<<CheminPackLocaux`

Représentation de Fresnel du circuit RLC série

Clear[fresnel,dephasage]

dephasage[r_,l_,c_,ω_]:=ArcSin[((l ω)/(Sqrt[(r^2)+(((l ω))^2)]))]/;N[c]==0.

dephasage[r_,l_,c_,ω_]:=ArcSin[((l ω-(1/(ω c)))/(Sqrt[(r^2)+(((l ω-(1/(ω c))))^2)]))]

fresnel[r_,l_,c_,u_,ω_]:=Module[{z,φ,i},(z=(Sqrt[(r^2)+(((l ω))^2)]);φ=dephasage[r,l,c,ω];i=(u/z);Print["Impédance  Z = ",z," Ω"];Print["Déphasage  φ = ",φ ," [rad]"];Print["Courant max. (Overscript[I, ∧]) = ",i, " A"];Show[Graphics[{HeadLength->0.05,
				Arrow[{{0,0},{r i,0}}],
	Arrow[{{0,0},{r i,(l ω)i}}],
			Arrow[{{1.02r i,0},{1.02r i,l ω i}}],
			Arrow[{{r i,l ω i},{1r i,(l ω)i}}],
					Circle[{0,0},r i 0.2,{0,φ}],
Text["R (Overscript[I, ∧])",{(1/2)r i,0},{0,1}],	Text["O",{0,0},{1,1}],
	Text["(Overscript[U, ∧])",0.5{r i,(l ω)i},{1,-1}],	Text["ω L (Overscript[I, ∧])",{1.04 r i,(1/2)l ω i },{-1,0}],			Text["φ",r i 0.25{Cos[(φ/2)],Sin[(φ/2)]}]
		}],AspectRatio->Automatic,PlotRange->All,ImageSize->{500,300}])/;N[c]==0.];

fresnel[r_,l_,c_,u_,ω_]:=Module[{z,φ,i},(z=(Sqrt[(r^2)+(((l ω-(1/(ω c))))^2)]);φ=dephasage[r,l,c,ω];i=(u/z);Print["Impédance  Z = ",z," Ω"];Print["Déphasage  φ = ",φ ," [rad]"];Print["Courant max. (Overscript[I, ∧]) = ",i, " A"];Show[Graphics[{HeadLength->0.05,
				Arrow[{{0,0},{r i,0}}],
	Arrow[{{0,0},{r i,(l ω-(1/(ω c)))i}}],
			Arrow[{{r i,0},{r i,l ω i}}],
			Arrow[{{1.02r i,l ω i},{1.02r i,(l ω-(1/(ω c)))i}}],
					Circle[{0,0},r i 0.2,{φ,0}],
Text["R (Overscript[I, ∧])",{(1/2)r i,0},{0,-1}],	Text["O",{0,0},{1,-1}],
	Text["(Overscript[U, ∧])",0.5{r i,(l ω-(1/(ω c)))i},{1,1}],	Text["ω L (Overscript[I, ∧])",{ 0.98r i,(1/2)l ω i },{1,0}],			Text["-\!\(\*FractionBox[OverscriptBox[\(I\), \(∧\)], \(ω\\ C\)]\)",{1.02r i,(l ω-(1/2)(1/(ω c)))i},{-1,0}],			Text["φ",r i 0.25{Cos[(φ/2)],Sin[(φ/2)]}]
		}],AspectRatio->Automatic,PlotRange->All,ImageSize->{500,300}])/;l ω<(1/(c ω))];

fresnel[r_,l_,c_,u_,ω_]:=Module[{z,φ,i},z=(Sqrt[(r^2)+(((l ω-(1/(ω c))))^2)]);φ=dephasage[r,l,c,ω];i=(u/z);Print["Impédance  Z = ",z," Ω"];Print["Déphasage  φ = ",φ ," [rad]"];Print["Courant max. (Overscript[I, ∧]) = ",i, " A"];Show[Graphics[{HeadLength->0.05,
				Arrow[{{0,0},{r i,0}}],
	Arrow[{{0,0},{r i,(l ω-(1/(ω c)))i}}],
			Arrow[{{1.02r i,0},{1.02r i,l ω i}}],
			Arrow[{{r i,l ω i},{1r i,(l ω-(1/(ω c)))i}}],
					Circle[{0,0},r i 0.2,{0,φ}],
Text["R (Overscript[I, ∧])",{(1/2)r i,0},{0,1}],	Text["O",{0,0},{1,1}],
	Text["(Overscript[U, ∧])",0.5{r i,(l ω-(1/(ω c)))i},{1,-1}],Text["ω L (Overscript[I, ∧])",{1.04 r i,(1/2)l ω i },{-1,0}],Text["-\!\(\*FractionBox[OverscriptBox[\(I\), \(∧\)], \(ω\\ C\)]\)",{r i,(l ω-(1/2)(1/(ω c)))i},{1,0}],			Text["φ",r i 0.25{Cos[(φ/2)],Sin[(φ/2)]}]
		}],AspectRatio->Automatic,PlotRange->All,ImageSize->{500,300}]];

fresnel[1000.,50. (10^(-3)),100. (10^(-9)),5.,2π 1000.]

fresnel[10000.,1500. (10^(-3)),5. (10^(-8)),5.,2π 1000.]

fresnel[1000.,0,100. (10^(-9)),5.,2π 1000.]

fresnel[1000.,1500. (10^(-3)),0,5.,2π 1000.]

fresnel[0,0,100. (10^(-9)),5.,2π 1000.]

fresnel[0,1500. (10^(-3)),0,5.,2π 1000.]