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IUFM de Basse Normandie Travaux dirigés Master 1TD 3 : Loi générale de l’électricitéMs. AVRIL & ERNOULT page 1 UE124-S2I C...
IUFM de Basse Normandie Travaux dirigés Master 1TD 3 : Loi générale de l’électricitéMs. AVRIL & ERNOULT page 2 UE124-S2I C...
IUFM de Basse Normandie Travaux dirigés Master 1TD 3 : Loi générale de l’électricitéMs. AVRIL & ERNOULT page 3 UE124-S2I C...
IUFM de Basse Normandie Travaux dirigés Master 1TD 3 : Loi générale de l’électricitéMs. AVRIL & ERNOULT page 4 UE124-S2I C...
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Td3 loi générale de l'électricité

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Principios de electricidade

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Td3 loi générale de l'électricité

  1. 1. IUFM de Basse Normandie Travaux dirigés Master 1TD 3 : Loi générale de l’électricitéMs. AVRIL & ERNOULT page 1 UE124-S2I Chaîne d’information et constituantsObjectifs :Apprendre la terminologie et à reconnaitre les constituants des circuits électriques.Utiliser les lois fondamentales des circuits électriques.Travaux à faire sur feuilles en s’appuyant sur le chapitre « D – Circuits et systèmeslinéaires » du polycopier de cours.Exercice N° 1 : A partir du circuit ci-contre :1. Enoncer les nœuds,2. Enoncer les branches,3. Enoncer les mailles.Exercice N°2 :1. On souhaite déterminer la résistance de la totalité du fil utilisé dans une installationbifilaire d’une entreprise. On dispose pour cela des informations suivantes :• Fil en cuivre isolé de diamètre 2.5 mm• Longueur total de fil utilisé (100 m)2. Proposer des solutions pour diminuer la résistance globale.Exercice N°3 : A partir du circuit ci-contre :1. Ecrire un système d’équationscaractérisant le circuit.2. Résoudre ce systèmeExercice N°4 : A partir du circuit ci-contre :1. Ecrire un système d’équations caractérisantle circuit.2. Résoudre ce système sachant que :U1 = 20 V ; U2 = 5 V et U4 = -8 VExercice N°5 : L’expressions des intensités des courants électriques i1(t) et i2(t) est donnéepar :i1(t) = 10 √2 sin (ωt - π/3)i2(t) = 10 √2 sin (ωt + π/3) i2 i3i11. Exprimez l’expression de i3(t) en fonction de i1(t) et i2(t).2. Exprimez l’expression de i3(t) sous la forme : I √2 sin (ωt-θ) et déterminer les valeurs del’intensité I et de l’angle θ.Nota : sin(a)-sin(b)= 2 cos ((a+b)/2) sin ((a-b)/2)
  2. 2. IUFM de Basse Normandie Travaux dirigés Master 1TD 3 : Loi générale de l’électricitéMs. AVRIL & ERNOULT page 2 UE124-S2I Chaîne d’information et constituantsCorrectionExercice N° 1 : A partir du circuit ci-contre :1. Enoncer les nœuds : A, B, C, D2. Enoncer les branches :• Entre D et A :o R1 ; e ; R3o R2o C1 ; R4 ; C2 ; L1o C1 ; R4 ; R5 ; L1• Entre A et B :o C1 ; R4o R2 ; L1 ; C2o R2 ; L1 ; R5o R1 ; e ; R3 ; L1 ; C2o R1 ; e ; R3 ; L1 ; R5• Entre B et C : 4 branches• Entre C et D : 5 branches3. Enoncer les mailles.