The differential coupling of two coils in series connection has self-inductance of 2 mH & 4 mH & a mutual inductance of 0.15 mH. The equivalent inductance of the combination is:  

Explanation:

Equivalent Inductance in Series Connection of Coils

Problem Statement: The differential coupling of two coils in series has self-inductances of 2 mH and 4 mH, with a mutual inductance of 0.15 mH. The task is to find the equivalent inductance of this combination.

Understanding the Concept:

When two inductors are connected in series, the equivalent inductance depends on their individual inductances and the mutual inductance between them. The equivalent inductance, denoted as L_eq, is given by:

Formula:

L_eq = L₁ + L₂ ± 2M

Where:

• L₁ = Self-inductance of the first coil (2 mH in this case)
• L₂ = Self-inductance of the second coil (4 mH in this case)
• M = Mutual inductance between the two coils (0.15 mH in this case)
• The sign of 2M depends on whether the mutual coupling is aiding or opposing. The positive sign is used if the coupling is aiding, and the negative sign is used if the coupling is opposing.

Calculation:

Assume the coupling is aiding (positive sign for 2M).

Substitute the given values into the formula:

L_eq = L₁ + L₂ + 2M

L_eq = 2 + 4 + 2 × 0.15

L_eq = 2 + 4 + 0.3

L_eq = 6.3 mH

However, the actual correct answer provided in the problem is 5.7 mH. This indicates that the coupling is opposing (negative sign for 2M). Let us re-calculate with the opposing case:

Substitute with the negative sign for 2M:

L_eq = L₁ + L₂ - 2M

L_eq = 2 + 4 - 2 × 0.15

L_eq = 2 + 4 - 0.3

L_eq = 5.7 mH

Correct Option Analysis:

The correct answer is Option 1: 5.7 mH. This is the equivalent inductance when the coupling is opposing.

Important Information:

To further understand the analysis, let’s evaluate why other values do not match:

• Option 2: 5.85 mH: This value could arise from an incorrect calculation where the mutual inductance is not properly considered.
• Option 3: 6 mH: This would be the result of ignoring the mutual inductance entirely, i.e., simply adding L₁ and L₂ without accounting for the coupling.
• Option 4: 6.15 mH: This might be a miscalculation involving an incorrect positive sign for 2M or an incorrect value for M.

Conclusion:

Understanding the role of mutual inductance is critical in calculating the equivalent inductance of coupled coils. The sign of the mutual inductance term depends on whether the coupling is aiding or opposing. In this case, the coupling is opposing, resulting in an equivalent inductance of 5.7 mH.