Conductors, Capacitors, Dielectrics Multiple-Choice Practice Questions | AP Physics C Electricity and Magnetism - Grade 9 PDF Download

 Page 1


Section I: Multiple Choice
1. A capacitor is fully charged by a battery. The battery is disconnected, and a dielectric is
inserted into the capacitor. Which of the following statements is/are true?
I. The voltage will remain the same.
II. The potential energy of the capacitor will increase.
III. The capacitance of the capacitor will increase.
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) III only
2. If the electric field does negative work on a negative charge as the charge undergoes a
displacement from Position A to Position B within an electric field, then the electrical
potential energy
(A) is negative
(B) is positive
(C) increases
(D) decreases
(E) cannot be determined from the information given
3. Three 6 µF capacitors are connected in parallel to a 9 V battery as shown above. Determine the
energy stored in each capacitor.
(A) 243 J
(B)    7.29 × 10
-4
 J
(C)    8.10 × 10
-5
 J
(D)    2.43 × 10
-4
 J
(E)  27 J
Page 2


Section I: Multiple Choice
1. A capacitor is fully charged by a battery. The battery is disconnected, and a dielectric is
inserted into the capacitor. Which of the following statements is/are true?
I. The voltage will remain the same.
II. The potential energy of the capacitor will increase.
III. The capacitance of the capacitor will increase.
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) III only
2. If the electric field does negative work on a negative charge as the charge undergoes a
displacement from Position A to Position B within an electric field, then the electrical
potential energy
(A) is negative
(B) is positive
(C) increases
(D) decreases
(E) cannot be determined from the information given
3. Three 6 µF capacitors are connected in parallel to a 9 V battery as shown above. Determine the
energy stored in each capacitor.
(A) 243 J
(B)    7.29 × 10
-4
 J
(C)    8.10 × 10
-5
 J
(D)    2.43 × 10
-4
 J
(E)  27 J
4. The picture above shows 4 charges fixed in position at the corners of a rectangle measuring 2
cm by 4 cm. Assuming the charges are all of equal magnitude, how many locations on either
Line A or Line B would be places with 0 net electric potential?
(A) 1
(B) 5
(C) All of Line A
(D) All of Line B
(E) All of both Line A and Line B
5. A particle with a charge of +q and mass m starts at rest and moves linearly from a position of
high potential, A, to a position of low potential, B. Which of the following expressions will give
the particle’s speed at position B?
(A)
(B)
(C)
(D)
(E)
6. Which points in this uniform electric field (between the plates of the capacitor) shown above
lie on the same equipotential?
Page 3


Section I: Multiple Choice
1. A capacitor is fully charged by a battery. The battery is disconnected, and a dielectric is
inserted into the capacitor. Which of the following statements is/are true?
I. The voltage will remain the same.
II. The potential energy of the capacitor will increase.
III. The capacitance of the capacitor will increase.
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) III only
2. If the electric field does negative work on a negative charge as the charge undergoes a
displacement from Position A to Position B within an electric field, then the electrical
potential energy
(A) is negative
(B) is positive
(C) increases
(D) decreases
(E) cannot be determined from the information given
3. Three 6 µF capacitors are connected in parallel to a 9 V battery as shown above. Determine the
energy stored in each capacitor.
(A) 243 J
(B)    7.29 × 10
-4
 J
(C)    8.10 × 10
-5
 J
(D)    2.43 × 10
-4
 J
(E)  27 J
4. The picture above shows 4 charges fixed in position at the corners of a rectangle measuring 2
cm by 4 cm. Assuming the charges are all of equal magnitude, how many locations on either
Line A or Line B would be places with 0 net electric potential?
(A) 1
(B) 5
(C) All of Line A
(D) All of Line B
(E) All of both Line A and Line B
5. A particle with a charge of +q and mass m starts at rest and moves linearly from a position of
high potential, A, to a position of low potential, B. Which of the following expressions will give
the particle’s speed at position B?
(A)
(B)
(C)
(D)
(E)
6. Which points in this uniform electric field (between the plates of the capacitor) shown above
lie on the same equipotential?
(A) 1 and 2 only
(B) 1 and 3 only
(C) 2 and 4 only
(D) 3 and 4 only
(E) 1, 2, 3, and 4 all lie on the same equipotential since the electric field is uniform.
7. Two isolated and widely separated conducting spheres each carry a charge of -Q. Sphere 1 has
a radius of a and Sphere 2 has a radius of 4a. If the spheres are now connected by a
conducting wire, what will be the final charge on each sphere?
 Sphere 1 Sphere 2
(A) -Q -Q
(B) -2Q/3 -4Q/3
(C) -4Q/3 -2Q/3
(D) -2Q/5 -8Q/5
(E) -8Q/5 -2Q/5
8. A parallel-plate capacitor is charged to a potential difference of ?V; this results in a charge of
+Q on one plate and a charge of -Q on the other. The capacitor is disconnected from the
charging source, and a dielectric is then inserted. What happens to the potential difference
and the stored electrical potential energy?
(A) The potential difference decreases, and the stored electrical potential energy decreases.
(B) The potential difference decreases, and the stored electrical potential energy increases.
(C) The potential difference increases, and the stored electrical potential energy decreases.
(D) The potential difference increases, and the stored electrical potential energy increases.
(E) The potential difference decreases, and the stored electrical potential energy remains
unchanged.
9. How much work would the electric field (created by the stationary charge Q) perform as a
charge q is moved from Point A to B along the curved path shown? V
A
 = 200 V, V
B
 = 100
V, q = -0.05 C, length of line segment AB = 10 cm, length of curved path = 20 cm.
Page 4


