Mastering Physics Set 4 Midterm #1

Suppose two parallel-plate capacitors have the same charge Q, but the area of capacitor 1 is A and the area of capacitor 2 is 2A. If the spacing between the plates in capacitor 1 is d, what should the spacing between the plates in capacitor 2 be to make the capacitance of the two capacitors equal? d/2 d 2d 4d

2d

A spherical capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 10.0 centimeters, and the separation between the spheres is 1.50 centimeters. The magnitude of the charge on each sphere is 3.30 nanocoulomb. What is the electric-field energy stored in the capacitor?

6.38×10^−8 J

Halve the plate area. Double the plate separation.

Consider a charged parallel-plate capacitor. How can its capacitance be halved? Check all that apply. Double the charge. Double the plate area. Double the plate separation. Halve the charge. Halve the plate area. Halve the plate separation.

Halve the plate separation and double the plate area.

Consider a charged parallel-plate capacitor. Which combination of changes would quadruple its capacitance? Double the charge and double the plate area. Double the charge and double the plate separation. Halve the charge and double the plate separation. Halve the charge and double the plate area. Halve the plate separation and double the plate area. Double the plate separation and halve the plate area.

Decrease the spacing between the plates of the capacitor.

Consider an air-filled charged capacitor. How can its capacitance be increased? Increase the charge on the capacitor. Decrease the charge on the capacitor. Increase the spacing between the plates of the capacitor. Decrease the spacing between the plates of the capacitor. Increase the length of the wires leading to the capacitor plates.

Ur = KU

Consider the same situation as in the previous part, except that the charging battery remains connected while the dielectric is inserted.(Figure 2) The battery is then disconnected and the capacitor is discharged. For this situation, what is Ur, the energy dissipated in the resistor? Express your answer in terms of U and other given quantities.

Ur = U/K

Find Ur, the the energy dissipated in the resistor. Express your answer in terms of U and other given quantities.

Q = CΔV1

Find the charge Q on the first capacitor. Express your answer in terms of C and ΔV1.

CA = 2.59 μF

Find the equivalent capacitance CA of the network of capacitors. Express your answer in microfarads.

ΔV1 = 6ΔV11

Find the voltage ΔV1 across the first capacitor. Express your answer in terms of ΔV.

2Q and 3Q

If the charge of the first capacitor (the one with capacitance C) is Q, then what are the charges of the second and third capacitors? 2Q and 3Q Q2 and Q3 Q and Q 0 and 0

V and 0

If the potential of plate 1 is V, then, in equilibrium, what are the potentials of plates 3 and 6? Assume that the negative terminal of the battery is at zero potential. V and V 2V and 3V V and 0 V2 and V3

1/2ΔV1 and 1/3ΔV1

If the voltage across the first capacitor (the one with capacitance C) is ΔV1, then what are the voltages across the second and third capacitors? 2ΔV1 and 3ΔV1 1/2ΔV1 and 1/3ΔV1 ΔV1 and ΔV1 0 and ΔV1

A=2cm^2 C=8nF >A=2cm^2 C=4nF > A=4cm^2 C=2nF = A=8cm^2 C=2nF > A=1cm^2 C=1nF = A=4cm^2 C=1nF

Rank the capacitors on the basis of the charge stored on the positive plate.

A=2cm^2 C=8nF >A=2cm^2 C=4nF > A=1cm^2 C=1nF >A=4cm^2 C=2nF > A=4cm^2 C=1nF = A=8cm^2 C=2nF

Rank the following capacitors on the basis of the dielectric constant of the material between the plates.

Ceq must be less than C4.

Suppose that you are given another network of the same form as the one analyzed in Part B, but with different values for the individual capacitances. How would you expect the equivalent capacitance Ceq to compare to the values of each individual capacitor in the network? Choose the statement below that is true regardless of the actual values for the individual capacitors. Ceq must be less than C3. The value of Ceq is not bounded by the value of any individual capacitance in the network. Ceq must be less than C4. Ceq must be less than C1+C2 .

Qtot = 6C

Suppose we consider the system of the three capacitors as a single "equivalent" capacitor. Given the charges of the three individual capacitors calculated in the previous part, find the total charge Qtot for this equivalent capacitor. Express your answer in terms of V and C.

C3 is in parallel with C1 and C2. C1 is in series with C2.

The four capacitors shown in the diagram are neither all in series nor all in parallel. You can, however, identify portions of the arrangement that are either in series or parallel, as described in the following statements. Which of these statements are correct for this problem? Check all that apply. C4 is in series with C1 and C2. C3 is in series with C4. C3 is in parallel with C1 and C2. C1 is in series with C2.

CB = 2.54 μF

Two capacitors of capacitance C5 = 6.00 μF and C6 = 3.00 μF are added to the network, as shown in the diagram.(Figure 2) Find the equivalent capacitance CB of the new network of capacitors. Express your answer in microfarads.

An air-filled parallel-plate capacitor has plate area A and plate separation d. The capacitor is connected to a battery that creates a constant voltage V. Find the energy U0 stored in the capacitor. Express your answer in terms of A, d, V, and ϵ0.

U0 = 1/2(ϵ0A/d)V^2

An air-filled parallel-plate capacitor has plate area A and plate separation d. The capacitor is connected to a battery that creates a constant voltage V. The capacitor is now disconnected from the battery, and the plates of the capacitor are then slowly pulled apart until the separation reaches 3d. Find the new energy U1 of the capacitor after this process. Express your answer in terms of A, d, V, and ϵ0.

U1 = 3ϵ0(AV^2)/2d

An air-filled parallel-plate capacitor has plate area A and plate separation d. The capacitor is connected to a battery that creates a constant voltage V. The capacitor is now reconnected to the battery, and the plate separation is restored to d. A dielectric plate is slowly moved into the capacitor until the entire space between the plates is filled. Find the energy U2 of the dielectric-filled capacitor. The capacitor remains connected to the battery. The dielectric constant is K. Express your answer in terms of A, d, V, K, and ϵ0.

U2 = 1/2(V^2)(Kϵ0A/d)

Ceq = 6C/11

Using the value of Q just calculated, find the equivalent capacitance Ceq for this combination of capacitors in series. Express your answer in terms of C.

Ceq = 6C

Using the value of Qtot, find the equivalent capacitance Ceq for this combination of capacitors. Express your answer in terms of C.

Suppose two parallel-plate capacitors have the same charge Q, but the area of capacitor 1 is A and the area of capacitor 2 is 2A. If the spacing between the plates, d, is the same in both capacitors, and the voltage across capacitor 1 is V, what is the voltage across capacitor 2? V/2 V 2V 4V

V/2

+Q and −Q

What are the charges on plates 3 and 6? +Q and +Q −Q and −Q +Q and −Q −Q and +Q 0 and +Q 0 and −Q

Ceq = 14.4 μF

What is the equivalent capacitance Ceq of the entire combination? Express your answer in microfarads to three significant figures.

the ability to store charge

What property of objects is best measured by their capacitance? the ability to conduct electric current the ability to distort an external electrostatic field the ability to store charge

A spherical capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 10.0 centimeters, and the separation between the spheres is 1.50 centimeters. The magnitude of the charge on each sphere is 3.30 nanocoulomb. What is the magnitude of the potential difference ΔV between the two spheres?

ΔV = 38.7 V