Conductors, Capacitors, and Dielectrics unit test
A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.
Capacitors in series and parallel
RC circuit discharging
Capacitor in a circuit at steady state
General method for capacitance
Capacitance definition
Energy density of an electric field
Partially filled dielectric
Why energy changes when a dielectric is inserted
Capacitance of a spherical capacitor
Energy stored in a capacitor
Dielectric constant
Cylindrical and spherical capacitors
Short answer 1. Define or explain: Force between capacitor plates
3 ptsShort answer 2. Define or explain: RC circuit charging
3 ptsShort answer 3. Define or explain: Charge redistribution between capacitors
3 ptsShort answer 4. Define or explain: Dielectric at constant charge vs constant voltage
3 ptsFree response
8 ptsA parallel-plate capacitor with plate separation d is connected to a battery of emf ε and allowed to charge fully. The plate separation is then doubled to 2d. In case 1 the battery remains connected while the plates are separated. In case 2 the battery is disconnected before the plates are separated. Fringing effects are negligible.
A. Indicate whether the energy stored in the capacitor after the plates are separated is greater in case 1, greater in case 2, or the same in both. Justify your answer using qualitative reasoning beyond referencing equations.
B. Derive expressions for the energy stored after separation in each case, in terms of the initial stored energy U₀.
C. Justify how your derived expressions in part B are or are not consistent with your comparison in part A, and identify the source of any energy gained.