Question 1

The voltage across 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 2

A capacitor of capacitance C holds a charge Q when the potential difference across the plates is V.If the charge Q on the plates is doubled to 2Q,

Accepted Answer

A) the capacitance becomes (1/2)V. 
B) the capacitance becomes 2C. 
C) the potential changes to (1/2)V. 
D) the potential changes to 2V. 
E) the potential does not change. 
A) the capacitance becomes (1/2)V. 
B) the capacitance becomes 2C. 
C) the potential changes to (1/2)V. 
D) the potential changes to 2V. 
E) the potential does not change.

Question 3

The equivalent capacitance of two capacitors in parallel is

Accepted Answer

A) the sum of the reciprocals of their capacitances. 
B) the reciprocal of 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 two capacitances. 
E) described by none of the above. 
A) the sum of the reciprocals of their capacitances. 
B) the reciprocal of 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 two capacitances. 
E) described by none of the above.

Question 4

Use the following figure to answer the next  problem:  
-You connect three capacitors as shown in the diagram below.If the potential difference between A and B is 24.5 V,what is the total energy stored in this system of capacitors if C1 = 5.0 µF,C2 = 4.0 µF,and C3 = 3.0 µF?

Accepted Answer

A) 1.7 $\times$ 10-4 J 
B) 1.5 $\times$ 10-4 J 
C) 2.2 $\times$ 10-5 J 
D) 6.8 $\times$ 10-4 J 
E) 4.0 $\times$ 10-4 J 
A) 1.7 $\times$ 10-4 J 
B) 1.5 $\times$ 10-4 J 
C) 2.2 $\times$ 10-5 J 
D) 6.8 $\times$ 10-4 J 
E) 4.0 $\times$ 10-4 J

Question 5

Two parallel plate air capacitors,each of capacitance X F are in series with a battery of 12-V.If a dielectric with $\kappa$ = 3 is inserted between the plates of one of the capacitors,then calculate the change in electrical charge (in Coulombs)that occurs on one of its plates.

Accepted Answer

A) 9X 
B) 3X/4 
C) 3X 
D) 16X 
E) none of the above 
A) 9X 
B) 3X/4 
C) 3X 
D) 16X 
E) none of the above

Question 6

A coaxial cable has the inner wire of radius a = 1 mm and the outside shield of radius b = 8 mm.The electric field strength between the wire and the shield is given by   .The electrostatic energy per meter of the cable is

Accepted Answer

A) 0.328 nJ 
B) 6.69 $\mu$J 
C) 3.34 $\mu$J 
D) 14.5 $\mu$J 
E) zero 
A) 0.328 nJ 
B) 6.69 $\mu$J 
C) 3.34 $\mu$J 
D) 14.5 $\mu$J 
E) zero

Question 7

The capacitance of a parallel-plate capacitor is 24 $\mu$F when the plates are separated by a material of dielectric constant 2.0.If this material is removed,leaving air between the plates,and the separation between the plates is tripled,the capacitance is

Accepted Answer

A) unchanged 
B) 16 $\mu$F 
C) 36 $\mu$F 
D) 0.14 mF 
E) 4.0 $\mu$F 
A) unchanged 
B) 16 $\mu$F 
C) 36 $\mu$F 
D) 0.14 mF 
E) 4.0 $\mu$F

Question 8

The equivalent capacitance of three capacitors in parallel is

Accepted Answer

A) the sum of the reciprocals of their capacitances. 
B) the reciprocal of 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 two capacitances. 
E) described by none of the above. 
A) the sum of the reciprocals of their capacitances. 
B) the reciprocal of 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 two capacitances. 
E) described by none of the above.

Question 9

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).The capacitance per meter is

Accepted Answer

A) 13.4 pF 
B) 26.8 pF 
C) 35.8 pF 
D) 56.2 pF 
E) 112 pF 
A) 13.4 pF 
B) 26.8 pF 
C) 35.8 pF 
D) 56.2 pF 
E) 112 pF

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 C1 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 20 capacitors,each of 100 $\mu$F,were connected in parallel across a 12-V battery,what would be the total energy stored in the capacitors?