• R1 ; e ; R3 ; R2• R2 ; L1 ; C2 ; R4 ; C1• C2 ; R5• R1 ; e ; R3 ; L1 ; C2 ; R4 ; C1• R1 ; e ; R3 ; L1 ; R5 ; R4 ; C1• R2 ; L1 ; R5 ; R4 ; C1Exercice N°2 :1. On souhaite déterminer la résistance de la totalité du fil utilisé dans une installationbifilaire d’une entreprise. On dispose pour cela des informations suivantes :• Fil en cuivre isolé de diamètre 2.5 mm• Longueur total de fil utilisé (100 m)R = ρ . l avec : l = longueur du fil (m) S = section du fil (m²)S ρ = résistivité du matériau (Ω.m)S= π R²= π D² = π (2.5 10-3)² = 4.908 10-6m²4 4ρ = 1.72 10-8Ωm d’où pour 1 m : R1m = 1.72 10-81 = 3.504 mΩ4.908 10-6D’où pour l’installation globale : RG = 100 R1m = 350 mΩ = 0.35Ω2. Proposer des solutions pour diminuer la résistance globale.D’après la formule :
  3. 3. IUFM de Basse Normandie Travaux dirigés Master 1TD 3 : Loi générale de l’électricitéMs. AVRIL & ERNOULT page 3 UE124-S2I Chaîne d’information et constituantsOn peut diminuer :Si on augmente la section du fil mais on augmente le poids et le coût de l’installation.Si on change de matériau conducteur mais attention aussi au coût.Exercice N°3 : A partir du circuit ci-contre :1. Ecrire un système d’équations caractérisant lecircuit.D’après la loi des nœuds, on a :En A : i3 = i1 + i2 En B : i6 = i1 + i12En C : i3 = i9 + i8 En D : i4 + i12 = i7 + i8En E : i5 = i4 + i11 En F : i10 = i9 + i52. Résoudre ce systèmei1 = 1A i2 = 0.9A i3 = 1.9A i4 = 0.2A i5 = 0.5A i12 = 0.7AExercice N°4 : A partir du circuit ci-contre :1. Ecrire un système d’équations caractérisantle circuit.D’après la loi des mailles :Maille 1 : A →B→C→D→E→FMaille 2 : A→B→E→FMaille 3 : B→C→D→EU1 = U2 + U3 - U4 – U6U1 = U2 + U5U5 = U3 - U42. Résoudre ce système sachant que :U1 = 20 V ; U2 = 5 V et U4 = -8 V(a) 20 = 5 + U3 – (-8) – U6(b) 20 = 5 + U5(c) U5 = U3 – (-8) d’où U3 = 7V U5 = 15V U6 = 0VExercice N°5 : L’expressions des intensités des courants électriques i1(t) et i2(t) est donnéepar :i1(t) = 10 √2 sin (ωt - π/3)i2(t) = 10 √2 sin (ωt + π/3)i2 i3i11. Exprimez l’expression de i3(t) en fonction de i1(t) et i2(t).i2(t) = i3(t) + i1(t)
  4. 4. IUFM de Basse Normandie Travaux dirigés Master 1TD 3 : Loi générale de l’électricitéMs. AVRIL & ERNOULT page 4 UE124-S2I Chaîne d’information et constituantsd’où i3(t) = i2(t) - i1(t)2. Exprimez l’expression de i3(t) sous la forme : I √2 sin (ωt-θ) et déterminer les valeurs del’intensité I et de l’angle θ.Nota : sin(a)-sin(b)= 2 cos ((a+b)/2) sin ((a-b)/2)i1(t) = 10 √2 sin (ωt - π/3)i2(t) = 10 √2 sin (ωt + π/3)i3(t) = i2(t) - i1(t)= 10 √2 sin (ωt + π/3) - 10 √2 sin (ωt - π/3)= 10 √2 [ sin (ωt + π/3) - sin (ωt - π/3)]= 10 √2 [ 2 cos (((ωt + π/3)+(ωt - π/3))/2) sin (((ωt + π/3)-(ωt - π/3))/2)]= 10 √2 [ 2 cos (ωt) sin (π/3)]Comme sin (π/3) = √3/2 on a :i3(t) = - 10 √2 √3 cos (ωt) = 10 √2 √3 sin (ωt - π/2 ) =D’où I = 10 √3 et θ = - π/2

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