When inductors are connected in series (assuming their magnetic fields do not affect each other), the total inductance is equal to which of the following?

When inductors are connected in series (assuming their magnetic fields do not affect each other), the total inductance is equal to which of the following?

• A. Equal to the sum of the individual inductances
• B. Equal to the reciprocal of the sum of reciprocals
• C. Zero
• D. Equal to the largest inductance

Answer: (A)

When inductors are in series and their magnetic fields don’t affect each other, the voltages across each inductor add because the same current flows through all of them. For each inductor, V_i = L_i di/dt, so the total voltage across the string is V_total = (L1 + L2 + ... ) di/dt. By definition, the total inductance L_eq is such that V_total = L_eq di/dt, so L_eq equals the sum of the individual inductances. This relies on no mutual coupling (M = 0); if there were coupling, the result could differ. So the total inductance is the sum of the individual inductances.

When inductors are in series and their magnetic fields don’t affect each other, the voltages across each inductor add because the same current flows through all of them. For each inductor, V_i = L_i di/dt, so the total voltage across the string is V_total = (L1 + L2 + ... ) di/dt. By definition, the total inductance L_eq is such that V_total = L_eq di/dt, so L_eq equals the sum of the individual inductances. This relies on no mutual coupling (M = 0); if there were coupling, the result could differ. So the total inductance is the sum of the individual inductances.