Accepted Answer

A) 2.9 $\times$ 10-1 J 
B) 7.2 $\times$ 10-3 J 
C) 1.2 $\times$ 10-2 J 
D) 1.4 $\times$ 10-1 J 
E) 3.6 $\times$ 10-4 J 
A) 2.9 $\times$ 10-1 J 
B) 7.2 $\times$ 10-3 J 
C) 1.2 $\times$ 10-2 J 
D) 1.4 $\times$ 10-1 J 
E) 3.6 $\times$ 10-4 J

Question 12

You charge a 4.0-µF capacitor to 150 V.How much additional energy must you add to charge it to 300 V?

Accepted Answer

A) 0.60 mJ 
B) 0.14 J 
C) 18 µJ 
D) 0.30 mJ 
E) 0.28 J 
A) 0.60 mJ 
B) 0.14 J 
C) 18 µJ 
D) 0.30 mJ 
E) 0.28 J

Question 13

If you increase the charge on a parallel-plate capacitor from 3 µC to 9 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) 9 
C) 3 
D) 8 
E) 1/3 
A) 27 
B) 9 
C) 3 
D) 8 
E) 1/3

Question 14

The equivalent capacitance of three 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 15

A cardiac defibrillator can be used to help an erratic heartbeat in a regular fashion.A defibrillator contains a capacitor charged to a voltage of 6000 V with an energy storage of 200 J.Calculate the capacitance of the capacitor.

Accepted Answer

A) 6.67 $\times$ 10-2 F 
B) 1.11 $\times$ 10-5 F 
C) 5.56 $\times$ 10-6 F 
D) 2.22 $\times$ 10-5 F 
E) 13.3 F 
A) 6.67 $\times$ 10-2 F 
B) 1.11 $\times$ 10-5 F 
C) 5.56 $\times$ 10-6 F 
D) 2.22 $\times$ 10-5 F 
E) 13.3 F

Question 16

Two large metallic plates are parallel to each other and charged.The distance between the plates is d.The potential difference between the plates is V.The magnitude of the electric field   in the region between the plates and away from the edges is given by

Accepted Answer

A) d/V 
B) V2/d 
C) dV 
D) V/d2  
E) None of these is correct. 
A) d/V 
B) V2/d 
C) dV 
D) V/d2  
E) None of these is correct.

Question 17

You make a homemade capacitor out of two flat circular metal plates,each of radius 5 cm,and hold them a distance of 1 cm apart.You then connect each plate to the terminals of a 6-V battery.What would be the capacitance of your capacitor?

Accepted Answer

A) 7.0 $\times$ 10-12 F 
B) 2.2 $\times$ 10-11 F 
C) 2.2 $\times$ 10-12 F 
D) 2.2 $\times$ 10-10 F 
E) 7.0 $\times$ 10-10 F 
A) 7.0 $\times$ 10-12 F 
B) 2.2 $\times$ 10-11 F 
C) 2.2 $\times$ 10-12 F 
D) 2.2 $\times$ 10-10 F 
E) 7.0 $\times$ 10-10 F

Question 18

You want to store 1010 excess electrons on the negative plate of a capacitor at 9.0 V.How large a capacitance must you use?

Accepted Answer

A) 0.014 µF 
B) 0.18 µF 
C) 0.18 nF 
D) 14 pF 
E) 5.6 pF 
A) 0.014 µF 
B) 0.18 µF 
C) 0.18 nF 
D) 14 pF 
E) 5.6 pF

Question 19

A parallel plate capacitor has a plate spacing of 1.5 mm,which is filled with a dielectric of $\kappa$ = 4.3,and its capacitance is 80 $\mu$F.If the dielectric is taken out and the plate spacing doubled,then what is the new capacitance?

Accepted Answer

A) 690 $\mu$F 
B) 37 $\mu$F 
C) 9.3 $\mu$F 
D) 170 $\mu$F 
E) 19 $\mu$F 
A) 690 $\mu$F 
B) 37 $\mu$F 
C) 9.3 $\mu$F 
D) 170 $\mu$F 
E) 19 $\mu$F

Question 20

A coaxial cable consists of a wire of radius 0.30 mm and an outer conducting shell of radius 1.0 mm.Its capacitance for a 2 m length of the cable is approximately

Accepted Answer

A) 0.22 nF 
B) 34 nF 
C) 46 pF 
D) 92 pF 
E) 184 pF 
A) 0.22 nF 
B) 34 nF 
C) 46 pF 
D) 92 pF 
E) 184 pF

Exam 24: Capacitance

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

A capacitor of capacitance C holds a charge Q when the potential difference across the plates is V.If the charge Q on the plates is doubled to 2Q,

The equivalent capacitance of two capacitors in parallel is

Use the following figure to answer the next problem: -You connect three capacitors as shown in the diagram below.If the potential difference between A and B is 24.5 V,what is the total energy stored in this system of capacitors if C1 = 5.0 µF,C2 = 4.0 µF,and C3 = 3.0 µF?