Section I: Multiple Choice
1. A capacitor is fully charged by a battery. The battery is disconnected, and a dielectric is
inserted into the capacitor. Which of the following statements is/are true?
I. The voltage will remain the same.
II. The potential energy of the capacitor will increase.
III. The capacitance of the capacitor will increase.
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) III only
2. If the electric field does negative work on a negative charge as the charge undergoes a
displacement from Position A to Position B within an electric field, then the electrical
potential energy
(A) is negative
(B) is positive
(C) increases
(D) decreases
(E) cannot be determined from the information given
3. Three 6 µF capacitors are connected in parallel to a 9 V battery as shown above. Determine the
energy stored in each capacitor.
(A) 243 J
(B)    7.29 × 10
-4
 J
(C)    8.10 × 10
-5
 J
(D)    2.43 × 10
-4
 J
(E)  27 J
4. The picture above shows 4 charges fixed in position at the corners of a rectangle measuring 2
cm by 4 cm. Assuming the charges are all of equal magnitude, how many locations on either
Line A or Line B would be places with 0 net electric potential?
(A) 1
(B) 5
(C) All of Line A
(D) All of Line B
(E) All of both Line A and Line B
5. A particle with a charge of +q and mass m starts at rest and moves linearly from a position of
high potential, A, to a position of low potential, B. Which of the following expressions will give
the particle’s speed at position B?
(A)
(B)
(C)
(D)
(E)
6. Which points in this uniform electric field (between the plates of the capacitor) shown above
lie on the same equipotential?
(A) 1 and 2 only
(B) 1 and 3 only
(C) 2 and 4 only
(D) 3 and 4 only
(E) 1, 2, 3, and 4 all lie on the same equipotential since the electric field is uniform.
7. Two isolated and widely separated conducting spheres each carry a charge of -Q. Sphere 1 has
a radius of a and Sphere 2 has a radius of 4a. If the spheres are now connected by a
conducting wire, what will be the final charge on each sphere?
 Sphere 1 Sphere 2
(A) -Q -Q
(B) -2Q/3 -4Q/3
(C) -4Q/3 -2Q/3
(D) -2Q/5 -8Q/5
(E) -8Q/5 -2Q/5
8. A parallel-plate capacitor is charged to a potential difference of ?V; this results in a charge of
+Q on one plate and a charge of -Q on the other. The capacitor is disconnected from the
charging source, and a dielectric is then inserted. What happens to the potential difference
and the stored electrical potential energy?
(A) The potential difference decreases, and the stored electrical potential energy decreases.
(B) The potential difference decreases, and the stored electrical potential energy increases.
(C) The potential difference increases, and the stored electrical potential energy decreases.
(D) The potential difference increases, and the stored electrical potential energy increases.
(E) The potential difference decreases, and the stored electrical potential energy remains
unchanged.
9. How much work would the electric field (created by the stationary charge Q) perform as a
charge q is moved from Point A to B along the curved path shown? V
A
 = 200 V, V
B
 = 100
V, q = -0.05 C, length of line segment AB = 10 cm, length of curved path = 20 cm.
(A) -10 J
(B)  -5 J
(C)  +5 J
(D) +10 J
(E)  +2 J
10. If each of the capacitors in the array shown above is C, what is the capacitance of the entire
combination?
(A) C/2
(B) 2C/3
(C) 5C/6
(D) 2C
(E) 5C/3
11. The diagram above shows equipotential lines produced by a charge distribution. A, B, C, D,
and E are points in the plane. An electron begins at point A. The electron is then moved to
point E and then from point E to point C. Which of the following correctly describes the work
done by the field for each part of the movement?
 Movement from A to E Movement from E to C
(A) Negative Positive
(B) Zero Positive
(C) Zero Negative
(D) Negative Zero
(E) Positive Positive
Page 5


