Conductors, Capacitors, and Dielectrics Practice Test 1

1.

Which of the following statements is true about the electric field inside a conductor in electrostatic equilibrium?

a) It is always nonzero b) It is always zero c) It depends on the shape d) It is maximum at the center

2.

Which of the following materials is a good electrical conductor?

a) Glass b) Copper c) Rubber d) Air

3.

For a parallel-plate capacitor with plate area A and separation d, what is the capacitance in vacuum?

a) \( \varepsilon_0 A/d \) b) \( A/(\varepsilon_0 d) \) c) \( \varepsilon_0 d/A \) d) \( d/(\varepsilon_0 A) \)

4.

What happens to the capacitance of a parallel-plate capacitor if the plate separation is doubled?

a) It doubles b) It is halved c) It is unchanged d) It becomes one-fourth as much

5.

Three capacitors (2 μF, 3 μF, and 6 μF) are connected in series. What is the equivalent capacitance?

a) 11 μF b) 1 μF c) 6 μF d) 0.5 μF

6.

What is the energy stored in a 4 μF capacitor charged to 50 V?

a) 0.005 J b) 0.01 J c) 0.25 J d) 0.005 C

7.

A dielectric with constant k is inserted between the plates of a charged, isolated capacitor. What happens to the stored energy?

a) It increases by a factor of k b) It decreases by a factor of k c) It is unchanged d) It doubles

8.

Which of the following is a property of conductors in electrostatic equilibrium?

a) The electric field just outside is zero b) The surface is an equipotential c) The charge resides in the center d) The field inside is nonzero

9.

Derivation: What is the equivalent capacitance of two capacitors, C1 and C2, connected in parallel?

a) C1 + C2 b) (C1 × C2)/(C1 + C2) c) C1 - C2 d) (C1 + C2)/2

10.

Which of the following best describes the effect of grounding a conductor?

a) It removes all charge from the conductor b) It brings the conductor to zero potential c) It increases the capacitance d) It makes the field inside nonzero

11.

What is the potential difference across a 8 μF capacitor that stores 0.016 J of energy?

a) 40 V b) 60 V c) 80 V d) 100 V

12.

For a spherical capacitor with inner radius a and outer radius b, what is the capacitance?

a) \( 4\pi\varepsilon_0 ab/(b-a) \) b) \( 4\pi\varepsilon_0(b-a)/ab \) c) \( 4\pi\varepsilon_0(a+b) \) d) \( 4\pi\varepsilon_0(a-b) \)

13.

Which of the following is true about the electric field just outside a charged conductor?

a) It is always zero b) It is perpendicular to the surface c) It is parallel to the surface d) It depends on the shape

14.

What happens to the capacitance of a parallel-plate capacitor if the area is tripled and the separation is halved?

a) It is multiplied by 1.5 b) It is multiplied by 3 c) It is multiplied by 6 d) It is multiplied by 9

15.

For a cylindrical capacitor with inner radius a and outer radius b, what is the capacitance per unit length?

a) \( 2\pi\varepsilon_0/\ln(b/a) \) b) \( 2\pi\varepsilon_0\ln(b/a) \) c) \( \pi\varepsilon_0/\ln(b/a) \) d) \( \pi\varepsilon_0\ln(b/a) \)

16.

What happens to the electric field inside a capacitor when a dielectric is inserted?

a) It increases by a factor of k b) It decreases by a factor of k c) It remains unchanged d) It becomes zero

17.

Derivation: What is the energy density in an electric field E?

a) \( \frac{1}{2}\varepsilon_0 E^2 \) b) \( \varepsilon_0 E^2 \) c) \( \frac{1}{2}\varepsilon_0 E \) d) \( \varepsilon_0 E \)

18.

What is the charge on a 12 μF capacitor connected to a 24 V battery?

a) 0.288 mC b) 0.5 mC c) 2 mC d) 288 mC

19.

Which of the following is true about the surface charge density on a conductor?

a) It is uniform everywhere b) It is highest where the radius of curvature is smallest c) It is highest where the radius of curvature is largest d) It is always zero

20.

What is the equivalent capacitance of a 3 μF and 6 μF capacitor connected in parallel?

a) 2 μF b) 3 μF c) 6 μF d) 9 μF

21.

Which of the following is true about the electric potential inside a conductor in electrostatic equilibrium?

a) It varies with position b) It is constant throughout c) It is maximum at the center d) It is zero everywhere

22.

What is the energy stored in a 15 μF capacitor charged to 40 V?

a) 0.012 J b) 0.024 J c) 0.06 J d) 0.12 J

23.

Four identical 2 μF capacitors are connected in a square configuration. What is the equivalent capacitance between opposite corners?

a) 1 μF b) 2 μF c) 4 μF d) 8 μF

24.

Which of the following best describes the effect of a dielectric on the breakdown voltage of a capacitor?

a) It always increases the breakdown voltage b) It always decreases the breakdown voltage c) It has no effect on breakdown voltage d) It depends on the dielectric material

25.

What is the charge density on the plates of a parallel-plate capacitor with capacitance 5 μF, plate area 0.1 m², and voltage 100 V?

a) 5×10⁻⁶ C/m² b) 5×10⁻⁵ C/m² c) 5×10⁻⁴ C/m² d) 5×10⁻³ C/m²

26.

Which of the following is true about the electric field between the plates of a charged parallel-plate capacitor?

a) It is uniform and directed from positive to negative plate b) It is non-uniform and strongest at the edges c) It is zero everywhere between the plates d) It varies sinusoidally with position

27.

Derivation: What is the force between the plates of a parallel-plate capacitor with charge Q and plate separation d?

a) Q²/(2ε₀A) b) Q²/(ε₀A) c) Q²/(4ε₀A) d) Q²/(8ε₀A)

28.

What is the equivalent capacitance of three capacitors (4 μF, 6 μF, 12 μF) connected in series?

a) 2 μF b) 4 μF c) 6 μF d) 22 μF

29.

Which of the following best describes the polarization of a dielectric in an electric field?

a) The dielectric becomes permanently charged b) The dielectric becomes a conductor c) The dielectric develops induced dipoles d) The dielectric loses all its electrons

30.

What is the potential difference across a 20 μF capacitor that stores 0.1 J of energy?

a) 50 V b) 100 V c) 150 V d) 200 V

Conductors, Capacitors, and Dielectrics Practice Test 1

30 Questions – AP Physics C Level