University:
Santa Fe College
Course:
ETS 2527C | Electromechanical Components and Mechanisms
Academic year:

2024
Views:

347

Pages:

5
Author:

Jabin F.

Mutual Inductance (M): Coil (i) current carries - I₁ And no current in coil-2 I₂ = 0 Magnetic flux through coil-2: Φ₂ = ∫ B₂ dA Φ₂ ∝ B₁ ∝ I₁ ⇒ Φ₂ ∝ I₁ ⇒ Φ₂ = MI₁ M - mutual inductance Like Capacitance(C) M is purely a geometrical parameter that does not depend on I₁, I₂ but depends on shape, size, distance with medium between the coils. if Resistance of coil-2 is R I₂(induced) = Ɛ₂ / R = -M/R * (dI₁/dt) (b) If I₁ = 0, I₂ = I Φ₁ = ∫ B₂ dA Φ₁ ∝ B₂ ∝ I₂ ⇒ Φ₁ = MI₂ - (4) ⇒ Ɛ₁ = -M * (dI₂/dt) - (5) I₁ (induced) = -M/R * (dI₂/dt) - (6) ⇒ I₁ = I, I₂ = 0 ⇒ Φ₂ = MI₁ = MI ⇒ I₂ = 0, I₁ = I ⇒ Φ₁ = MI Conclusion: If we interchange current of both coils, then their flux are also interchanged. Ques. 8 Page-66 I_short = I, I_long = 0 Φ_long = ? Φ_long ∝ B_short ⇒ Φ_long = ∫ B_short dS_long For long solenoid: B_in = μ₀nI B_out = 0 Assume I_long = I, I_short = 0 Φ_short = ∫ B_long dS_short Φ_short = ∫ (μ₀n₂I) (πa²) (n₁l) Φ_short = μ₀n₁n₂lπa²I Find the mutual inductance of the combination. Ques. 54 Page-64 Mutual inductance & self inductance is independent of current in the coil. But depends on shape, size, medium and distance of the coils. Induced: R₁R₂ Let I_bigger = I I_smaller = 0 B_bigger = (μ₀I) / (2R₁) ○ Φ_smaller = (μ₀I / (2R₁)) * πR₂² - (i) Φ_smaller = MI_bigger M = (μ₀πR₂²) / (8R₁) (option - G)