Inductors in Series

When the magnetic fields around inductors do not interact, inductances in series add like resistances in series. The total value is the sum of the individual values. It’s important to be sure that you are using the same size units for all the inductors when you add their values. After that, you can convert the result to any inductance unit you want.

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Inductances in series simply add up, as long as the inductors do not interact.

Problem 1

Suppose three 40.0-μH inductors are connected in series, and there is no interaction, or mutual inductance, among them (above figure). What is the total inductance?
Add up the values. Call the inductances of the individual components L1, L2, and L3, and the total inductance L. Then L = L1 + L2 + L3 = 40.0 + 40.0 + 40.0 = 120 μH.

Problem 2

Imagine three inductors, with no mutual inductance, with values of 20.0 mH, 55.0 μH, and 400 nH. What is the total inductance, in millihenrys, of these components if they are connected in series as shown in above figure ?
First, convert all the inductances to the same units. Microhenrys are a good choice because that unit makes the calculation process the least messy. Call L1 = 20.0 mH = 20,000 μH, L2 = 55.0 μH, and L3 = 400 nH = 0.400 μH. The total inductance is therefore L = 20,000 + 55.0 + 0.400 = 20,055.4 μH. This is 20.1 mH after converting and rounding off.