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[:NZ:vyyuy:>:<::::::AB:;JD<:;::::::::::::vYxI:;Z::::::::::::::::::::ya y=J:B:::::::::::::::::::jysy:>:<:::::::::3:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 142 "A \"real\" inductor has induct ance, L, and resistance, RL. Suppose this component is connected in p arallel with an ideal capacitor, C as shown." }}{PARA 0 "" 0 "" {TEXT -1 101 "(a) Find the magnitude of the effective impedance of the comb ination as a function of the frequency." }}{PARA 0 "" 0 "" {TEXT -1 103 "(b) Find the phase relationship between the voltage across the c ombination and the current through it." }}{PARA 0 "" 0 "" {TEXT -1 107 "(c) Suppose the combination is connected in series with a pure r esistance, R as shown. A voltage given by" }}{PARA 0 "" 0 "" {TEXT -1 70 " Vin=V0 \+ cos(wt)" }}{PARA 0 "" 0 "" {TEXT -1 99 " is applied to the entire circuit. Find Vout(t), the voltage across the parallel combination. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 139 "(d) \+ Let V0=5, L=3 mH,C=10 uF,RL=3 ohms, R=1000 ohms. Plot the magnitude \+ of the frequency response of the circuit for f = 0 Hz to 2000 Hz." }} {PARA 0 "" 0 "" {TEXT -1 9 "Solution:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "assume(ome ga>0,C>0,L>0,RL>0,V0>0,f>0,t>0);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Part A" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "capacitor impediance" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "ZC:=1/( I*omega*C);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "inductor impedianc e" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "ZL:=I*omega*L;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "resistor impediance" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "ZR:=RL;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "impedi ance of the combination of elements" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "Zeff:=1/(1/(ZL+ZR)+1/ZC);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Zeff:=simplify(Zeff);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "ma gnitue of the impediance" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "magZeff :=simplify(abs(Zeff));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Part B" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 47 "Convert the complex impediance into polar form." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 77 "The first term is the magnitude, a nd the second term is the angle in radians." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "sol:=convert(Zeff,polar);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Evaluate the phase angle of the impediance." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "evalc(convert(sol,list)[2]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "Simplify \+ the result." }}{PARA 0 "" 0 "" {TEXT -1 64 "Since Z=V/I, \"angle\" = ( angle of V phasor) - (angle of I phasor)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "angle:=simplify(\");" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 6 "Part C" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "Input voltage in phasor f orm" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "Vin:=V0;" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 47 "Use voltage division to find the output voltage" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Vout:=Vin*Zeff/(Zeff+R);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Vout:=simplify(Vout);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Convert to polar form" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 25 "sol:=convert(Vout,polar);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Find the magnitude of the output voltage" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "magVout:=evalc(convert(sol,list)[1] );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Find the phase angle of the output voltage." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "evalc(convert(s ol,list)[2]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "Simplify the result." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "angleV:=simplify(\");" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Fi nd Vout as a function of time." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "' Vout(t)'=magVout*cos(omega*t+angleV);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Part D" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 "Find the magnitude of the frequency responce." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "magVout:=evalc(abs(Vout));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "Vout1:=simplify(subs(\{V0=5,omega=2 *Pi*f,L=3*10^(-3),C=10*10^(-6),RL=3,R=1000\},magVout));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "plot(Vout1,f=0..2000,title=`Frequen cy Response of Circuit (Vout vs f)`);" }}}}{MARK "21 0 0" 72 } {VIEWOPTS 1 1 0 1 1 1803 }