Two parallel plate air capacitors,each of capacitance X F are in series with a battery of 12-V.If a dielectric with κ\kappaκ = 3 is inserted between the plates of one of the capacitors,then calculate the change in electrical charge (in Coulombs)that occurs on one of its plates.

A coaxial cable has the inner wire of radius a = 1 mm and the outside shield of radius b = 8 mm.The electric field strength between the wire and the shield is given by .The electrostatic energy per meter of the cable is

The capacitance of a parallel-plate capacitor is 24 μ\muμ F when the plates are separated by a material of dielectric constant 2.0.If this material is removed,leaving air between the plates,and the separation between the plates is tripled,the capacitance is

The equivalent capacitance of three capacitors in parallel is

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).The capacitance per meter is

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 C1 after the system has come to equilibrium is

If 20 capacitors,each of 100 μ\muμ F,were connected in parallel across a 12-V battery,what would be the total energy stored in the capacitors?

You charge a 4.0-µF capacitor to 150 V.How much additional energy must you add to charge it to 300 V?

If you increase the charge on a parallel-plate capacitor from 3 µC to 9 µC and increase the plate separation from 1 mm to 3 mm,the energy stored in the capacitor changes by a factor of

The equivalent capacitance of three capacitors in series is

A cardiac defibrillator can be used to help an erratic heartbeat in a regular fashion.A defibrillator contains a capacitor charged to a voltage of 6000 V with an energy storage of 200 J.Calculate the capacitance of the capacitor.

Two large metallic plates are parallel to each other and charged.The distance between the plates is d.The potential difference between the plates is V.The magnitude of the electric field in the region between the plates and away from the edges is given by

You make a homemade capacitor out of two flat circular metal plates,each of radius 5 cm,and hold them a distance of 1 cm apart.You then connect each plate to the terminals of a 6-V battery.What would be the capacitance of your capacitor?

You want to store 1010 excess electrons on the negative plate of a capacitor at 9.0 V.How large a capacitance must you use?

A parallel plate capacitor has a plate spacing of 1.5 mm,which is filled with a dielectric of κ\kappaκ = 4.3,and its capacitance is 80 μ\muμ F.If the dielectric is taken out and the plate spacing doubled,then what is the new capacitance?

A coaxial cable consists of a wire of radius 0.30 mm and an outer conducting shell of radius 1.0 mm.Its capacitance for a 2 m length of the cable is approximately

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Use the following figure to answer the next problem: -You connect three capacitors as shown in the diagram below.If the potential difference between A and B is 24.5 V,what is the total energy stored in this system of capacitors if C₁ = 5.0 µF,C₂ = 4.0 µF,and C₃ = 3.0 µF?

Two parallel plate air capacitors,each of capacitance X F are in series with a battery of 12-V.If a dielectric with $\kappa$ = 3 is inserted between the plates of one of the capacitors,then calculate the change in electrical charge (in Coulombs)that occurs on one of its plates.

The capacitance of a parallel-plate capacitor is 24 $\mu$ F when the plates are separated by a material of dielectric constant 2.0.If this material is removed,leaving air between the plates,and the separation between the plates is tripled,the capacitance is

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).The capacitance per meter 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 charge on C₁ after the system has come to equilibrium is

If 20 capacitors,each of 100 $\mu$ F,were connected in parallel across a 12-V battery,what would be the total energy stored in the capacitors?

You want to store 10¹⁰ excess electrons on the negative plate of a capacitor at 9.0 V.How large a capacitance must you use?

A parallel plate capacitor has a plate spacing of 1.5 mm,which is filled with a dielectric of $\kappa$ = 4.3,and its capacitance is 80 $\mu$ F.If the dielectric is taken out and the plate spacing doubled,then what is the new capacitance?