Physics 16

Charges 6.8 μC, 6.1 μC, and -1.5 μC 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?

(a) 1.8 Joules (b) 1.6 × 106 volts

A parallel plate capacitor is constructed with Teflon (dielectric constant 2.1) between the plates. This 12.6 μF 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?

(a) 19 μC (b) 3.2 volts

A 0.67 μF 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?

(a) 25. m2 (b) ± 2.0 μC

1.8 μF and 3.6 μF 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?

(a) 29. μC (b) 58. μC (c) 11. volts

A 1 mF, a 2 mF, and a 3 mF capacitor are connected in parallel, the combination being connected across a 9 volt battery. (a) Which capacitor has the greatest charge? (b) Which capacitor has the greatest voltage?

(a) 3 mF. (b) They all have the same voltage.

A 1 pF capacitor is connected in parallel with a 2 pF capacitor, the parallel combination then being connected in series with a 3 pF capacitor. The resulting combination is then connected across a battery. (a) Which capacitor has the greatest charge? (b) Which capacitor has the greatest voltage?

(a) 3 pF (b) They all have the same voltage.

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

(a) 432 μJ (b) 72.0 μC

A 4.0 μF and a 1.0 μF 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?

(a) 48. μC & 12. μC (b) 36. μC (c) 7.1 volts

A 1 mF, a 2 mF, and a 3 mF capacitor are connected in series, the combination being connected across a 9 volt battery. (a) Which capacitor has the greatest charge? (b) Which capacitor has the greatest voltage?

(a) They all have the same charge. (b) 1 mF

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 μC?

0.42 MV

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?

0.42 μC

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

1.98 μF

Capacitances of 10. μF and 20. μF are connected in parallel, and this pair is then connected in series with a 30. μF capacitor. What is the equivalent capacitance of this arrangement?

15. μF

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 μC, a = 30. mm, and b = 40. mm?

2.9 × 106 V

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

20.00 μF

What charge appears on the plates of a 2.00 μF capacitor when it is charged to 100. V?

200. μC

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

4.8 × 105 m/s

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

5.4 J

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?

9.0 × 106 m/s

A 1 pF capacitor is connected in parallel with a 2 pF capacitor, the parallel combination then being connected in series with a 3 pF capacitor. The resulting equivalent capacitance is A) 1.5 pF. B) 6 pF. C) 3 pF. D) 4.5 pF. E) 5 pF.

A

A 15. μF 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. μF B) 20. μF C) 3.0 μF D) 45. μF E) 95. μF

A

A dielectric is inserted between the plates of an isolated parallel-plate capacitor that carries a charge Q. What happens to the potential energy stored in the capacitor? A) The potential energy of the capacitor decreases. B) The potential energy of the capacitor increases or decreases depending on the value of the dielectric constant of the capacitor. C) The potential energy of the capacitor remains the same. D) The potential energy of the capacitor increases. E) More information is needed to answer the question.

A

In Fig. 16-7, three capacitors with capacitances C1 = 4 μF, C2 = 3μF, and C3 = 2 μF, are connected to a battery of voltage V = 12 V. What is the charge on capacitor C2? A) 16 μC B) 32 μC C) 2μC D) 8 μC E) 4 μC

A

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

A

The electric potential at the origin of an xy-coordinate system is 40 V. A -8.0-μC charge is brought from x = +∞ to that point. What is the electric potential energy of this charge at the origin? A) -3.2 × 10-4 J B) 3.2 × 10-4 J C) -40 μJ D) 40 μJ E) 8.0 μJ

A

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

A

Three capacitors are connected as shown in Fig. 16-4. What is the equivalent capacitance between points A and B? A) 1.7 μF B) 4.0 μC C) 7.1 μF D) 12 μF E) 8.0 μF

A

When two or more capacitors are connected in parallel to a battery, A) the voltage across each capacitor is the same. B) each capacitor carries the same amount of charge. C) the equivalent capacitance of the combination is less than the capacitance of any one of the capacitors. D) all of the given answers E) none of the given answers

A

A 15. μF 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) 10. V C) 2.0 V D) 0.10 kV E) 20. V

B

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

B

A charge of 2.0 μC flows onto the plates of a capacitor when it is connected to a 12. V battery. How much work was done in charging this capacitor? A) 24. μJ B) 12. μJ C) 48. μJ D) 0.14 mJ E) 21. μJ

B

A negative charge, if free, tries to move A) from high potential to low potential. B) from low potential to high potential. C) toward infinity. D) away from infinity. E) in the direction of the electric field.

