The total inductance of two inductors in series equals the sum of their inductances under which condition?

The total inductance of two inductors in series equals the sum of their inductances under which condition?

• A. When the magnetic fields of the inductors do not affect each other
• B. When the inductors are wound on the same core
• C. When the inductances are equal
• D. In any series connection

Answer: (A)

When the magnetic fields of the two inductors do not influence each other, their mutual inductance is zero, so the voltages add directly as v = L1 di/dt + L2 di/dt. With the same current flowing through both, the total voltage is (L1 + L2) di/dt, which means the total inductance in series is simply L1 + L2. If there is magnetic coupling—such as inductors wound on the same core or placed close enough that their fields interact—the total inductance in series is not just L1 + L2. You get additional terms from the mutual inductance, making the total L1 + L2 ± 2M instead of a plain sum, depending on the orientation of the windings. So the requirement for the sum to hold is zero coupling between the magnetic fields. That’s why the other ideas don’t guarantee simple addition: coupling exists on a shared core or with close proximity, and equal values or any series arrangement don’t inherently remove that coupling.

When the magnetic fields of the two inductors do not influence each other, their mutual inductance is zero, so the voltages add directly as v = L1 di/dt + L2 di/dt. With the same current flowing through both, the total voltage is (L1 + L2) di/dt, which means the total inductance in series is simply L1 + L2.

If there is magnetic coupling—such as inductors wound on the same core or placed close enough that their fields interact—the total inductance in series is not just L1 + L2. You get additional terms from the mutual inductance, making the total L1 + L2 ± 2M instead of a plain sum, depending on the orientation of the windings. So the requirement for the sum to hold is zero coupling between the magnetic fields.

That’s why the other ideas don’t guarantee simple addition: coupling exists on a shared core or with close proximity, and equal values or any series arrangement don’t inherently remove that coupling.