82 µC 
B) 5.74 µC 
C) 9.23 µC 
D) 15.8 µC 
E) 36.9 µC 
A) 1.82 µC 
B) 5.74 µC 
C) 9.23 µC 
D) 15.8 µC 
E) 36.9 µC

Question 20

Consider a capacitor that consists of two parallel plates,one of which can move relative to the other.Air fills the space between the plates,the capacitance is 25.0 pF when the separation between plates is d = 0.450 cm.A battery with potential difference V=11.1 V is connected to the plates.What is the charge density  $\sigma$ on the left plate?

Accepted Answer

A) 1.1 * 10-8 C/m2 
B) 2.2 * 10-8 C/m2 
C) 3.3 * 10-8 C/m2 
D) 4.4 * 10-8 C/m2 
E) 6.3 * 10-8 C/m2 
A) 1.1 * 10-8 C/m2 
B) 2.2 * 10-8 C/m2 
C) 3.3 * 10-8 C/m2 
D) 4.4 * 10-8 C/m2 
E) 6.3 * 10-8 C/m2

Exam 24: Capacitors

Capacitors connected in series always have the same

Suppose we have two capacitors connected in parallel with a 10 V battery.What is the energy stored in the circuit if the capacitance of one is C1 = 50 mF and the other is C2 = 100 mF?

Which of the following capacitors have the smallest charge?

Consider the assembly of capacitors shown here.Let C1 = C2 = C3 = C4 = 20 mF.What is the equivalent capacitance of this circuit?

What is the radius of a steel sphere having a capacitance of radius 1.5 pF?

An uncharged parallel plate capacitor with an air gap is connected to a 6.0-V battery.After charging,the energy stored in the capacitor is 40 nJ.If each of the plates has an area of 10 cm2,what is the magnitude of the electric field between the plates?

Which of the following capacitors have the largest charge?

A 10-nF is connected in series with a 20-nF capacitor.This combination is then placed in parallel with a 30-nF capacitor.This combination is then placed parallel to a 9.0-V battery.What is the charge on the 20-nF capacitor.

A spherical shell capacitor is 1 cm in radius with the outside shell 1 mm beyond this.What is the capacitance of this combination?

A 1.50-µF capacitor charged to 40.0 V and a 2.40-µF capacitor charged to 15.0 V are connected to each other,with the positive plate of each connected to the negative plate of the other.What is the final electric potential across the 1.50-µF capacitor?

What is the capacitance of two parallel plates 0.9 mm apart with an area of 12 cm2 if the space between the plates is filled with a material with dielectric constant of 3.7?

In circuit shown,calculate the charge on C3,where ε\varepsilonε = 10 V,C1 = C2 = 6 μ\muμ F and C3 = 3 μ\muμ F.

A 1.50-µF capacitor charged to 40.0 V and a 2.40-µF capacitor charged to 15.0 V are connected to each other,with the positive plate of each connected to the negative plate of the other.What is the final charge on the 2.4-µF capacitor?

A parallel plate capacitor connected to a 2-V battery consists of two 1-cm square plates separated by 1 mm of air.How much work is done in inserting a sheet with a dielectric constant of 1.5 between the plates (in units of 10-13 J)?

Two capacitors C1 = 2.5 mF and C2 = 5.0 mF are connected in parallel.If a voltage of V = 120 volts is applied across the capacitors,what is the energy stored in the capacitors?

Three capacitors of capacity 4,6,and 8 µF are connected in series with a battery of 13 V.The potential difference across the 6-µF capacitance is

A 1.50-µF capacitor charged to 40.0 V and a 2.40-µF capacitor charged to 15.0 V are connected to each other,with the positive plate of each connected to the negative plate of the other.What is the final charge on the 1.50-µF capacitor?

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Filters

Suppose we have two capacitors connected in parallel with a 10 V battery.What is the energy stored in the circuit if the capacitance of one is C₁ = 50 mF and the other is C₂ = 100 mF?

Consider the assembly of capacitors shown here.Let C₁ = C₂ = C₃ = C₄ = 20 mF.What is the equivalent capacitance of this circuit?

An uncharged parallel plate capacitor with an air gap is connected to a 6.0-V battery.After charging,the energy stored in the capacitor is 40 nJ.If each of the plates has an area of 10 cm²,what is the magnitude of the electric field between the plates?

What is the capacitance of two parallel plates 0.9 mm apart with an area of 12 cm² if the space between the plates is filled with a material with dielectric constant of 3.7?

In circuit shown,calculate the charge on C₃,where $\varepsilon$ = 10 V,C₁ = C₂ = 6 $\mu$ F and C₃ = 3 $\mu$ F. $In circuit shown,calculate the charge on C<sub>3</sub>,where \varepsilon = 10 V,C<sub>1</sub> = C<sub>2</sub> = 6 \mu F and C<sub>3</sub> = 3 \mu F.$

A parallel plate capacitor connected to a 2-V battery consists of two 1-cm square plates separated by 1 mm of air.How much work is done in inserting a sheet with a dielectric constant of 1.5 between the plates (in units of 10^-13 J)?

Two capacitors C₁ = 2.5 mF and C₂ = 5.0 mF are connected in parallel.If a voltage of V = 120 volts is applied across the capacitors,what is the energy stored in the capacitors?