Sommaire général

Bobines d'induction en régime sinusoïdal

III. Influences entre plusieurs bobines

3. Inductance mutuelle (Mutuelle)

e. Relations entre les tensions et les courants

Les équations entre les tensions et les courants sont établies pour le dispositif représenté ci-dessous. Les bobines présentent des résistances notées `r_1` pour la bobine de gauche et `r_2` pour la bobine de droite.

Pour la bobine de gauche :

D'après la loi d'Ohm et la loi des mailles `v_1(t) = r_1 . i_1(t) - e_1(t)`

Comme `e_1(t) = - {d Phi_"T1"(t)}/{dt}` alors

`v_1(t) = r_1 . i_1(t) + {d Phi_"T1"(t)}/{dt}`

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B1B2i1(t)v1(t)B1B2i2(t)v2(t)e2(t)e1(t)Φ(t)

ce qui donne en remplaçant `Phi_"T1"(t)` par son expression en fonction des intensités :

`v_1(t) = r_1 . i_1(t) + L_1{d i_1(t)}/{dt} + M {d i_2(t)}/{dt}`

Pour la bobine de droite :

D'après la loi d'Ohm et la loi des mailles `v_2(t) = r_2 . i_2(t) + {d Phi_"T2"(t)}/{dt}` ce qui donne en remplaçant `Phi_"T2"(t)` par son expression en fonction des intensités :

`v_2(t) = r_2 . i_2(t) + M{d i_1(t)}/{dt} + L_2 {d i_2(t)}/{dt}`