1 of 2 pages University of Rochester Department of Electrical & Computer Engineering ECE111 Examination #2 corrected 11-17-08 This is a closed-book examination, but you may use a hand-held calculator. Do all work in the exam booklet provided, clearly indicating your answers. Partial credit is more likely for neat, well-organized writing. Put your name on your exam booklet. All problems are weighted equally. 1) Two voltage steps of opposite sign are applied at different times to the RC circuit below. Use superposition and Thevenin/Norton equivalents to find the voltage across the resistor R. For your answer, all that is required is to sketch this voltage waveform carefully, labeling all important voltage and time values. You do not need to provide an analytical expression! Be sure to provide a full explanation of how you arrived at your answer. 2) In the circuit below, an input voltage source vin(t) is connected to the inverting input terminal of an op-amp with a resistor R and an inductor L in the feedback path. (a) Using the standard op-amp model, redraw the circuit. (b) Use nodal analysis to write the integral equation relating the voltages at the node. (c) Assuming that the open-loop gain A is very large, simplify your equation to obtain a differential equation relating the output voltage vout(t) to the input vin(t). - + L R vout vin Vo v2(t) t -Vo v1(t) T R C v1(t) R R v2(t) vR(t)2 of 2 pages 3) A DC voltage Vo is applied to a capacitor C for a long time, then at t = 0, the switch is thrown so that the charged capacitor is disconnected from the voltage source and connected to a series RL. Solve for the voltage across the resistor vR(t), using the following step-by-step approach. (a) Write a general solution for the voltage across the resistor vR(t), making sure to define the decay factor and the resonant frequency in terms of the ckt quantities. Use unknown coefficients for the amplitudes of the various terms in this solution. (b) Prepare a table containing the values for vC(t), vL(t), and vR(t) at times t = 0-, t = 0+, and t → ∞. (c) Use your knowledge of the time-dependent behavior of inductors and capacitors to eliminate any terms from the general solution that are not needed to express the voltage vR(t). (d) Plot the solution with care, labeling important amplitude and time values. (e) Determine the coefficient of the remaining term in your expression for vR(t). vR(t) L R C + Vo - t =