Deck 16: Electric Potential, Energy, and Capacitance

Question 1

If you find you are able to move a positive charge from infinity (far away) to a particular point without doing any work, can you infer that no other charges are nearby?

Answer 1

NO. For example, consider 2 rows of opposite charge. If you had moved half way between the charges, no work would have been done.

Question 2

Why is it dangerous to probe inside a television set even hours after it has been unplugged?

Answer 2

Capacitors are charged to large potentials and store considerable charge within the TV sets and they still hold charge long after being disconnected from the power supply.

Question 3

Sort these materials in order of increasing dielectric constant: paper, vacuum, air.

Answer 3

vacuum, air, paper

Question 4

A charged capacitor stores energy, and when the Teflon dielectric between the plates is pulled out the energy stored more than doubles. Where did the extra energy come from?

Question 5

For a pair of oppositely charged parallel plates, the negatively charged plate is at a lower electric potential than the positively charged one by an amount $\Delta$ V.

Question 6

Negative charges, when released, accelerate toward regions of lower electric potential.

Question 7

Electric potential decreases when moving farther from positive charges or nearer to negative charges.

Question 8

Equipotential surfaces are always at right angles to the electric field.

Question 9

Electric Potential Energy per unit charge is called

A) power.
B) eV.
C) electric field.
D) dielectric constant.
E) potential.

Question 10

The absolute potential at the center of a square is 3. V when a charge of +Q is located at one of the square's corners. What is the absolute potential at the square's center when a second charge of -Q is placed at one of the remaining corners?

A) -6 V
B) -12 V
C) 6 V
D) 12 V
E) zero

Question 11

Capacitance is A/d for

A) concentric cylinders.
B) all capacitors.
C) parallel plates.
D) parallel wires.

Question 12

A voltage has been applied across a capacitor. If the dielectric is replaced with another dielectric constant eight times as great and the voltage is reduced to half of what it was, the ENERGY STORED in the capacitor is how many times the original stored energy?

A) 1/4
B) 1/2
C) 4
D) 2
E) 8

Question 13

The plates of a parallel-plate capacitor are maintained with constant voltage by a battery as they are pulled apart. What happens to the strength of the electric field during this process?

A) There is no way to tell from the information given.
B) It decreases.
C) It remains constant.
D) It increases.

Question 14

A battery charges a parallel-plate capacitor fully and then is removed. The plates are immediately pulled apart. (With the battery disconnected, the amount of charge on the plates remains constant.) What happens to the potential difference between the plates as they are being separated?

A) It remains constant.
B) It increases.
C) There is no way to tell from the information given.
D) It decreases.

Question 15

The plates of a parallel-plate capacitor are maintained with constant voltage by a battery as they are pulled apart. During this process, the amount of charge on the plates must

A) decrease.
B) increase.
C) There is no way to tell from the information given.
D) remain constant.

Question 16

The dielectric constant of a vacuum is

A) 1000.
B) 1.000.
C) zero.
D) 8.99 × 10⁹.
E) _o.

Question 17

Capacitors connected in series always have ________ total capacitance than any of the individual capacities.

A) the same
B) less
C) more
D) Not enough information given.

Question 18

An electron moving from the negative terminal to the positive terminal of a 12. volt battery gains (or loses) how much energy? (Be sure to indicate whether it is a gain or loss.)

Question 19

A metal sphere of radius 80. mm is charged to a potential of -0.50 kV. With what velocity must an electron be fired toward the sphere if it is to just barely reach the sphere when started from a position 15. cm from the center of the sphere?

Question 20

How much energy is necessary to place three charges, each of 2.0 ?C, at the corners of an equilateral triangle of side 2.0 cm?

Question 21

Four charges of equal charge +q are placed at the corners of a rectangle of sides a and b. What is the potential at the center of the rectangle if q = 2.0 $\mu$ C, a = 30. mm, and b = 40. mm?

Question 22

Starting from rest, a proton falls through a potential difference of 1.2 kV. What speed does it acquire?

Question 23

What is the electric potential at the center of a hollow metal sphere of outside diameter 14. cm which holds a net charge of 3.3 $\mu$ C?

Question 24

Charges 6.8 $\mu$ C, 6.1 $\mu$ C, and -1.5 $\mu$ C are brought from infinity to the respective vertices of an equilateral triangle with 11. cm sides.
(a) How much energy did it take to move the charges to the triangle vertices?
(b) What is the potential at the center of the triangle?

Question 25

What charge appears on the plates of a 2.00 $\mu$ F capacitor when it is charged to 100. V?

Question 26

A parallel plate capacitor is constructed with plate area of 0.40 m² and a plate separation of 0.10 mm. How much charge is stored on it when it is charged to a potential difference of 12 V?

Question 27

When a 12.0 volt battery is connected to a 6.00 $\mu$ F capacitor:
(a) how much energy is stored?
(b) how much charge is stored on the positive plate of the capacitor?

Question 28

A 0.67 $\mu$ F parallel plate capacitor has air between the plates with a separation of 0.33 mm.
(a) What is the plate area?
(b) What charge is on the plates when connected to a 3.0 volt battery?

Question 29

A parallel plate capacitor is constructed with Teflon (dielectric constant 2.1) between the plates. This 12.6 ?F capacitor has been charged to 1.5 volts. The Teflon is then pulled out (removed).
(a) What charge was originally stored?
(b) After removing the Teflon, what potential is across the plates?