Section I: Multiple Choice
1. A capacitor is fully charged by a battery. The battery is disconnected, and a dielectric is
inserted into the capacitor. Which of the following statements is/are true?
I. The voltage will remain the same.
II. The potential energy of the capacitor will increase.
III. The capacitance of the capacitor will increase.
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) III only
2. If the electric field does negative work on a negative charge as the charge undergoes a
displacement from Position A to Position B within an electric field, then the electrical
potential energy
(A) is negative
(B) is positive
(C) increases
(D) decreases
(E) cannot be determined from the information given
3. Three 6 µF capacitors are connected in parallel to a 9 V battery as shown above. Determine the
energy stored in each capacitor.
(A) 243 J
(B)    7.29 × 10
-4
 J
(C)    8.10 × 10
-5
 J
(D)    2.43 × 10
-4
 J
(E)  27 J
4. The picture above shows 4 charges fixed in position at the corners of a rectangle measuring 2
cm by 4 cm. Assuming the charges are all of equal magnitude, how many locations on either
Line A or Line B would be places with 0 net electric potential?
(A) 1
(B) 5
(C) All of Line A
(D) All of Line B
(E) All of both Line A and Line B
5. A particle with a charge of +q and mass m starts at rest and moves linearly from a position of
high potential, A, to a position of low potential, B. Which of the following expressions will give
the particle’s speed at position B?
(A)
(B)
(C)
(D)
(E)
6. Which points in this uniform electric field (between the plates of the capacitor) shown above
lie on the same equipotential?
(A) 1 and 2 only
(B) 1 and 3 only
(C) 2 and 4 only
(D) 3 and 4 only
(E) 1, 2, 3, and 4 all lie on the same equipotential since the electric field is uniform.
7. Two isolated and widely separated conducting spheres each carry a charge of -Q. Sphere 1 has
a radius of a and Sphere 2 has a radius of 4a. If the spheres are now connected by a
conducting wire, what will be the final charge on each sphere?
 Sphere 1 Sphere 2
(A) -Q -Q
(B) -2Q/3 -4Q/3
(C) -4Q/3 -2Q/3
(D) -2Q/5 -8Q/5
(E) -8Q/5 -2Q/5
8. A parallel-plate capacitor is charged to a potential difference of ?V; this results in a charge of
+Q on one plate and a charge of -Q on the other. The capacitor is disconnected from the
charging source, and a dielectric is then inserted. What happens to the potential difference
and the stored electrical potential energy?
(A) The potential difference decreases, and the stored electrical potential energy decreases.
(B) The potential difference decreases, and the stored electrical potential energy increases.
(C) The potential difference increases, and the stored electrical potential energy decreases.
(D) The potential difference increases, and the stored electrical potential energy increases.
(E) The potential difference decreases, and the stored electrical potential energy remains
unchanged.
9. How much work would the electric field (created by the stationary charge Q) perform as a
charge q is moved from Point A to B along the curved path shown? V
A
 = 200 V, V
B
 = 100
V, q = -0.05 C, length of line segment AB = 10 cm, length of curved path = 20 cm.
(A) -10 J
(B)  -5 J
(C)  +5 J
(D) +10 J
(E)  +2 J
10. If each of the capacitors in the array shown above is C, what is the capacitance of the entire
combination?
(A) C/2
(B) 2C/3
(C) 5C/6
(D) 2C
(E) 5C/3
11. The diagram above shows equipotential lines produced by a charge distribution. A, B, C, D,
and E are points in the plane. An electron begins at point A. The electron is then moved to
point E and then from point E to point C. Which of the following correctly describes the work
done by the field for each part of the movement?
 Movement from A to E Movement from E to C
(A) Negative Positive
(B) Zero Positive
(C) Zero Negative
(D) Negative Zero
(E) Positive Positive
Section I: Multiple Choice
1. E
If a dielectric is added, the electric field will be reduced (due to the electric field of the
dielectric opposing the field of the capacitor’s plates). Because V = Ed, voltage will
decrease. If the battery were still attached, it would send more charge to restore the
voltage, but that isn’t the case here. The potential energy of a capacitor is given by the
equation U
cap
 = QV. Charge hasn’t changed, and voltage has decreased, which means
potential energy will decrease as well. Finally, capacitance is a measure of Q/ V. This
quantity will increase, so the capacitance will be higher.
2. C
By definition, ? U
E
 = - W
E
, so if W
E
 is negative, then ? U
E
 is positive. This implies that the
potential energy, U
E
, increases.
3. D
You may be tempted to solve for the equivalent capacitance and then use that to
determine the total charge stored on the capacitors, but we can already tell the potential
difference across each capacitor is 9 V. The energy stored in a capacitor is given by the
equation
4. E
Anywhere along either line will be a location of 0 net electric potential. At any location on
the lines, the two charges closest to that point will cancel each other’s electric potential,
and the two charges farthest from that point will cancel each other’s electric potential.
5. A
First, find the change in potential energy.
? U = q? V  
    = q( V
B
 - V
A
)
Next, we know that the change in potential energy will be the negative change in kinetic
energy.
? K = -? U  
   = q(V
A
 - V
B
)
Because the particle started at rest ( K = 0), the change in kinetic energy will be equal to
its kinetic energy at position B.