1 of 2 pagesUniversity of RochesterDepartment of Electrical & Computer EngineeringECE111 Examination #2 11-17-06This 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 neat,well-organized, and easy to read work. All problems are weighted equally.Do not overstate or understate the precision of numerical answers.1) As appropriate, find algebraic or numerical values for the first-order,exponential transient time constant t of each of the three circuits shownbelow. Explain your methods in words and a few circuit diagrams.Assume all voltage and current sources are independent. For thenumerical problem (c), specify the uncertainty of t in ± seconds.R+-2RRC+-RL1L2L3+-RC1C2(a)(b)(c)For (c), assume that C1 = 1 nF (±10%), C2 = 10 nF (±2%), & R = 1 MW (±2%)Note: 1 nF = 10-9 F.2) For the inverting op-amp circuit below, find the differential equation (NOINTEGRALS) relating the input voltage vin(t) and output voltage vout(t).You must show how you obtained the equation.In your derivation, use the assumption that the open-loop gain of the op-amp isvery large, that is, A ~ 105.-+LRfvoutvin2 of 2 pages3) The series RC circuit shown below is subjected to a current step ofmagnitude Io at t = 0. Find and carefully plot time-dependent expressionsfor the voltages across the resistor and the capacitor.4) A step change of voltage from V1 to V2 is applied at t = 0 to the seriesRLC circuit shown below. (a) Replicate the table below in your exambooklet and then fill it in with expressions for the various voltages andcurrents at the times given.t = 0-t = 0+t ‡ ∞vR(t)vL(t)vC(t)i(t)di/dt(b) Provide a general, time-dependent expression for the current i(t) anddefine all coefficients and exponential factors used in this expression.Do not solve for the