B

A parallel plate capacitor with plate separation of 4.0 cm has a plate area of 4.0 × 10-2 . What is the capacitance of this capacitor with air between these plates? A) 8.9 × 10-11 F B) 8.9 × 10-12 F C) 8.9 × 10-13 F D) 8.9 × 10-14 F E) 8.9 × 10-15 F

B

A proton (being 1836 times heavier than an electron) gains how much energy when moving through a potential increase of one volt? A) 1836. eV B) 1. eV C) 0 eV D) 1. Joule E) 1836. J

B

An equipotential surface must be A) parallel to the electric field at any point. B) perpendicular to the electric field at any point. C) randomly oriented with respect to the electric field. D) equal to the electric field at any point.

B

At a certain point in space the electric potential is 20 V. A 4.0-μC charge is brought from infinity to that point. What is the electric potential energy of this charge at that point? A) - 80 μJ B) 80 μJ C) - 20 μJ D) 20 μJ E) 4.0 μJ

B

Capacitors connected in series always have ________ total capacitance than any of the individual capacities. A) more B) less C) the same D) Not enough information given.

B

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) 30. kV E) impossible to calculate from the information given

B

For an electron moving in a direction opposite to the electric field A) its potential energy increases and its electric potential decreases. B) its potential energy decreases and its electric potential increases. C) its potential energy increases and its electric potential increases. D) its potential energy decreases and its electric potential decreases. E) both its potential energy and it electric potential remain constant.

B

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

B

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

B

Two point charges of magnitude 4.0 μC and -4.0 μC are situated along the x-axis at x1 = 2.0 m and x2 = -2.0 m, respectively. What is the electric potential at the origin of the xy-coordinate system? A) -36 × 103 V B) 0 V C) 36 × 103 V D) -48 × 103 V E) 48 × 103 V

B

What is the equivalent capacitance of the capacitor network shown in Fig. 16-5? (All the capacitors have a capacitance C = 5 μF. The voltage of the battery is V = 6V.) A) 20 μF B) 3 μF C) 10 μF D) 5 μF E) 1 μF

B

A 12 mF capacitor is connected in series with a 4 mF capacitor, the combination being connected across a 6 V power supply. The charge on the 12 mF capacitor is A) 24 mC. B) 12 mC. C) 18 mC. D) 72 mC. E) 36 mC.

C

A dielectric material such as paper is placed between the plates of a capacitor holding a fixed charge. What happens to the electric field between the plates? A) no change B) becomes stronger C) becomes weaker D) reduces to zero E) cannot be determined without additional information

C

A parallel-plate capacitor has a capacitance of 10 mF and is charged with a 20 V power supply. The power supply is then removed and a dielectric of dielectric constant 4 is used to fill the space between the plates. The voltage now across the capacitor is A) zero. B) 20 V. C) 5 V. D) 10 V. E) 80 V.

C

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/mC D) 12. N/C E) 6.0 N/C

C

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) 40. F C) 1.8 nF D) 0.35 nF E) 22. μF

C

A parallel-plate capacitor has plates of area 0.80 m2 separated by a distance of 3.0 mm. What is this capacitor's capacitance? A) 270 F B) 70 F C) 2.4 × 10-9 F D) 4.8 × 10-10 F E) 3.6 × 10-10 F

C

A surface on which all points are at the same potential is referred to as A) a constant electric force surface. B) a constant electric field surface. C) an equipotential surface. D) an equivoltage surface. E) a dielectric surface.

C

Capacitance is ε o A/d for A) all capacitors. B) parallel wires. C) parallel plates. D) concentric cylinders.

C

Fig. 16-2 shows three capacitors connected to a battery of voltage V = 6 V. The charges on the capacitors are known to be Q = 24 μC for C1 and C2, and Q3 = 96 μC for C3. What are the values of the capacitances C1, C2, and C3? A) C1 = 8 μF, C2 = 16 μF, C3 = 24 μF B) C1 = 6 μF, C2 = 12 μF, C3 = 16 μF C) C1 = 10 μF, C2 = 20 μF, C3 = 30 μF D) C1 = 21 μF, C2 = 7 μF, C3 = 3 μF E) C1 = 5 μF, C2 = 14 μF, C3 = 18 μF

C

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

C

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

C

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 Fig. 16-3 is A) zero. B) +1.6 × 10-17 J. C) -1.6 × 10-17 J. D) -1.6 J. E) not to be determined; not enough information given.

C

Three capacitors C1, C2, and C3are connected to a battery as shown in Fig. 16-2. The three capacitors have equal capacitances. Which capacitor stores the most potential energy? A) C3 B) C2 C) C1 D) C2or C3. They store the same amount of energy E) All three capacitors store the same amount of energy.

