2016 USA Physics Olympiad Exam Part A 4 Question A2 A student designs a simple integrated circuit device that has two inputs,Va and V,and two outputs, Vo and V.The inputs are effectively connected internally to a single resistor with effectively infinite resistance.The outputs are effectively connected internally to a perfect source of emf &The integrated circuit is configured so that &=G(Va-V),where G is a very large number somewhere between 107 and 109.The circuits below are chosen so that the precise value of G is unimportant. On the left is an internal schematic for the device;on the right is the symbol that is used in circuit diagrams. a o- a.Consider the following circuit.R=8.2 kn and R2=560 are two resistors.Terminal g and the negative side of Vin are connected to ground,so both are at a potential of 0 volts. Determine the ratio Vout/Vin. Vout R R2 b.Consider the following circuit.All four resistors have identical resistance R.Determine Vout in terms of any or all of Vi,V2,and R. R R Vout R c.Consider the following circuit.The circuit has a capacitor C and a resistor R with time constant RC =T.The source on the left provides variable,but bounded voltage.Assume Vin is a function of time.Determine Vout as a function of Vin,and any or all of time t and T. R Vout in Copyright C2016 American Association of Physics Teachers2016 USA Physics Olympiad Exam Part A 4 Question A2 A student designs a simple integrated circuit device that has two inputs, Va and Vb, and two outputs, Vo and Vg. The inputs are effectively connected internally to a single resistor with effectively infinite resistance. The outputs are effectively connected internally to a perfect source of emf E. The integrated circuit is configured so that E = G(Va − Vb), where G is a very large number somewhere between 107 and 109 . The circuits below are chosen so that the precise value of G is unimportant. On the left is an internal schematic for the device; on the right is the symbol that is used in circuit diagrams. Va Vb Vo Vg a b o g a. Consider the following circuit. R1 = 8.2 kΩ and R2 = 560 Ω are two resistors. Terminal g and the negative side of Vin are connected to ground, so both are at a potential of 0 volts. Determine the ratio Vout/Vin. a b o g R1 R2 Vout Vin b. Consider the following circuit. All four resistors have identical resistance R. Determine Vout in terms of any or all of V1, V2, and R. a b o g R R Vout V1 V2 R R c. Consider the following circuit. The circuit has a capacitor C and a resistor R with time constant RC = τ . The source on the left provides variable, but bounded voltage. Assume Vin is a function of time. Determine Vout as a function of Vin, and any or all of time t and τ . a b o g R Vout Vin C Copyright c 2016 American Association of Physics Teachers