1 of 4 pagesUniversity of RochesterDepartment of Electrical & Computer EngineeringECE111 Final Examination 12-18-06This is a closed-book examination, but you may use a hand-held calculator. Write your name on your exambooklet and then do all work in it. Clearly indicate your answers. Partial credit is more likely for workthat is neat, well-organized, and easy to read. All problems are weighted equally.Do not overstate or understate the precision of numerical answers.1) Four (4) resistors, R1, R2, R3, and R4, each having the same nominal valueR and the same ± precision, are used in the design for the 4:1 voltagedivider shown below. If the divider ratio is specified to be vout/vin = 0.25with a precision of ±3%, use worst-case analysis to determine therequirement on the ±% precision for the four resistors.2) The steady-state AC voltage & current sources in the circuit belowoperate at different frequencies: f1 and f2 in Hz, that is:vs(t) = Vo cos(2pf1t) & is(t) = Io sin(2pf2t).(a) Find a time-dependent, algebraic expression for the AC voltageacross the resistor vR(t). (b) In a few well-written sentences, summarizethe linear circuit principles used to solve this problem.R2R4R1R3vout(t)vin(t)+RvR(t)vsC+is2 of 4 pages3) Using phasors, solve the equation below for steady-state AC voltage v(t). † d2vdt2+ 2dvdt+v= cos(t+p/ 4)4) A step change of voltage from V1 to V2 occurs at t = 0 to the RLCcircuit shown below. (a) Replicate the table below in your exam bookletand then fill it in with algebraic expressions for the various voltages andcurrents at the times given. (b) Explain concisely and clearly how theseanswers were obtained.t = 0-t = 0+t ‡ ∞vLC(t)iL(t)iC(t)i(t)vR(t)V1V2vs(t)LCRvLC(t)vR(t)+vs(t)-i(t)3 of 4 pages5) Consider the circuit below. (a) At frequency f = 100 kHz, find numericalvalues for the real & imaginary parts of the complex impedance Z(w),that is, R(w) and X(w), where Z(w) = R(w) + jX(w). Do not overstateprecision and be sure to specify units. (b) What is the frequency inHertz at which X = 0?6) Find the Thevenin equivalent in the frequency domain for the AC circuitshown below. Explain your methods.7) At t = 0, a step voltage Vo is applied to the series RC circuit shownbelow. (a) Find time-dependent expressions for (a) the electric currenti(t) and (b) the voltage across the capacitor vc(t). (c) What is the totalstored energy of the circuit w(t) as a function of time?Vo cos(wt-p/3)CRLR1 = 5 kWR2 = 10 kWC = 500 pFL = 10 mHR1R2CLvs(t)VotvC(t)RCvs(t)+i(t)4 of 4 pages8) Consider the twin-T AC filter circuit shown below. (a) How many nodeswith independent unknown voltages are there? (b) Sketch the circuit inyour exam booklet and in this sketch clearly identify these nodes anddefine voltages for them. (c) Use nodal analysis to obtain a complete setof independent equations for these voltages. DO NOT SOLVE FOR THESEVOLTAGES.1 WVs = Vo1 W1 W1 WZL1 W1