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AP Physics C: Electricity and Magnetism Unit 2: Conductors, Capacitors, Dielectrics

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Unit 2: Conductors, Capacitors, Dielectrics

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Question 1

A parallel-plate capacitor with plate area $A = 0.10 m^{2}$ and gap $d = 2 mm$ is filled with a dielectric of $κ = 5$ . A voltage $V = 100 V$ is applied. The surface charge density $σ_{f}$ on the capacitor plates (free charge) is:

σ_{f} = κ ϵ_{0} V / d \approx 2.21 μ C/m^{2}

σ_{f} = ϵ_{0} V / d \approx 0.44 μ C/m^{2}

σ_{f} = ϵ_{0} V / (κ d) \approx 0.089 μ C/m^{2}

σ_{f} = κ^{2} ϵ_{0} V / d \approx 11.1 μ C/m^{2}

Question 2

A parallel-plate capacitor has plate area $A$ and plate separation $d$ . The capacitance is:

C = \frac{ϵ _{0} A}{d}

C = \frac{ϵ _{0} d}{A}

C = \frac{A}{4 π ϵ _{0} d}

C = \frac{ϵ _{0} A}{2 d}

Question 3

A parallel-plate capacitor (area $A$ , separation $d$ , no dielectric) is connected to a constant voltage source $V$ . A dielectric slab of thickness $t < d$ and dielectric constant $κ$ is inserted so that it fills the cross-section but only part of the gap. The capacitance of the resulting configuration is:

C = \frac{ϵ _{0} A}{d - t + t / κ}

C = \frac{κ ϵ _{0} A}{d}

C = \frac{ϵ _{0} A}{d + t ( κ - 1 )}

C = \frac{κ ϵ _{0} A}{d - t}

Question 4

Two capacitors $C_{1} = 4 μ F$ (initially charged to $V_{1} = 12 V$ ) and $C_{2} = 8 μ F$ (initially uncharged) are connected in parallel by closing a switch. The final common voltage and the energy dissipated in the connecting wires are:

V_{f} = 4 V

;

Δ U_{dissipated} = 192 μ J

V_{f} = 6 V

;

Δ U_{dissipated} = 144 μ J

V_{f} = 4 V

;

Δ U_{dissipated} = 0

V_{f} = 12 V

;

Δ U_{dissipated} = 576 μ J

Question 5

A spherical capacitor consists of an inner shell of radius $a$ and a concentric outer shell of radius $b$ ( $b > a$ ). The capacitance of this spherical capacitor is:

C = 4 π ϵ_{0} ab / (b - a)

C = 4 π ϵ_{0} (b - a) / (ab)

C = 4 π ϵ_{0} a

C = ϵ_{0} \cdot 4 π a^{2} / (b - a)

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Question 6

A charged isolated conductor has a sharp point (small radius of curvature $r$ ) and a flat region (large radius of curvature). Which statement correctly describes the charge distribution?

A.Surface charge density and electric field are highest at the sharp point.B.Surface charge density is uniform across the entire conductor surface.C.The electric field is stronger over flat regions because there is more area for charge to spread.D.Electric field inside the conductor is largest near the sharp point.

Question 7

A conductor in electrostatic equilibrium has which of the following properties?

A.The electric field just outside the surface is

σ / ϵ_{0}

, directed perpendicular to the surface.B.The electric field inside the conductor is

σ / ϵ_{0}

.C.The electric potential varies parabolically throughout the conductor's volume.D.Excess charge distributes uniformly throughout the conductor's volume.

Question 8

Three capacitors $C_{1} = 6 μ F$ , $C_{2} = 3 μ F$ , and $C_{3} = 2 μ F$ are connected in series across a $12 V$ battery. The total energy stored in the combination is:

72 μ J

648 μ J

144 μ J

36 μ J

Question 9

The energy density stored in the electric field of a parallel-plate capacitor filled with dielectric $κ$ and field $E$ is:

u = \frac{1}{2} κ ϵ_{0} E^{2}

u = \frac{1}{2} ϵ_{0} E^{2}

u = \frac{1}{2 κ ϵ _{0} E ^{2}}

u = κ ϵ_{0} E^{2}

Question 10

A capacitor $C = 10 μ F$ is charged by a battery $V = 100 V$ and then disconnected. The plates are then pulled apart from separation $d$ to separation $2 d$ . Which of the following correctly describes the new voltage across the capacitor?

A.The voltage doubles to

200 V

.B.The voltage stays at

100 V

, because charge is conserved.C.The voltage halves to

50 V

.D.The voltage stays at

100 V

, because the electric field

E = V / d

is unchanged when

d

doubles.

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Question 11

A capacitor of capacitance $C$ is fully charged to voltage $V_{0}$ and then disconnected from the battery. A dielectric of dielectric constant $κ$ is then inserted, filling the gap completely. What happens to the stored energy?

A.The energy decreases by a factor of

κ

.B.The energy increases by a factor of

κ

.C.The energy remains the same, because charge is conserved.D.The energy increases by a factor of

κ^{2}

Question 12

A coaxial cylindrical capacitor has inner radius $a$ , outer radius $b$ , and length $L$ . The capacitance per unit length is:

C / L = \frac{2 π ϵ _{0}}{ln ( b / a )}

C / L = \frac{π ϵ _{0}}{ln ( b / a )}

C / L = \frac{2 π ϵ _{0} ( b - a )}{ab ln ( b / a )}

C / L = \frac{2 π ϵ _{0}}{b - a}

AP Physics C: Electricity and Magnetism Unit 2: Conductors, Capacitors, Dielectrics — Free with Answer Explanations | Test Practice Hub