Question 30

Given 3 capacitors: 4.00 $\mu$ F, 7.00 $\mu$ F, and 9.00 $\mu$ F; what is the equivalent capacity if they are connected in series?

Question 31

Given 3 capacitors: 4.00 $\mu$ F, 7.00 $\mu$ F, and 9.00 $\mu$ F; what is the equivalent capacity if they are connected in parallel?

Question 32

1.8 $\mu$ F and 3.6 $\mu$ F capacitors are connected in series and then charged by a 24. volt battery. The battery and capacitors are disconnected and the capacitors reconnected in parallel (plus to plus, minus to minus)
(a) What charge initially flowed from the battery to the series combination?
(b) What total charge is on the final positive plates?
(c) What final voltage is across the parallel combination?

Question 33

A 4.0 $\mu$ F and a 1.0 $\mu$ F capacitor are connected in parallel and both are charged with a 12. volt battery. They are disconnected from the battery and reconnected positive side of the 1st to negative side of 2nd, and neg. side of 1st to pos. side of 2nd.
(a) How much was each charged when connected to the battery?
(b) After reconnecting, how much charge is stored?
(c) What potential exists across the final parallel combination?

Question 34

Consider capacitors C₁, C₂, and C₃, which are connected in series in a closed loop. A switch is placed between C₁ and C₂. With the switch open, C₁ is charged to 12.0 volts by a battery. The battery is then disconnected and the switch is closed. Determine the final charge on each capacitor, and the potential difference across each, given that C₁ = 2.00 μF, and C₂ = C₃ = 3.00 μF.

Question 35

A proton (being 1836 times heavier than an electron) gains how much energy when moving through a potential increase of one volt?

A) 1. eV
B) 1. Joule
C) 0 eV
D) 1836. J
E) 1836. eV

Question 36

An electron which moves from the negative to the positive terminal of a 2.0 volt battery loses how much potential energy?

A) 2.0 × 10^-19 J
B) 4.2 × 10^-19 J
C) 3.2 J
D) 2.0 J
E) 2.0 eV

Question 37

If a Cu²⁺ ion drops through a potential difference of 12. V, it will acquire a kinetic energy (in the absence of friction) of

A) 12. J.
B) 12. eV.
C) 24. eV.
D) 6.0 J.
E) 6.0 eV.

Question 38

The absolute potential at a distance of 2.0 m from a negative point charge is -100. V. What is the absolute potential 4.0 m away from the same point charge?

A) -0.40 kV
B) -0.50 kV
C) -0.20 kV
D) -25. V
E) -50. V

Question 39

It takes 10. J of energy to move 2.0 C of charge from point A to point B. What is the potential difference between points A and B?

A) 5.0 V
B) 20. V
C) zero
D) 0.20 V
E) 0.50 V

Question 40

The net work done in moving an electron from point A at -50. V to point B at +50. V along the semi-circle path shown in Figure 16-1 is

A) zero.
B) -1.6 J.
C) +1.6 × 10^-17 J.
D) -1.6 × 10^-17 J.
E) not to be determined; not enough information given.

Question 41

Consider a uniform electric field of 50. N/C directed toward the East. If the voltage measured relative to ground at a given point in the field is 80. V, what is the voltage at a point 1.0 m directly East of the point?

A) 15. V
B) 30. V
C) 0.15 kV
D) impossible to calculate from the information given
E) 30. kV

Question 42

Consider a uniform electric field of 50. N/C directed toward the East. If the voltage measured relative to ground at a given point in the field is 80. V, what is the voltage at a point 1.0 m directly South of that point?

A) 50 V
B) 50. kV
C) 30 V
D) zero
E) 80 V

Question 43

A charge of 2.0 $\mu$ C flows onto the plates of a capacitor when it is connected to a12.V battery. How much work was done in charging this capacitor?

A) 12. $\mu$ J
B) 0.14 mJ
C) 21. $\mu$ J
D) 48. $\mu$ J
E) 24. $\mu$ J

Question 44

A parallel-plate capacitor has plates of area 0.20 m² separated by a distance of
1)0 mm. What is the strength of the electric field between these plates when this capacitor is connected to a 6.0 V battery?

A) 3.0 kN/C
B) 1.2 kN/C
C) 6.0 N/C
D) 6.0 N/mC
E) 12. N/C

Question 45

A parallel-plate capacitor has plates of area 0.20 m² separated by a distance of
1.0 mm. What is this capacitor's capacitance?

A) 2.0 × 10² F
B) 1.8 nF
C) 0.35 nF
D) 40. F
E) 22. $\mu$ F

Question 46

A 15. $\mu$ F capacitor is connected to a 50. V battery and becomes fully charged. The battery is removed and a slab of dielectric that completely fills the space between the plates is inserted. If the dielectric has a dielectric constant of 5.0, what is the voltage across the capacitor's plates after the slab is inserted?

A) 0.25 kV
B) 0.10 kV
C) 2.0 V
D) 10. V
E) 20. V

Question 47

A 15. $\mu$ F capacitor is connected to a 50. V battery and becomes fully charged. The battery is removed and a slab of dielectric that completely fills the space between the plates is inserted. If the dielectric has a dielectric constant of 5.0, what is the capacitance of the capacitor after the slab is inserted?

A) 75. $\mu$ F
B) 3.0 $\mu$ F
C) 45. $\mu$ F
D) 20. $\mu$ F
E) 95. $\mu$ F