The total inductance of two coils, A and B, when connected in series is 0.5 H or 0.2 H, depending upon the relative directions of the current in the coils. Coil A, when isolated from coil B, has a self-inductance of 0.2 H. The mutual inductance between the two coils is

Explanation:

Mutual Inductance Between Two Coils

Definition: Mutual inductance is a measure of the interaction between two coils, where the magnetic field generated by the current in one coil induces a voltage in the other coil. It depends on the geometry of the coils, the number of turns in each coil, and the relative positioning or orientation of the coils.

Problem Statement: The total inductance of two coils, A and B, when connected in series is given as either 0.5 H or 0.2 H, depending upon the relative directions of the current in the coils. The self-inductance of coil A is 0.2 H, and we need to determine the mutual inductance (M) between the two coils.

Solution:

When two coils are connected in series, the equivalent inductance (L_total) can be calculated using the following formula:

Case 1: Currents in the same direction

The total inductance is given by:

L_total = L_A + L_B + 2M

Where:

• L_A = Self-inductance of coil A
• L_B = Self-inductance of coil B
• M = Mutual inductance between the two coils

In this case, L_total = 0.5 H (as given in the problem).

Substituting the values:

0.5 = 0.2 + L_B + 2M

Case 2: Currents in opposite directions

The total inductance is given by:

L_total = L_A + L_B - 2M

In this case, L_total = 0.2 H (as given in the problem).

Substituting the values:

0.2 = 0.2 + L_B - 2M

Step-by-Step Calculation:

From Case 2:

0.2 = 0.2 + L_B - 2M

Rearranging:

L_B - 2M = 0

L_B = 2M

From Case 1:

0.5 = 0.2 + L_B + 2M

Substitute L_B = 2M:

0.5 = 0.2 + 2M + 2M

0.5 = 0.2 + 4M

Rearranging:

4M = 0.5 - 0.2

4M = 0.3

M = 0.3 ÷ 4

M = 0.075 H

Conclusion:

The mutual inductance between the two coils is 0.075 H, which corresponds to Option 4.

Important Information

To further analyze the other options:

• Option 1: 0.25 H - This value is incorrect. If mutual inductance were 0.25 H, the calculated total inductance values would not match the given problem statement.
• Option 2: 0.05 H - This value is too low and does not satisfy the equations for total inductance in both cases (same direction and opposite direction currents).
• Option 3: 0.15 H - This value is incorrect. Substituting M = 0.15 H into the equations for total inductance leads to inconsistencies with the given values of 0.5 H and 0.2 H.
• Option 4: 0.075 H - This is the correct answer, as demonstrated above.