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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 22 " Solve an LRC circuit." }}
{PARA 0 "" 0 "" {TEXT -1 36 "Must first define types of variables" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "interface(showassumed=1);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "assume(i0,complex);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "assume(v0,real);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "assume(Zr,complex);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "assume(Zc,complex);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "assume(Zl,complex);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "assume(R,real);assume(R>0);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "assume(C,real);assume(C>0);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "assume(L,real);assume(L
>0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "assume(omega,real);
assume(omega>0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "assume(
t,real);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Define complex impeda
nces" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Zr:=R;Zc:=1/(I*omeg
a*C);Zl:=I*omega*L;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ZrG%#R|irG" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ZcG*&^#!\"\"\"\"\"*&%'omega|irGF(
%#C|irGF(F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ZlG*(^#\"\"\"F'%'ome
ga|irGF'%#L|irGF'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Find Total I
mpedance Amplitude and Phase" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 21 "assume(Ztot,complex);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
23 "Ztot:=Zl+Zr*Zc/(Zr+Zc);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Ztot
G,&*(^#\"\"\"F(%'omega|irGF(%#L|irGF(F(*&*&^#!\"\"F(%#R|irGF(F(*(F)F(%
#C|irGF(,&F/F(*&F-F(*&F)F(F1F(F.F(F(F.F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 75 "assume(X,real);assume(Xreal,real);assume(Ximaginary,r
eal);assume(phi,real);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "X
real:=Re(evalc(Ztot));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&XrealG*&%
#R|irG\"\"\"*()%'omega|irG\"\"#F')%#C|irGF+F',&*$)F&F+F'F'*&F'F'*&F)F'
F,F'!\"\"F'F'F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Ximagina
ry:=Im(evalc(Ztot));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+XimaginaryG
,&*&%'omega|irG\"\"\"%#L|irGF(F(*&*$)%#R|irG\"\"#F(F(*(F'F(%#C|irGF(,&
*$F,F(F(*&F(F(*&)F'F.F()F0F.F(!\"\"F(F(F7F7" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 42 "X:=simplify(sqrt(Xreal**2+Ximaginary**2));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG*&*$-%%sqrtG6#,***)%'omega|irG\"
\"%\"\"\")%#L|irG\"\"#F/)%#R|irGF2F/)%#C|irGF2F/F/*,F2F/)F-F2F/F1F/F3F
/F6F/!\"\"*&F8F/F0F/F/*$F3F/F/F/F/*$-F(6#,&*(F3F/F8F/F5F/F/F/F/F/F9" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "   Now calculate the Phase" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "phi:=arctan(Ximaginary,Xreal
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$phiG-%'arctanG6#*&**,&*&%'ome
ga|irG\"\"\"%#L|irGF-F-*&*$)%#R|irG\"\"#F-F-*(F,F-%#C|irGF-,&*$F1F-F-*
&F-F-*&)F,F3F-)F5F3F-!\"\"F-F-F<F<F-F:F-F;F-F6F-F-F2F<" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 27 "  Now calculate the Current" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "phi:='phi';assume(phi,real);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$phiGF$" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 15 "assume(i,real);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "i:=Re(evalc(combine(v0*exp(I*omega*t-I*phi))))/X;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG*&*(%$v0|irG\"\"\"-%$cosG6#,&*&%
'omega|irGF(%#t|irGF(!\"\"%%phi|irGF(F(-%%sqrtG6#,&*()%#R|irG\"\"#F()F
.F9F()%#C|irGF9F(F(F(F(F(F(*$-F36#,***)F.\"\"%F()%#L|irGF9F(F7F(F;F(F(
*,F9F(F:F(FEF(F7F(F<F(F0*&F:F(FDF(F(*$F7F(F(F(F0" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 17 " Now calculate vc" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "assume(vl,real);;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 42 "Note: signum is the sign of the expression" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 53 "vl:=Re(evalc(combine(v0*Zc*exp(I*omega*t-I*p
hi))))/X;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vlG,$*&*(%$v0|irG\"\"
\"-%$sinG6#,&*&%'omega|irGF)%#t|irGF)!\"\"%%phi|irGF)F)-%%sqrtG6#,&*()
%#R|irG\"\"#F))F/F:F))%#C|irGF:F)F)F)F)F)F)*(F/F)F=F)-F46#,***)F/\"\"%
F))%#L|irGF:F)F8F)F<F)F)*,F:F)F;F)FFF)F8F)F=F)F1*&F;F)FEF)F)*$F8F)F)F)
F1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "26 0 0
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