1 of 3 pagesUniversity of RochesterDepartment of Electrical & Computer EngineeringECE111 Examination #2 11-16-07This is a closed-book examination, but you may use a hand-held calculator. Do all work in the exambooklet provided, clearly indicating your answers. Partial credit is more likely for neat, well-organizedwriting. Put your name on your exam booklet. All problems are weighted equally.1) In this problem, you will match the transient voltage waveforms belowon the left to corresponding first-order RC and RL circuits on the right.transient waveforms circuitsABCDE+RC-(2)voutVou(t)+RL-(3)voutVou(t)+R1C-(1)voutVot = 0R2+C-(4)voutVou(t)RR+L-(5)voutVou(t)RR(a) Copy all waveforms into your exam booklet, then indicate whichcircuit with defined output vout gives that response by marking thewaveform with the appropriate number. There is a one-to-onecorrespondence with no duplicates.(b) On each plot, label critical voltage values including asymptotes.(c) Write an algebraic expression for the first-order time constant tof each circuit.2 of 3 pages2) In the circuit below, an input voltage source vin(t) is connected to theinverting input terminal of an op-amp with a capacitor C.vin-+RCNODE for KCLvout(a) Using the standard op-amp model, redraw the circuit.(b) Use nodal analysis to write the equation relating voltages atthe node indicated. The expression will be a differentialequation.(c) Relying on the knowledge that the open-loop gain is very large,that is, A ª 105, simplify your equation to obtain a differentialequation relating the output voltage vout(t) to the input vin(t).3 of 3 pages3) A DC voltage Vo, applied to a series RLC circuit for a long time, issuddenly removed at t = 0. You are to describe the transientbehavior of this circuit in terms of voltage and current values atvarious, specified critical times.RLC+-Vou(-t) i(t)vRvLvCit = 0-t = 0+t Æ •(a) Copy the table above into your exam booklet and then fill in theblanks with expressions for the voltages vR, vL, and vC and thecurrent i.HINT: You can check answers to see if KVL is satisfied at all times.(b) Using i(0+) from the table and your knowledge of the behaviorof an under-damped 2nd order system, carefully sketch thecurrent i(t) versus time. Be sure to provide labels for allcritical values in your sketch.(c) By inspection of your answer to (b), use your knowledge of thetransient behavior of RLC (2nd order) circuits to write down anexpression for i(t). Define all variables used in the