2018 USA Physics Olympiad Exam Part A 8 c.Sketch the new potential difference VCp Vc-Vp as a function of time on the answer sheet. For your convenience,VAB is shown in light gray.Assume that VAB has been running for a long time. Solution Let the voltage on the capacitor be Vs.Whenever VAB>Vs+2Vo,current flows through the diodes,charging the capacitor up to voltage VABI-2Vo.Whenever IVABI<V+2Vo,no current flows through the diodes,and the capacitor and resistor simply discharge as an RC circuit with time constant RC=250 ms. Since RC is much longer than the timescale on the answer sheets,the discharge is approxi- mately linear,with dVs 1.0V dt-83.3 ms Thus the capacitor charges completely to 3.0 V every cycle,then discharges approximately linearly by about a half volt during the reminder of the cycle.On the graph we show charging as red and discharging as blue. 6 4 3 9 0 -1 -2 -3 -4 -5 - 0 10 20 3040 506070 8090 100110 120 Time (ms) Copyright C2018 American Association of Physics Teachers2018 USA Physics Olympiad Exam Part A 8 c. Sketch the new potential difference VCD = VC −VD as a function of time on the answer sheet. For your convenience, VAB is shown in light gray. Assume that VAB has been running for a long time. Solution Let the voltage on the capacitor be Vs. Whenever |VAB| ≥ Vs + 2V0, current flows through the diodes, charging the capacitor up to voltage |VAB| − 2V0. Whenever |VAB| < Vs + 2V0, no current flows through the diodes, and the capacitor and resistor simply discharge as an RC circuit with time constant RC = 250 ms. Since RC is much longer than the timescale on the answer sheets, the discharge is approxi￾mately linear, with dVs dt = 1.0 V 83.3 ms . Thus the capacitor charges completely to 3.0 V every cycle, then discharges approximately linearly by about a half volt during the reminder of the cycle. On the graph we show charging as red and discharging as blue. 0 10 20 30 40 50 60 70 80 90 100 110 120 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 Time (ms) Voltage (V) Copyright c 2018 American Association of Physics Teachers