How do you calculate the total inductance in a series combination of inductors?

Mathematically, the formula for calculating the total inductance in a series combination of inductors is:

L_total = L1 + L2 + L3 + ... + Ln

where L1, L2, L3, ..., Ln are the individual inductance values of the inductors connected in series.

Keep in mind that the unit of inductance is the henry (H). So, if the inductance values of the individual inductors are given in henrys, you simply add them up to get the total inductance in henrys. If the inductance values are given in millihenrys (mH) or microhenrys (μH), make sure to convert them to henrys before adding.

For example, let's say you have three inductors connected in series with inductance values of 10 mH, 20 mH, and 30 mH. To find the total inductance (L_total), you would perform the following calculation:

L_total = 10 mH + 20 mH + 30 mH = 60 mH (or 0.060 H)

So, the total inductance in this series combination of inductors would be 60 millihenrys (mH) or 0.060 henrys (H).

1 / L_total = 1 / L1 + 1 / L2 + 1 / L3 + ... + 1 / Ln

Alternatively, you can express it as:

L_total = L1 + L2 + L3 + ... + Ln

Keep in mind that the inductances should be in the same unit (usually measured in henries, H) for accurate results. If the inductances are given in millihenries (mH) or microhenries (μH), make sure to convert them to henries before performing the calculation.

This formula is based on the principle that the total inductance in a series combination is equal to the reciprocal of the sum of the reciprocals of the individual inductances. This is different from the calculation of total resistance in a series combination of resistors, where you simply sum up the resistances. The behavior of inductors in series is opposite to resistors; inductances add up directly, while resistances add up inversely.