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Unformatted text preview: Exam 2  9‘3 06 %omlx‘0n W
Name: ID # :
Problem (1) ( 15 point)
For the OP. Amp circuits shown below, find the output voltage V0
Assume that the OP—AMPs are ideal.
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E i: 5 A‘U’cﬁ Name: Problem (2) D#: ( 10 point) For the element shown, the waveforms for the element voltage and element current are found to be: v(t) = 5 cos (500t) V i(t) = 10 sin (50m) A + v(t) _
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«’5’ 0 Sketch the two waveforms, on the same graph, and show which one in leading .  Determine the phasors representing the waveforms of the voltage and the current. For the circuit shown ﬁnd the equivalent capacitance, . Cab between terminals (a) and (b)
. Cac between terminals (a) and (c) a
25 nF
b SOnF
25 nF
C . Deﬁne the element type ( inductor, capacitor, resistor) and ﬁnd its value. ‘ vbl‘taﬁe legals cowmall =3) \\I’\§’(L§€i’ét}€‘ . ,l
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’23“? 423ml: ., gonf‘: @254? W Name: ID # 3 Problem (3) ( 15 point)
The switch in the circuit shown has been open for a longtime before closing at t = 0. 6k§2 12kg ZkQ a) Find vc(0+). “(£65 =Mg(d)
: [3.26m][q.z\s]
= 2‘88\ V b) Find vc(oo). (1mg)
125+6‘5 Mom) : 3" c) Find the time constant T for l‘ 2 0. Re} : 61$ lﬂ2 K
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d) Find capacitor voltage v60) , t2 0 .
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New: 24+ [288’ 3 e) Sketch v60) for t 2 0. Name: ID # : Problem (4) ( 20 point) The OP.AMP circuit shown below is ideal. Assume that no energy stored in the inductor at t = 0. Lilo l a O
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a) For t 2 0, derive the differential equation for vp (t) . N? (on) = VA
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b) Find expression for VP (1‘) in terms of the circuit parameters( VS R and L).
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‘c) Find the output voltage v00) in terms of( st R, R1 ,R2 and L).
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d) Find v00) for(VS = 2 V, R=100£2, R1=1k£2,R2 = IOkQ and L=0.01H), “if“ z t\ :J is = ‘00 3 \03000 ’c
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e) Find the time required for the OP. AMP to saturate. a a?
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+ — [(7)000 t, émfmimmiiums Name: ID # : Problem (5) ( 20 point) For the circuit shown , the switch was closed for long time and it is open at t = 0. (LU? 3: {116) _ (V
'Vc... ”I. ~\ R00 300 = NL + mum) ~00 Name: ID #: b) The differential equation describing the circuit for I 2 0+ is : diL +(5x106)iL=0 """""""""""""""""""""""""""""""" Wr ite’therreiatedwharacterist'rceguation’f WWWW WWWWW WWWW ’ WW WW W'WWWWWW WWWWW
$2+ 2000$ +Q5 M0) = o c) Find the roots s1 and S2 of the characteristic equation . g : i000+ ' 2000
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2 d) Write the solution form in terms of constants and deﬁne its type ( overdamped, critically
damped , underdamped). .iooob
{Lou}: [was zooo’c + 82. sin moot} e Linwoolamved e) Calculate the constants and write the solution for i L (t) . .t.
. Rom some“ {mm at he t=° 1‘29. : Qoooxm + 290082. \00m Ug/ = — 03(63 + L2)“ )82
0:05 \. , _L _, l WW”W“W*WW":T(3§0‘FW§ Semen 9. $11 ct): {2 cos 1000’“ +059“ moot] e wwwé' Name: ID # : Problem (6) (20 point)
For the circuit shown below, the switch was open for long time and closed at t = 0 a) At t = 0— (switch is open ) find : vc(0_) and iL (0*)
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b) At I = 0+ (switch is closed) ﬁnd : vC(0+) and i L (0*)
NQL0* } : NC L6) : D (LL01): l'dO ) : 0
c) At t = 00 (switch is closed ) find : vc(00) and iL (0°)
Nclm): 0 (LL00) : 5%)
d) Derive the differential equation describing the circuit in terms of ~15» t 2 0+ Vs: W; + UK liet Link“: V9: vc .mc £1.32; + ewe/Angeli. —_— V5’ 9 Vc=VL . {cH‘l— = A‘R e) Derive the differential equation describing the circuit in terms of i L . MIAWMWAKWWYAMM» ...
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 Spring '07
 Oliver

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