ECE 201 Spring 2006 Final Exam May 5 2006 8 00am 10 00am Instructions There are 20 multiple choice questions Each is worth 10 points Our goal is to assess what you know not what you do not know To maximize our assessment of your knowledge and understanding do NOT dwell on a single problem If you get stuck move on to the next problem and return later time permitting It is important to work patiently efficiently and in an organized manner This is a closed book closed notes exam No scrap paper is permitted You are permitted only a calculator All students are expected to abide by the usual ethical standards of the university i e your answers must reflect only your own knowledge and reasoning ability 1 Possible useful equations 1 Trigonometry identities cos cos 2 cos cos sin sin 2 cos cos 2 First order circuits x t x x to x e t to 3 Second order circuits 2 Question 1 Find node voltage VC in V 1 1 2 2 3 3 4 4 5 5 6 6 7 7 A 10 S B 5S C 1S D 8V 12 A 3S 1S 3 Question 2 Find the current I in the circuit below in A 1 1 2 2 3 3 4 4 5 5 6 6 7 6 3 4 4A 1 4 I 0 3Vd 2 V d 2 4 Question 3 The nodal and mesh equations of circuits containing inductors and capacitors are differential equations or integral differential equations Shown below is a circuit having three resistors and an inductor The mesh equations in terms of the designated currents i1 t and i2 t are 1 6 i1 t 2i 2 t v s t di t dv t 2 i 1 t 7i 2 t 2 2 s dt dt 3 6 i1 t 2i 2 t v s t di t 2 i 1 t 7i 2 t 2 2 0 dt 5 6 i1 t 2i 2 t v s t di t 2 i1 t 3i 2 t 2 2 0 dt 2 6 i1 t 2i 2 t v s t di t dv t 2 i1 t 7i 2 t 2 2 s dt dt 4 6 i1 t 2i 2 t v s t di t 2 i 1 t 7i 2 t 2 2 0 dt 6 6 i1 t 2i 2 t v s t di t 2 i1 t 3i 2 t 2 2 0 dt none of the above vs t ix 4 7 i1 5 i2 2 5 2 H Question 4 For the ideal op amp circuit below the output voltage Vout is in Volts 1 26 2 15 3 14 4 16 5 25 6 24 7 24 10 2 4V out 4 V 1V 6 Question 5 100 300 a 200 2 V b The Thevenin equivalent circuit of the ideal op amp circuit shown above is 7 1 2 a 1 V a 100 100 1 V b b 3 4 a 1 V a 200 200 1 V b b 5 6 a 1 V a 300 1 V b b 7 a 1 V 300 75 b 8 Question 6 A linear circuit is driven by a constant voltage source V s1 and a constant current source Is2 The output voltage Vout is 3 V when Vs1 3 V and Is2 8 A On the other hand if V s1 6 V and Is2 4 A Vout is again 3 V If Vs1 0 V and Vout 4 V Is2 in A is 1 16 2 2 3 4 4 5 8 6 V 7 64 s1 L in e a r c irc u it V out 9 Is 2 Question 7 Find the Thevenin equivalent resistance RTH for the circuit below in 1 10 2 20 3 7 5 4 40 5 5 6 15 7 30 20 ix 0 5 iy ix iy 20 20 10 Question 8 The Thevenin equivalent of the circuit below is 1 a single 3 resistor 2 a single 3 resistor 3 a short circuit 4 an open circuit 5 a single 3V independent voltage source 6 a 3V independent voltage source in series with a 1 resistor 7 none of the above 11 Question 9 In the circuit below the maximum power that can be transferred to the variable resistance R is in W 1 2 5 2 5 3 6 25 4 10 5 12 5 6 25 7 none of the above 2 V s1 10 V 2 2 R 12 V s2 5 V Question 10 The switch in the circuit below opens at t 0 after having been closed for a long time The sum of energy stored in the inductor and energy stored in the capacitor is 1J at t 0 The value of the inductance L is in H 1 0 2 0 01 3 0 02 4 0 1 5 0 2 6 1 7 none of the above 13 Question 11 In the ideal op amp circuit shown below the capacitor voltage vc t is 0 V for t 0 The input voltage is vin t 7 e 2t u t V The output voltage vout t in V for t 0 is e 2t 4 e 2t 2 e 2t 5 7e 2t 3 e 2t 6 7 1 e 2t 7 7 1 e 2t 10 vc t 0 0 5 F v in t v o u t t 14 Question 12 The switch in the RL circuit shown below has been opened for a long time and it closes at t 0 Then the inductor current iL t in A for t 0 is 1 2 2 e 10t 2 2 2 e 10t 3 4 4 e 10t 4 4 4 e 10t 5 4 2 e 10t 6 4 2 e 10t 7 2 4 e 10t iL 2 H t 0 4 A 10 15 10 Question 13 For the circuit below the response for the capacitor voltage v C t is desired If the general solution is of the form x t xn t XF select the final value XF in appropriate units 1 75 V 2 0V 3 3 A 4 4 A 5 5 V 6 6 A 7 0 A iL t 25 75 V vc t 4 mF 16 15 20 mH Question 14 The switch in the circuit below has been opened for a long time It closes at t 0 s The initial capacitor voltage prior to the switch closing is 0 V The roots to the characteristics equation are s1 2 s 1 and s2 3 s 1 The complete response of the circuit is 1 vc t 8 e 2t 8 e 3t V 2 vc t 12 e 2t 8 e 3t V 3 vc t 12 e 2t 8 e 3t V 4 vc t 4 12 e 2t 8 e 3t V 5 vc t 4 8 e 2t 12 e 3t V 6 vc t 4 …
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