2018 USA Physics Olympiad Exam Part A 6 10 2 (1/1) -2 -4 -6 -8 -10L -10 -8 -6 -4 -2 0 2 8 10 Voltage (V/Vo) Shown is a schematic for the device.Positive voltage means that the electric potential of the left hand side of the device is higher than the right hand side.For this device,Io=25pA and %=1.0V. ViVR Below is a circuit made up of these elements.The voltage supplied the circuit is sinusoidal, VAB =VA-VB Vs sinwt,and is also shown on answer sheets.The resistance is R=5.00 and V=5.0V. VA VD VB Copyright C2018 American Association of Physics Teachers
2018 USA Physics Olympiad Exam Part A 6 −10 −8 −6 −4 −2 0 2 4 6 8 10 −10 −8 −6 −4 −2 0 2 4 6 8 10 Voltage (V /V0) Current (I/I0) Shown is a schematic for the device. Positive voltage means that the electric potential of the left hand side of the device is higher than the right hand side. For this device, I0 = 25 µA and V0 = 1.0 V. VL VR Below is a circuit made up of these elements. The voltage supplied the circuit is sinusoidal, VAB = VA − VB = Vs sin ωt, and is also shown on answer sheets. The resistance is R = 5.0 Ω and Vs = 5.0 V. VB VA VC VD R Copyright c 2018 American Association of Physics Teachers
2018 USA Physics Olympiad Exam Part A 7 b.Sketch the 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 When VAB 2Vo,no current flows.When IVABl>2Vo,current begins to fow,with each diode subtracting a potential difference of Vo.Note that the current flows in the same direction for both positive and negative VAB.This device is a rectifier. 2 (A) 0 -1 -2 -3 -4 -5 -6 010 2030405060708090100110120 Time (ms) A capacitor is connected to the circuit as shown below.The capacitance is C=50mF. VA- VB Copyright C2018 American Association of Physics Teachers
2018 USA Physics Olympiad Exam Part A 7 b. Sketch the 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 When |VAB| < 2V0, no current flows. When |VAB| > 2V0, current begins to flow, with each diode subtracting a potential difference of V0. Note that the current flows in the same direction for both positive and negative VAB. This device is a rectifier. 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) A capacitor is connected to the circuit as shown below. The capacitance is C = 50 mF. VB VA VC VD C R Copyright c 2018 American Association of Physics Teachers
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 Teachers
2018 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 approximately 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