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.
Energy stored in a capacitor
Capacitance definition
Parallel plate capacitance
Energy density of an electric field
Force between capacitor plates
Capacitors in series and parallel
Capacitor in a circuit at steady state
Partially filled dielectric
Charge redistribution between capacitors
Dielectric constant
RC circuit charging
Why energy changes when a dielectric is inserted
Short answer 1. Define or explain: General method for capacitance
3 ptsShort answer 2. Define or explain: Dielectric at constant charge vs constant voltage
3 ptsShort answer 3. Define or explain: Capacitance of a spherical capacitor
3 ptsShort answer 4. Define or explain: Time constant
3 ptsFree response
10 ptsThis course has no free-response prompt tagged to this unit, so one from elsewhere in the course is used. It is still worth writing — the skill transfers.
A 12 V battery of negligible internal resistance, a switch, a 50 kΩ resistor, and an initially uncharged 20 μF capacitor are connected in series. The switch is closed at t = 0.
Determine the current immediately after the switch is closed and the final charge on the capacitor.
Apply Kirchhoff’s loop rule to obtain the differential equation for q(t) and show by substitution that q(t) = CV(1 − e^(−t/RC)) is its solution.
Determine the time constant and the time required for the capacitor to reach half its final charge.
Determine the final energy stored in the capacitor and the total energy delivered by the battery, and account for the difference.
The 50 kΩ resistor is replaced by a 100 kΩ resistor. State how the final charge and the charging time change, with justification.