ECEN 2250 Introduction to Circuits & Electronics Fall 201110-01-11 P. MathysProblem Set 6 (Solutions are due Fri. 10-07-11)Note: For all problems you have to explain how you arrived at the solution legibly and ina logical order. This includes (i) Statement of problem, (ii) strategie(s) for solution, (iii)execution of the strategy, identifying each step and including a check of the solution(s), and(iv) logical and legible presentation of the solution.1) Use node-voltage analysis to determine vAand vBin the following circuit.•+−••iS8R12R5 vORL−+vOvAvB2) Problem 8-10 in the book.3) Problem 8-28 in the book. Use LTspice instead of OrCAD.4) Problem 8-42 in the book.5) The following RL circuit with input vS(t) ⇔ VScan be used as a filter.◦◦••◦◦−vS(t)+−vO(t)+R+ −vR(t)L(a) Determine the output vO(t) ⇔ VOin the time and phasor domains, assuming thatvS(t) = A cos(ωt). LetH(jω) =VOVS,1denote the frequency response of the circuit. Sketch and label the magnitude |H(jω)| andthe phase ∠H(jω) (in degrees) of the frequency response for ω = 0 . . . 4000π rad/sec (i.e.,f = 0 . . . 2000 Hz) when the time constant of the circuit is L/R = (1000π)−1s. Is this alowpass (LPF) or a highpass (HPF) filter?(b) Repeat (a) for the case when the filter output is the voltage vR(t) across the resistorinstead of vO(t).6) The following circuit is operated in the sinusoidal steady-state.+−••vS(t)Z1Z2Z3Z4↓ i(t)−+v(t)When vS(t) = 20 cos(300000t) V, i(t) and v(t) are measured as i(t) = 200 cos(300000t +15◦)mA and v(t) = 10 cos(300000t+60◦)V. Find elements (R, L, C) and values for Z1. . . Z4such that this i(t) and this v(t) are produced in response to the given vS(t). The valuesfor resistors, capacitors, and inductors in your solution must be in the range 10 . . . 100 Ω,0.01 . . . 1 µF, and 0.01 . . . 1 mH, respectively. Verify your solution using LTspice. Is thesolution unique?c2001–2011, P. Mathys. Last revised: 10-02-11,