Mastering Physics Set 4 Midterm #1

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

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.

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.

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.

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

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

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.

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

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

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

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

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

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.

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.

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

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 .

V/2

2d

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

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.

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

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.

ΔV = 38.7 V

6.38×10^−8 J

U0 = 1/2(ϵ0A/d)V^2

U1 = 3ϵ0(AV^2)/2d

U2 = 1/2(V^2)(Kϵ0A/d)

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

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