Question Use nodal analysis to find vo in the circuit given below, where Is = 40 sin(wt) A. Let @ = 2000 rad/s. Please report your answer so the magnitude is positive and all angles are in the range of negative 180 degrees to positive 180 degrees. 2 uF Is 2 k0 50 mH 0.1 ༧r 4 k0 The value of vo(t) = sin(2000t+ °) V.

What is the flow through bulb A? (Hint: think of the similarities/differences between bulb A and bulb B. Compare how the two bulbs are treated by the battery.) 12] What is the obstacle presented by the two bulbs C and D in series? Compare this obstacle with the obstacle presented by bulb A. Use statement 2 c to say if the flow through bulb A is bigger than, What is the flow through bulb A? (Hint: think of the similarities/differences between bulb A and bulb B. Compare how the two bulbs are treated by the battery.) 12] What is the obstacle presented by the two bulbs C and D in series? Compare this obstacle with the obstacle presented by bulb A. Use statement 2 c to say if the flow through bulb A is bigger than, smaller than or equal to the flow through bulbs C and D. Use your previous answers to rank the bulbs in order of decreasing brightness. Put an 'equals' sign between bulbs of the same brightness. (For example, E> D>C- B- A would mean that Bulb E is brightest, followed by bulb D and then bulb C which is of the same brightness as bulbs B and A.) 1]

Problem 3 (30 points) Consider the unity feedback system given below. a) Draw the root locus showing open-loop poles and zeros, and asymptotes. (20 pts) OUF b) Determine if a test point so = -4+j is on the root locus, where j² = -1. Justify your answer. (10 pts) R(S)+ Hint. The equations of the asymptotes of the Root Locus are given by: #aymptotes = #finite Problem 3 (30 points) Consider the unity feedback system given below. a) Draw the root locus showing open-loop poles and zeros, and asymptotes. (20 pts) OUF b) Determine if a test point so = -4+j is on the root locus, where j² = -1. Justify your answer. (10 pts) R(S)+ Hint. The equations of the asymptotes of the Root Locus are given by: #aymptotes = #finite poles - #finite zeros, - K(s+1) (s+2)(s+3)(s+4) Efinite poles-E finite zeros #aymptotes 0a= (2 #ay

Water at 20°C flows through a horizontal 6.0 mm diameter tube where two pressure tappings at a distance 12.0 m apart are attached. Water density and dynamic viscosity at 20 °C are 998 kg/m and 0.001002 Pa.s, respectively. What is the maximum head loss (to 2 decimal places) allowed if the flow is to be laminar (i.e., Re = 2000.0)? HL=

3.26. An LTI system has the impulse response h(t) = e ault – 1), where a > 0. = (a) Determine whether this system is causal. (b) Determine whether this system is stable.

Part A - Ideal op amp circuits with a voltage source: part 1 For the circuit shown, determine V. iz. and i, when V= 2 V R = 4 kN Rg = 4 k22 and R3 = 25 kN2 Assume that the op amp is in its linear region of operation Express your answer to two significant figures using appropriate units. View Available Hints) R3 = 25 kg w 1 ix = VCC mA R = 42 w V = 2 v -V R2 = 42 Vo = V 10 = IMA Part B - Ideal op amp circuits with a voltage source: part 2 For the circuit shown (Figure 1), determine the range (ie, maximum and minimum values) of V, so that the op amp operates in the linear region. Assume that R1 = 8 kN. R2 = 8 kN. R3 = 15 k2 and Va = 10 V Express your answer in volts to two significant figures separated by a comma. View Available Hint(s) V Η ΑΣΦ UT vec ? minimum V.. maximum V. = V Submit Part C - Ideal op amp circuits with voltage and current sources Determine V. when V =3V.I, = 1.6 mA R1 = 2 ks2. R2 = 20 kN2, and R3 = 10 k12. Assume that the op amp is in its linear region of operation. (Figure 2) Express your answer to two significant figures and include the appropriate units. | View Available Hint(s) μΑ ? V. = Value Units Submit

P2 Consider the linear system of two ODES dy = Ay, dt where A= : [ -1 -2 2 -1 a Find the eigenvalues of the matrix A. [1 mark] b Calculate the bound h for the stepsize h such that h <h characterizes asymptotic stability of the zero solution when Euler's method is applied to this system. [3 marks]