Sommaire général

Bobines d'induction en régime sinusoïdal

III. Influences entre plusieurs bobines

3. Inductance mutuelle (Mutuelle)

b. Signe de la mutuelle

Première situation

On considère le dispositif ci-contre constitué de deux bobines placées sur un même cylindre. Les vecteurs surface des bobines sont orientés à partir des sens des courants en utilisant la règle de la main droite.

Pour les inductances propres

Si `i_1(t) > 0` alors le flux engendré par la bobine du haut sur elle même, noté `Phi_11(t)`, est positif car `vec B_1` et `vec S_1` sont colinéaires et de même sens. Si `i_1(t) < 0` alors `Phi_11(t)` est négatif car `vec B_1` et `vec S_1` sont colinéaires et de sens contraires.

Dans les deux cas, le flux et le courant ont le même signe, l'inductance propre `L_1` est donc positive.

Pour la bobine du bas, si `i_2(t) > 0` alors `Phi_22(t) > 0` et si `i_2(t) < 0` alors `Phi_22(t) < 0`, l'inductance propre `L_2` est donc positive.

Pour la mutuelle

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B1B2i1(t)v1(t)B1B2i2(t)v2(t)

Dans ce cas le flux engendré par la bobine du haut à travers celle du bas a le même signe que le courant : la mutuelle est positive.

Deuxième situation

Le dispositif ci-dessous est identique au précédent sauf que le sens d'enroulement du bobinage du bas a été modifié. Ceci a une influence sur le sens du vecteur surface de la bobine du bas.

Pour les inductances propres

Si `i_1(t) > 0` alors alors le flux engendré par la bobine du haut sur elle même est positif : `Phi_11(t) > 0`. Si `i_1(t) < 0` alors `Phi_11(t) < 0`, l'inductance propre `L_1` est donc positive.

Pour la bobine du bas, si `i_2(t) > 0` alors `Phi_22(t) > 0` et si `i_2(t) < 0` alors `Phi_22(t) < 0`, l'inductance propre `L_2` est donc positive.

Le changement de sens du bobinage n'a pas d'influence sur le signe des inductances propres.

Pour la mutuelle

Si `i_1(t) ≠ 0` et `i_2(t) = 0` :

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Dans ce cas le flux engendré par la bobine du haut à travers celle du bas est de signe contraire à celui du courant : la mutuelle est négative.