C

Three identical capacitors are connected in series to a battery. If a total charge of Q flows from the battery, how much charge does each capacitor carry? A) 9Q B) 3Q C) Q D) Q/3 E) Q/9

C

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

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

A 2.0 μF and a 4.0 μF capacitor are connected in series across an 8.0-V DC source. What is the charge on the 2.0 μF capacitor? A) 2.0 μC B) 4.0 μC C) 12 μC D) 11 μC E) 25 μC

D

A 6.0-μF air capacitor is connected across a 100-V battery. After the battery fully charges the capacitor, the capacitor is immersed in transformer oil (dielectric constant = 4.5). How much additional charge flows from the battery, which remained connected during the process? A) 1.2 mC B) 1.5 mC C) 1.7 mC D) 2.1 mC E) 2.5 mC

D

A system of capacitors is connected across a 90 V DC voltage source as shown in Fig. 16-6. What is the equivalent capacitance of this system? A) 1.5 μF B) 15 μF C) 3.6 μF D) 3.3 μF E) None of the other answers is correct.

D

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

D

Capacitance of capacitors depends upon A) the material between the conductors. B) the geometry of the conductors. C) the space between the conductors. D) all of these answers. E) none of these answers.

D

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

D

For a proton moving in the direction of the electric field A) its potential energy increases and its electric potential decreases. B) its potential energy decreases and its electric potential increases. C) its potential energy increases and its electric potential increases. D) its potential energy decreases and its electric potential decreases. E) both its potential energy and it electric potential remain constant.

D

Three identical capacitors are connected in parallel to a battery. If a total charge of Q flows from the battery, how much charge does each capacitor carry? A) 9Q B) 3Q C) Q D) Q/3 E) Q/9

D

When a dielectric material is introduced between the plates of a parallel plate capacitor the capacitance increases by a factor of 4. What is the dielectric constant of the material introduced between the plates? A) 0.4 B) 1/4 C) 2 D) 4 E) None of the other choices is correct.

D

When two or more capacitors are connected in series to a battery, A) the total voltage across the combination is the algebraic sum of the voltages across the individual capacitors. B) each capacitor carries the same amount of charge. C) the equivalent capacitance of the combination is less than the capacitance of any of the capacitors. D) all of the given answers E) none of the given answers

D

Which of the following will increase the capacitance of a parallel plate capacitor? A) a decrease in the plate area and an increase in the plate separation B) a decrease in the potential difference between the plates C) an increase in the potential difference between the plates D) an increase in the plate area and a decrease in the plate separation E) none of the above

D

A 4.0 μF and a 6.0 μF capacitor are connected in series across an 8.0-V DC source. What is the charge on the 6.0 μF capacitor? A) 2.0 μC B) 4.0 μC C) 12 μC D) 25 μC E) 19 μC

E

A 5.0 μF and a 7.0 μF capacitor are connected in series across an 8.0-V DC source. What is the voltage across the 5.0 μF capacitor? A) 0 V B) 8.0 V C) 2.7 V D) 3.6 V E) 4.7 V

E

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

E

At a certain point in space there is a potential of 400 V. What is the potential energy of a +2- μC charge at that point in space? A) 80 × 10-6 J B) 800 J C) 400 J D) 200 J E) 8 × 10-4 J

E

Fig. 16-1 shows three capacitors connected to a battery. The capacitances are such that C1 = 2C2 and C1 = 3C3. Which capacitor stores the smallest amount of charge? A) C2 B) C3 C) C1 D) C2 or C3 E) All three capacitors store the same amount of charge

E

The dielectric constant of a vacuum is A) zero. B) 8.99 × 109. C) ε o. D) 1000. E) 1.000.

E

The magnitude of the charge on each plate of a parallel plate capacitor is 4 μC and the potential difference between the plates is 80 V. What is the capacitance of this capacitor? A) 0.1 × 10-6 F B) 300 × 10-6 F C) 100 × 10-6 F D) 20 × 10-6 F E) 5 × 10-8 F

E

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

FALSE

The capacitance of a parallel plate capacitor is directly proportional to its plate separation.

FALSE

If you were a parallel plate capacitor manufacturer, state three ways you might make larger valued capacitors.

Increase plate area, decrease separation, and increase the dielectric constant.

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.)

Loses 12. eV = 1.9 × 10-19 J

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?

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

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, C1is 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.

Q1 = 13.7 μF; V1 = 6.88 V Q2 = Q3 = 10.3 μC; V2 = V3 = 3.43 V

A capacitor, in addition to storing charge, also stores electrical energy.

TRUE

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

TRUE

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

TRUE

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 △V.

TRUE

The electric field between the plates of a parallel plate capacitor is inversely proportional to the plate separation.

TRUE

After being charged from a battery, the plates of a parallel plate capacitor are moved closer together. When they are half as far apart as originally, by how much does the stored energy change?

The capacity doubles but charge remains the same so energy, Q2/(2C), reduces to half of what it was.

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?

The charged plates have a net attraction to the polarized charges in the dielectric as the dielectric is removed. We must do work to remove the Teflon which puts extra energy into the capacitor system.

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

vacuum, air, paper