Exam 2 Solutions ECE 221 Electric Circuits

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1 Nme: PSU Student ID Numer: Exm 2 Solutions ECE 221 Electric Circuits Novemer 12, 2008 Dr. Jmes McNmes Keep your exm flt during the entire exm If you hve to leve the exm temporrily, close the exm nd leve it fce down while you re out of the room Turn off your cell phone Do not open the exm until instructed to do so Do not use seprte scrtch pper. If you need more spce use the ck of the previous pge, nd write note directing my ttention to it If you hve extr time, doule check your nswers Include units with ech of your nswers Show ll of your work for full credit For multiple choice prolems 1 point will e deducted for ech wrong nswer, ut the totl numer of points will not e less thn zero. Numeric nswers should e stted in deciml form with 3 significnt digits. Prolem 1: /10 Prolem 2: /19 Prolem 3: /21 Totl /50

2 ECE 221 Exm 2 2 of 8 1. Fundmentl Concepts (10 points).. (1 point) When performing nodl nlysis of circuit it is sometimes necessry to dd n extr vrile or use super-node. This occurs when rnch contins single circuit element. Which of the following circuit elements cuse this need? (Circle ll tht pply) Idependent Voltge Source Independent Current Source Dependent Voltge Source Dependent Current Source. (1 point) When performing mesh nlysis of circuit it is sometimes necessry to dd n extr vrile or use super-mesh. This occurs when rnch contins single circuit element. Which of the following circuit elements cuse this need? (Circle ll tht pply) Idependent Voltge Source Independent Current Source Dependent Voltge Source Dependent Current Source c. (1 point) Which of the following re equivlent to voltge source with vlue of V s = 0 V? (Circle ll tht pply) Short circuit Open circuit Resistor with R = 0 Ω Resistor with R = Ω d. (1 point) Which of the following re equivlent to current source with vlue of I s = 0 A? (Circle ll tht pply) Short circuit Open circuit Resistor with R = 0 Ω Resistor with R = Ω e. (2 points) Suppose circuit contins n indepent voltge source with vlue of 5 V nd nd independent current source with current of 2 ma. You solve for the contriutions to voltge in the circuit nd find tht the voltge is v = = 13 V where 5 V is due to the voltge source nd 8 V is due to the current source. Wht would the voltge e if the voltge source ws replced with 10 V source? v = = 18 V f. (2 points) For the previous question with the 5 V voltge source nd 2 ma current source, wht would the voltge e if the current source ws inverted such tht it forced current to flow in the opposite direction? v =5-8 = -3 V g. (2 points) Wht re the two ssumptions tht lwys pply to idel opertionl mplifiers with negtive feedck? v + = v nd i + = i = 0

3 ECE 221 Exm 2 3 of 8 2. Thévenin nd Norton Equivlents (19 points).. (4 points) Drw the Thévenin nd Norton equivlent of Circuit 2. 5 V 3 kω 8 V 6 kω 8 kω Circuit 2 17 kω 3 V ma 17 kω. (3 points) Solve for the short circuit current from to in Circuit 2. 9 kω 4 kω 6 kω 2 ma 8 V Circuit 2 8 kω 8 6k + 8k + = 0 i sc = 2m + 8 4k + = 3.31 V i sc = 4.37 ma

4 ECE 221 Exm 2 4 of 8 c. (3 points) Solve for the open circuit voltge drop from to in Circuit 2. 9 kω 4 kω 6 kω 2 ma 8 V Circuit 2 8 kω [( k 8k + 2m k ( 1 6k + 1 8k + 1 = 6.96 V v oc = 13.2 V ) ( ) 1 ) ( 1 4k + 1 )] [ v1 ] = 0 = 0 = [ ] 8 6k 8 4k + 2m = 13.2 V d. (3 points) Solve for the Thévenin equivlent resistnce in Circuit 2. R eq = 4k [ + (6k 8k)] = 4k [ k] = 4k 12.4k = 3.03k e. (4 points) Drw the Thévenin nd Norton equivlents of Circuit 2 elow kω 13.2 V 4.37 ma 3.03 kω

5 ECE 221 Exm 2 5 of 8 f. (1 point) Wht resistnce connected etween the terminls nd will mximize the power trnsferred to tht resistnce in Circuit 2? R mx =3.03k g. (1 point) When the resistnce tht mximizes power trnsfer is connected to the terminls nd, how much power is dissipted y this resistnce? P mx = V 2 th 4R eq = 14.4 mw

6 ECE 221 Exm 2 6 of 8 3. Opertionl Amplifiers (21 points).. (1 point) Solve n expression for v o for Circuit 3. R L v o Opertionl mplifier Circuit 3. v o =. (1 points) Wht is the Thévenin or Norton equivlent input resistnce t the output terminl of Circuit 3? R eq = c. (4 points) For the circuit elow circle ll of the circuit elements tht do NOT ffect the output voltge. A point will e deducted for ech wrong nswer. R6 R7 R4 i 5 R L v o Opertionl mplifier Circuit 3. R 4 R 5 R 6 R 7 R L d. (3 points) For Circuit 3 solve for the output voltge. v = v + = i 1 R 5 0 = i 1 R 5 + v o i 1 R 5 + i 1R 5 R 6 v o = R ( i 1 R 5 R ) R 6

7 ECE 221 Exm 2 7 of 8 v o1 i 3 R 4 R R 5 6 v o2 Opertion Amplifier Circuit 3c. e. (2 points) Solve for v o1 in Circuit 3c. Do not include v o2 in your nswer. v o1 = f. (2 points) Solve for v o2 in Circuit 3c. Do not include v o1 in your nswer. v o2 = R 4+R 5 R 5 g. (2 points) Solve for i 3 in Circuit 3c. Do not include v o1 or v o2 in your finl nswer. Simplify your nswer s much s possile. i 3 = v o1 v o2 = R 4+R 5 R 5

8 ECE 221 Exm 2 8 of 8 v o1 i 3 R 4 R R 5 6 v o2 Opertion Amplifier Circuit 3d. h. (2 points) Solve for i 3 in Circuit 3d. Do not include v o1 or v o2 in your finl nswer. i 3 = i. (2 points) Solve for v o1 in Circuit 3d. Do not include v o2 in your finl nswer. + v o1 = 0 v o1 = j. (2 points) Solve for v o2 in Circuit 3d. Do not include v o1 in your finl nswer. Simplify your nswer s much s possile. v o2 R 4 + R 5 = 0 ) v o2 =v o2 = (1 + R 4 + R 4 R 5

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