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ECE 301 Fall Semester, 2004 HW Set 5 Due: October 12, 2004 wlg Name__________________ Print (last, first) Use engineering paper. Work only on one side of the paper. Use this sheet as your cover sheet, placed on top of your work and stapled in the top left-hand corner. Number the problems at the top of the page, in the center of the sheet. Do neat work. Underline your answers. Show how you got your equations. Be sure to show how you got your answers. Each problem counts 10 points. (1) If the switch in the circuit below has been open for a long time and is closed at t = 0, find vc(t) for t . Ans: vc(t) = 8(1 – e-0.25t) V 2 t=0 + 12 v + _ 4 3F _ vc(t) (2) For the circuit below, the switch has been closed for a very long time. At t = 0 the switch is opened. Answer the following. Assume t 0. (a) Develop the differential equation that will allow you to solve for vL(t). diL (t ) R iL (t ) 0 R = 100 , L = 0.5 H dt L (b) Solve the differential equation of part (a). iL(t) = 0.002e-200t A (c) What is the time constant for the circuit? 5 milliseconds. (d) At what time will the current iL(t) reach 0.001 A? 0.003 seconds 10 k i L(t) t=0 + 20 V + _ 0.5 H 100 v L(t) _ (3) For the circuit below, is(t) = 5u(t). Find v(t) for 0. Ans: v(t) = 30(1 – e-.5t) V 2 + 6 iS(t) v(t) 0.25 F _ (4) In the circuit below, the switch has been closed for a very long time. At t = 0 the switch is opened. Find iL(t) for t 0 . 12 V 2H _ + t=0 6 3 i L(t) 6 12 Ans: On your own. (5) Determine v0(t) for t 0 in the circuit below. Assume v0(0-) = 0. Ans: v0(t) = 6e-4t V t=0 6 4 + 18 V + _ 3 1.5 H v0(t) _